VALVE

1. Introduction

How about building a tube amplifier with the transformer output and at the same time with less than 0.01% distortion at full power, near clipping? Majority would say it is impossible, as feedback depth is practically limited (by the transformer and interstage coupling capacitors) to about 20dB or at best 30dB.

Some would probably comment, that even it were possible to achieve extra-low distortion, that would devoid such tube amplifier of its valued "warm tube" tone and would make it as "sterile", "lifeless" and "boring" as any solid-state one, just much heavier and with lower output power. Why bother with the valves then?

On the other hand, it might happen that an ultra-low distortion class A tube amplifier will perform better, more "natural", as relative distortion gradially diminishes virtually to zero with decreasing volume, unlike in a class AB transistorised amplifier where distortion factor tends to remain constant or even rise at low level.

The above points will remain speculations until one actually builds a low distortion valve amplifier, listens to it and forms an opinion. The article explains how to build such an amplifier -- challenging but achievable task. In short, the trick is to take the output transformer out of the feedback loop outside audio frequency range and consequently be able to apply a very heavy negative feedback.

 

2. Linearity of valves

It is commonly believed that a tube with its power of 3/2 law produces less distortion than a field-effect transistor (quadratic law) or a bipolar transistor (exponential law). In reality however, if a tube is driven all the way from cut-off to saturation, distortion can be quite substantial. Consider an idealised amplifier with heavy negative feedback (Fig. 1) and observe waveforms on the control grid (top trace) and the load (bottom trace). The picture is taken of a real amplifier.

                                  Fig. 1. A heavy feedback audio amplifier with tube output.

 

            Fig. 2. Output (bottom trace) and grid (top trace) voltage waveforms in the amplifier as per Fig. 1.

You can see that to produce a clean output, the grid voltage has to be severely distorted. Negative excursions of the grid voltage are elongated comared to positive peaks. It happens because the tube non-linearity -- its transconductance falls at the "tail" of its control characteristic close to cut-off. Every tube, particularly a bad quality one with inconsistently untidy wound and misaligned grids, becomes a remote cut-off tube to some extent. \

You might also notice "bumps" on the positive peaks. These artifacts result from plate current saturation. At low plate voltages, more cathode current gets diverted (partitioned) to the screen grid. Therefore to achieve a required plate current, the feedback has to excessively "crank up" cathode current (and hence grid voltage).

Thus, to produce undistorted output, the feedback has to work hard to create substantial (probably about 20% in this case) and quite "aggressive" predistortion of the grid voltage. Pointy shape of the curve indicates presence of high order harmonics. This illustates a known fact that negative feedback enriches spectrum with high order components. That is why negative feedback is sometimes blamed for replacing "good", "warm" low order harmonics with "bad" high-order artifacts and ruining sonic perception.

Negative feedback has to be very deep (heavy) to reduce all distortion products referred to input to inaudible level under 0.01%. For example, with 20% of pre-distortion on the grid, 66dB of loop gain is needed to achieve 0.01% THD at output. Given that voltage gain of an audio amplifier is 20...30dB, error amplifier gain shall be about 90dB (30,000) over the whole audio frequencies range. At a glance, that would require 600MHz unity gain bandwidth from the error amplifier (Fig. 1). Such benchmarks are unheard of in the tube amplifier design practice.

This article will explain how to deal with stability problems and achieve the ultra-deep feedback and ultra-low distortion in a transformer output valve amplifier. Note that the above THD figures apply to near clipping operation. At lower levels distortion progressively reduces to diminishing levels, higher order harmonics going down faster. That is a beauty of a tubed single ended class A as opposed to push-pull class AB transistor stages, where distortion level might remain constant or even rise at low power.

 

3. Ultra-low distortion "back door" precautions

Everyone knows that (closed loop THD) = (open loop THD) / (loop gain). This equation works well... on paper. In the real world, however, there are many "back doors" through which distortion can penetrate, sneaking around the feedback loop.

 

3.1. Stray capacitances

In the idealised circuit (Fig. 1) source impedance is zero, but in reality there is a volume control potentiometer at the input, which makes source impedance Rin non-zero (Fig. 3).

                          Fig. 3. Stray coupling to the input of the error amplifier.

As the grid voltage is "dirty" -- distorted to 20...30% -- any stray capacitance to input (Cs3) or to the feedback chain (Cs2) will feed some portion of the distortion to the input. Since this distortion penetration path is outside of the loop, no amount of negative feedback can help. For example, with Cs2 = 0.1pF, Rin = 12.5K (which is equivalent to a 50K volume control in mid position), assuming voltage gain is 13, grid distortion is 20% at 10kHz, distortion referred to input will be of the order of 0.02% and it will not be possible to reduce it any further by increasing the error amplifier gain.

To "close" this stray capacitive coupling "back door" the following measures are recommended: (a) keep input and output circuits physically away and stretching in opposite directions, (b) use the smallest possible value of the volume control potentiometer and reasonably small values of the feedback divider Rfb1/Rfb2, (c) split gain in more than one stage and use as high as possible gain in stage A2, so that reverse transfer capacitance of the first stage A1 has less effect, (d) if A1 is an operational amplifier, use a single op-amp, as input pins 2 and 3 and output pin 6 are at the opposite sides of the package (unlike in dual op-amps where they are next to each other), (e) use ground plane on a PCB and "pour copper" under and around A1 components, (f) if A1 is a tube, use a pentode for low Cg-a, (g) if A1 discrete, use cascode topology to reduce Cs1, (h) for point-to-point wiring use schielded cables at the input and short wires at the A2 output, keeping them close to chassis.

Note that stray capacitance from the output tube plate to input has no adverse effect as plate voltage is "clean".

 

3.2. Distortion penetration in push-pull amplifiers

Extra care shall be taken with push-pull stages. For example, Fig. 4 illustrates ground pollution with supply ripple current. Though output of a push-pull amplifier is clean, plate current in each leg (tube) is more (in class AB) or less (in class A) distorted. Even harmonics of the distorion add up at the centre tap of the transformer and are dumped through a filter capacitor C1 to ground.

                  Fig. 4. Distortion current penetration into the signal ground of a push-pull valve amplifier.

If a grounding point of C1 is incorrectly chosen, an undesirable ground loop can be created between C1 and cathode current return R2. Distortion current, passing through this parasitic ground loop resistance R1, can develop distortion voltage applied in series with the input audio signal. This "dirty" component is injected outside of the feedback loop, and can not be reduced no matter how deep, heavy and powerful the feedback is. Ideally C1 and R2 shall be grounded at the same "star point" to avoid the issue.

Another potential problem can arise if the error amplifier is powered from the common "+B" supply rail. Inadequate filtering and insufficient power supply rejection ratio of the error amplifier can cause distortion superimposed on the input signal. To close this "back door", a quality op-amp powered from a separate supply should be used.

Another subtle distortion propagation mechanism is magnetic coupling of the output transformer to the input circuits. Any transformer has some leakage inductance and radiates magnetic field. Each half of the primary carries distorted plate currents and can induce distortion voltages on the wiring of the amplifier. Even if the sensitive input circuits are located away from the transformer, the udesirable coupling may occur through the chassis.

                      Fig. 5. Magnetic coupling: Eddy currents carry distortion from output to input.

Magnetic fields, radiated by leakage inductances Ls1 and Ls2 (Fig. 5) create Eddy currents flowing in the chassis. It is unlikely these two fields cancel each other, as the halves of the primary winding are not physically identical. Magnitude and direction of these currents depend on the transformer construction, mounting, orientation and chassis cutout shape. In turn these Eddy currents can produce potential difference (distortion voltage) between different points of the chassis. In practice, voltages about 20...50mV were measured in the vicinity of the output transformer, between the heads of the mounting screws, on a stainless steel chassis. Thick aluminium chassis with higher conductivity, would develop lower voltage, besides Eddy currents in high conductivity material tend to repel stray field. If, for example, input RCA connectors are mounted on the chassis in one location, and signal ground of the front end is connected to the chassis somewhere else, there well may be a distortion potential difference created between these points and superimposed on the input signal. Magnetic shielding of the transformer, lifting the transformer above the chassis, insulating mounting screws can reduce the effect, but adds to complexity and cost.

 

4. Single-ended versus push-pull

Note that it is not push-pull topology as such which causes potential problems, but distorted currents anywhere. For example, one can design a push-pull class A amplifier (Fig. 6) where each leg is independently linearised by the additional "servo" feedback amplifiers U3 and U4, turning the tubes into linear voltage controlled current sources. Such amplifier would work perfectly, even better than single-ended, as there will be no current ripple at all in the power supply rail.

               Fig. 6. Idealised block diagram of a linearised push-pull class A tube amplifier.

In such circuit currents in both legs would be clean and will not be able to contaminate input signal through conductive or inductive stray coupling.

Digressing a little, we can say that the same precautions and "back doors" apply to the transistor output stages, even to a greater extent, as the currents in a transistor stage are typically 20...30 times larger due to absence of an output transformer. A sightest mistake with signal ground / power supply star point or feedback pick-up point -- and the signal can become contaminated by unbalanced voltage drop coming from distorted current in each leg of the push-pull stage.

Fig. 7. Toplogies of a push-pull output stage: (A) -- common; (B) -- soft crossover; (C) -- linearised for class A. 

The most common topology (Fig. 7A) produces undesirable crossover distortion (in class AB) because of the thermal runaway prevention resistors R3, R4. When one leg is sourcing high current, voltage drop on the resistor is sending the opposite leg into complete cut-off. Subsequent abrupt recovery from cut-off into conduction adds to distortion at high frequencies. If Fig. 7A toplogy idle current is substantially increased (say to 0.5...1A) for class A operation, crossover distortion is eliminated, but still, near clipping, once current in a leg falls below 50mA, the circuit exhibits somewhat "remote cut-off", and leg current becomes "unclean". Therefore, near clipping this circuit (Fig. 7A) is still prone to conductive stray coupling "back door" distortion penetration.

To reduce crossover distortion, a circuit Fig. 7B has been proposed, where a local servo loop with Q5, Q6 (frequency compensated by C1) precisely maintains 2*Vbe bias voltage between the bases of power transistors Q3, Q4. Transistors Q5. Q6 are termally coupled to Q3, Q4 (mounted on the same heatsink). Besides, Q1 and Q2 are inside the servo loop, and their temperature has absolutely no effect. As a result thermal runaway is prevented without any emitter series resistors. This circuit (Fig. 7B) exhibits soft "remote cut-off" current steering. Suppose, quiescent current is 50mA. Suppose, at some moment one leg is sourcing 500mA -- ten times the idle bias current. Then, due to the exponential characteristics of a bipolar transistor, current in the opposite leg will reduce 10 times -- to 5mA. But, importantly, it never goes to full cut-off, and the transistors are always "ready for action". Thus crossover recovery related artefacts are minimal.

Unfortunately, in class A this circuit is even worse than Fig. 7A. Suppose, idle current is 500mA. Suppose that at some point in time current in one of the legs doubled to 1A. Then the other leg, due to the exponential transistor characteristics, would be delivering twice less, i.e. 250mA. Thus, in one leg the current increased by 500mA, while in the opposite leg decreased only by 250mA. This is exactly the unbalanced "dity" power supply current with 50% distortion only waiting for a minutest star point mistake to destroy THD performance of the whole amplifier. For that reason, the circuit Fig. 7B can not be recommended for class A.

For class A, consider a circuit in Fig. 7C. Here, a local servo feedback, similar to Fig. 7B, maintains perfectly stable voltage 2*Vbe across R3/R4. As a result, current deviations in each leg are always equal in magnitude and "clean" all the way up to clipping. Besides, the circuit in Fig. 7C naturally operates as an output short circuit protection device which would not allow current in any leg to exceed double the quiescent value. Further, idle current decreases with temperature which helps prevent overheating. For the above reasons Fig. 7C is highly recommended for pure sound class A transistor amplifier.

But... back to the valves. Though push-pull power stages are more powerful, efficient, generate less distortion they are more prone to "back door" distortion creation, less forgiving for design and layout mistakes and much more complex. Therefore it is reasonable and recommended to base an ultra-low distortion tube amplifier design on a simple single-ended power stage, where the currents are clean, well, almost clean.

 

5. Current recycling (current recirculation)

The only "unclean" current in a single-ended stage (Fig. 1) is screen grid current. When an output pentode or beam tetrode, particularly with excessive plate load impedance, is driven close to saturation, and instantaneous plate voltage is dropping below 50...100V, screen current is spiking. Thus even if the global negative feedback is keeping plate current undistorted, screen grid current and consequently cathode current and voltage across self-biasing circuit will become distorted. This "cathode bias dirt" would be undesirable not so much because it can cause ground contamination, but rather because it could superimpose  on the input through DC bias stabilisation loop. as will be explained below. Fortunately, the self-bias current distortion can be easily prevented by the screen grid current recycling (Fig. 8).

                                Fig. 8. Recycling (recirculating) screen grid current to cathode.

The distorted screen grid current is returned back to its origin -- to the cathode -- via a relatively large capacitor C1, located physically close to the tube socket. Thus the distorted screen grid current always stays within the recirculation loop (marked red). All "outside world" currents -- plate, cathode and screen grid supply via R1, as well as transformer magnetic radiation -- remain clean.

Further, screen grid supply dropping resistor R1 provides extra protection to the tube. If the power stage, running with no load, is overdriven into saturation, average screen grid current increases. R1 helps limit the screen grid current, reduce voltage and power dissipation.

 

6. Stability with heavy negative feedback

Having discussed various hidden pitfalls on the road to extra-low distortion, having chosen the most convenient topology (single-ended) and having considered dirty current recycling approach, it is time to tackle the main goal -- how to make a tube transformer based amplifier with say 60dB+ feedback stable both at low and high frequencies. Obviously, the output ptansformer is the root of all evil and the main obstacle on the path. A short answer is as follows. At low frequencies -- get rid of the interstage coulpling capacitors, use DC coupling instead. At high frequencies -- take the output transformer out of the feedback loop, still keeping the output tube in the loop. Below, in step-by-step fashion, it will be shown how to achieve the goal.

 

7. Emulated self-bias

Self bias or automatic bias (Fig. 9A) is so common and well known, so not much attention is paid to what it really is. However, if you think about it, it is in fact a current-to-voltage conversion process by way of a current sensing resistor R1.

 Fig. 9. Self-bias: (A) -- conventional passive; (B) -- active; (C) -- active with attenuated error signal.

Developing that principle, automatic bias can be turned into an active current-to-voltage conversion. Instead of a large cathode resistor, a small current sensing resistor is installed (Fig. 9B), its voltage inverted and multiplied by an operational amplifier U1. Suppose we need to emulate a 300 Ohm self bias resistor. Of that value, 10 Ohms is the physical resistor R1, and the remaining 290 Ohm is emulated by multiplying R1 voltage drop 29 times (R3/R2 = 29).

Note that the circuit allows for a series resistor R5 (Fig. 9C) provided that the op-amp has small input current. Similarly, the circuit permits some attenuation of error voltage at the summing node by a shunting resistor R4. For example, if the permissible grid bias voltage variation is say +/-0.5V and the op-amp U1 offset is +/-2mV, then the "noise gain" shall not exceed 250. Thus, R4 shall not be smaller than R3/250 or approximately 12K. The more precise the op-amp is, the more attenuation (smaller R4) can be applied. Importance of this aspect will be explaned below.

 

8. Low frequency stability and DC bias stabilisation

Emulated self bias is not just a fancy useless construct. Adding audio negative feedback turns the circuit into an amplifier, as shown in Fig. 10.

                              Fig. 10. Feedback branches in the amplifier with automatic bias emulation.

Three feedback loops are created. Let us trace and analyse them from point "A" (op-amp output) to point "B" (op-amp input).

Audio feedback loop is marked green. It includes a non-inverting op-amp U1, inverting valve V1 and a non-inverting output transformer. This loop creates an inverting amplifier with signal gain of R2 / R1 = 15, in this case, the non-inverting op-amp input acting as the summing junction.

Emulated automatic bias arrangement (refer to Fig. 9C) creates two more loop paths. One of them (brown, "Bias 1") is formed by a resistive divider R5R4. The last one (pink, "Bias 2") results from V1 acting as a cathode follower, with quite low gain though, due to a relatively small current sensing resistor R7, further attenuated by divider R6R4.

"Green" loop is the main voltage negative feedback. It encompasses all three elements -- op-amp, tube and transformer -- and does everything required: controls and linearises output voltage of the amplifier, flattens frequency response, reduces distortion and output impedance.

"Bias 2" loop is current feedback, which tends to increase output impedance of the amplifier and thus counteracts the main feedback to some extent. It tries to linearise cathode current and does not care about output voltage as such, as the transformerr is outside of this loop. Due to the screen grid current recycling via C2, which is explained above (Fig. 8), clean cathode current produces clean plate current. Thus, overall, this "Bias 2" feedfack component is not so harmful, though undesirable at low frequencies where the transformer becomes less linear. Note that without current recycling, plate current would have been more distorted to the detriment of the overall distortion performance. So, importance of current recycling technique becomes obvious from this discussion.

"Bias 1" feedback branch does not encompass any of nonlinear components at all. It only runs around the error amplifier, limits its gain, consequently limits the amount of the main "green" feedback, thus not allowing the main feedback to perform to full capacity. Needless to say, "Bias 1" feedback component is highly undesirable and shall be suppressed at audio frequencies, while allowed to work at infra-low frequencies and DC for bias generation.

Since both undesirable "Bias 1" and "Bias 2" feedbacks effectively merge together, capacitors C3 and C4 switch both of them off above certain crossover frequency. To choose the right crossover frequency and the capacitor values, signal gains in the respective feedback paths need to be evaluated.

Gain Km from "A" to "B"  (at medium frequency, e.g., 1kHz) through the main "green" path is determined by the tube gain and the feedback divider:

Km = Gm * (SQRT ( Ra * Rsp )) * (R1 / (R1 + R2)),                                             (1)

where:

Gm -- tube transconductance;

Ra -- plate load;

Rsp -- load (speaker) resistance;

R1 and R2 -- input and feedback resistors (Fig. 10) respectively.

Combined gain Kb of "pink" and 'brown" bias emulation related feedbacks can be defined as (assuming R7 is relatively small):

Kb = R7 * Geff * (R4 / (R4 + R6)),                                                                          (2)

where:

R7 -- cathode current sensing resistor;

R4 and R6 -- bias emulation attenuation divider (as per Fig. 10 and discussed in connection with Fig. 9C);

Geff -- is virtual "transconductance" to express combined action of the "pink" and "brown" feedbacks, as if only one feedback applies through the cathode "pink" path, but with a larger effective transconductance Geff.

Geff can be caclulated by the following equation:

Geff = Gm + (Ik / Vg),                                                                                              (3)

where:

Ik -- DC quiescent cathode current;

Vg -- quiescent control grid negative DC bias voltage.

"Gm" term in (3) represents the effect of the "pink" path, taking current recycling into account, therefore plate transconductance rather than triode connected transconductance is involved. Ik/ Vg term in (3) accounts for divider R5R6 attenuation.

As an example, Table 1 lists values of Geff for some common audio output pentodes and beam tetrodes in class A.

Valve	Va, V	Vg2, V	-Vg1, V	Ia, mA	Ik, mA	Gm, mA/V	Geff, mA/V	Geff/Gm
6V6	250	250	-12.5	45	50	4.1	8.1	2
6V6	315	225	-13	34	37	3.75	6.6	1.8
6L6	250	250	-14	72	78	6	11.6	1.9
6L6	350	200	-12.5	48	51	5.3	9.4	1.8
6L6	350	250	-18	54	57	5.2	8.4	1.6
EL34	250	265	-14	100	115	12	20.2	1.7
EL84	250	250	-7.3	48	54	11.3	18.7	1.65
ECL86	250	250	-7.3	36	42	10	15.8	1.6
ECL82	200	200	-16	35	42	6.4	9	1.4
6П15П	300	150	-2.5	30	35	15	29	1.9
6П18П	180	180	-6.8	53	62	11	20.1	1.8
6П13С	200	200	-19	80	88	9.5	14.1	1.5
6П43П	185	185	-16.3	45	48	7.5	10.4	1.4

      Table 1. Effective transconductance Geff and Geff/Gm ratio for power output tubes.

Most of the valves have Geff approximately 1.6...1.9 times larger than the actual tube transconductance Gm. TV sweep and vertical deflection tubes, typically having lower g2g1 mu, exhibit lower Geff/Gm. In other words, contribution of the harmful "brown" feedback is smaller for for TV sweep tubes, which might be beneficial. Similarly, lower Geff/Gm can be achieved by running a power tube with elevated screen grid voltage, and at the same time with larger negative control grid bias.

 

9. Component values selection and calculations

Refer to Fig. 10. Current sensing resistor R7 is not critical, but should be rather small in order not to waste more than 500mV on it and not to degenerate transconductance and not add to increase error amplifier voltage swing. On the other hand, it should not be wire wound inductive resistor. Thus, 2...8R range is the best. Once R7 is selected, R5R6 is calculated to obtain required emulated grid bias, as explained above. R5 and R6 should be large, so that capacitors C4 and C3 can be smaller. So, it is reasonable to select R5 in the Megohm range.

Input resistor R1 should be as small as possible (to reduce stray distortion penetration), but large enough not to overload a signal source. 10K looks like acceptable. R2 is selected to get required amplifier gain, and C1 -- to pass low frequencies from 20Hz (or higher if the amplifier is designed for small speakers).

To properly design and calculate bias emulation crossover parameters, refer to the Bode plot in Fig. 11.

  Fig. 11. Bode plot of the main feedback (green) and bias emulation combined feedback (red) gain.

Main feedback partial loop gain plot from point "A" to point "B" is shown in green. In this example, a 5K : 8R ratio, 25H primary inductance transformer and EL84 tube with Gm = 10...11mA/V are assumed. The curve shape depends on the signal source impedance Zin, which can be anywhere from zero (volume control is at minimum) to infinity (input is open circuit). If Zin is infinite (open circuit), the plot begins at Km = 2 (refer to (1)) and starts to roll off at 30Hz (Ra =5K, Lprimary = 25H) as the frequency goes down. If Zin is zero, a "shelf" is created from about 15Hz to about 1/16-th of it, i.e., at about 1Hz (solid green). Circuit compobnents "responsible" for certain knee frequencies are shown in the plot too. At intermediate Zin values, the plot can be anywhere in the area covered by the family of dotted green curves. Below 1Hz the plot follows the 6dB/octave slope created by the transformer, regardless of Zin. In other words, below 1Hz the gain of the main loop is stable and predictable.

Therefore, the crossover shall be chosen in that stable and well defined area -- as a safety margin, 2...3 times below the frequency of R2C1, that is about 0.3Hz. DC bias emulation feedback prevails below this crossover frequency, while main audio feedback prevails above the crossover frequency.

Main loop gain at this chosen crossover frequency is about 0.025, as can be easily worked out from (1) and considering 6dB/octave slope.

Therefore, at the crossover point, DC bias feedback gain (red curve) shall also be set to 0.025. From (2) it follows, that a certain attenuation by way of R4 will be required, and R4 value can be derived from resolving (2). In this case R4 is about 33K -- large enough for adequate bias emulation precision.

Bias feedback is subdued in the audio range by R3C3 filter. For a smooth crossover, R3C3 corner frequency shall also be 2...3 times "away" from the crossover point. At higher frequencies, bias feedback is further suppressed by another filter R4C4, and its corner frequency, in turn, should be staggered away from R3C3 by a factor of at least 2...3. This is to avoid extra phase lag created by C4 at the crossover frequency. As a result of both low-pass suppression filters, attenuation of the bias emulation feedback at 20Hz would already reach 52dB! It means that anticipated full power distortion of the amplifier at 20Hz is already as low as 0.05%, and will be further falling four times per octave. Though 0.05% is still larger than the "target" 0.01%, it is of a little worry at 20Hz, as a speaker would generate several decimal orders higher distortion or noise (due to a relatively large voice coil travel, rattle and/or air puffing through a speaker port).

 

10. Infra-low frequency feedback crossover

It is very important that the two feedback signals, competing at the crossover point, differ in phase by about 90 degrees, nowhere close to 180 degrees. For example, in Fig.11 DC bias feedback is flat around the crossover, and the main feedback, sloped at 20dB/decade, has a +90 degrees phase shift. For that reason, an attenuation resistor R4 is used, and time constants in the bias emulation are not overly large.

To see what happens if the "90 degree crossover" rule is violated, refer to Fig. 12.

                     Fig. 12. An example of incorrect crossover parameters.

In this example, two mistakes have been made deliberately. Firstly, attenuation resistor R4 is deliberately not used (Kb=0.09), which would seem to improve bias emulation precision. Secondly, R3C3 time constant is chosen large as it would seem to better suppress bias emulation feedback in the audio range. Therefore, at the crossover, bias emulation path has 90 degrees lag, while main feedback has 90 degrees advance. As a result, at the crossover frequency (about 0.5Hz) both feedback signals, having equal amplitudes, but opposite phases, almost cancel each other. A deep notch is created in the overall feedback gain curve. The notch means that at the crossover frequency there is virtually no feedback at all, and the system is undamped. in other words, it is prone to oscillations at this frequency. In reality, continuous oscillations might not happen, but annoying infra-low frequency slow decaying undulations will take place -- after power-up, overloading or supply voltage fluctuations. Though not audible, such undulations swing the bias point of the tube, taking away from the amplifier dynamic range. So, the aim of the above example is to help a designer avoid this pitfall.

 

Correctly designed bias emulation crossover (Fig. 10, Fig. 11) results in a nice and clean amplifier transient response. Fig. 12A gives an example of an output waveform from a real amplifier driven by 0.5Hz square waveform.

Fig. 12A. Long time base transient response of an amplifier with correctly designed bias emulation crossover.

Transient response is classic -- ideal exponential, without any undulations, oversoot or "tail". Needless to say, in respect of low frequency sound reproduction, such amplifier will deliver precise tight well controlled bass, well defined drums, percussion, bass guitar, etc. There will be no sound coloration, no boom, no flaccid flappy-floppy speakers, no other undesirable sonic artifacts.

 

11. Non-inverting amplifier topology

A non-inverting amplifier can be designed around bias emulation too, as shown in Fig. 13.

                           Fig. 13. DC stabilisation in a non-inverting ultra-low distortion amplifier.

Here (Fig. 13) input signal is superimposed onto DC stabiliasation op-amp input, and main audio feedback network is grounded at C1. Operation and Bode plots are similar to Fig. 11. There is no room for variation in the main feedback gain curve -- it always follows the lowest "shelf" (bold green line in Fig. 11). Note that in respect of DC bias feedback path, R9C5 forms an additional filter, particularly if the signal impedance is low, when volume control is at minimum. For that reason, R3C4 can be even omitted for simplicity or filter time constants can be made a bit smaller (less aggressive suppression) compared to Fig. 10.

When making a decision whether to choose an inverting (Fig. 10) or non-inverting (Fig. 13) topology, the following should be considered.

In an inverting topology (Fig. 10) the operational amplifier can potentially give the lowest distortion, as common mode rejection related distortion does not apply. However, main feedback impedance can not be too low, particularly if there is no preceeding tone stack amplifier or buffer. Practically R1 should not be less than 10K. That in turn puts a limit on noise reduction (10K alone translates to 12nV/SQRT(Hz), besides the op-amp noise) and requires stringent summing junction shielding measures to prevent stray capacitive "back door" distortion penetration (see Fig. 3).

Non-inverting topology (Fig. 13) obviously has high input impedance (equal to R9). That makes it perfect for upgrading vintage tube radios where an audio amplifier works directly from a high impedance (500K...1M) volume control potentiometer. Main feedback impedance can be reduced (compare values in Fig. 10 and Fig. 13) in order make it virtually not susceptible to stray capacitance related distortion. On the other hand, high signal source impedance can make this problem even worse, as capacitively coupled distortion can equally affect either input of the operational amplifier. Another potential issue is added distortion due to non-linear common mode suppression in the op-amp. This kind of added distortion source can be particularly bad with so called "rail-to-rail input" operational amplifiers. At high common mode voltage, usually a few volts below the positive supply rail, such rail-to-rail op-amps switch over from the primary input differential stage to the second complementary one. Crossover from one to the other translates to distortion, directly applied to input, which equals to the difference between the offset voltages of the respective op-amp input stages. For the above reason, it is not recommended to use rail-to-rail input specified op-amps if common mode voltage is above half supply rail.

In case of small amplifier signal gain (gain of five in Fig. 14)), capacitor C1 can be eliminated for simplicity. In this circuit load resistance is assumed 3 Ohm. Second bias stabilisation feedback suppression filter is deleted too.

 

 

          Fig. 14. Simplified feedback                               Fig. 15. Feedback crossover plot for Fig. 15.

As illustrated by Fig. 15, main feedback rolls off from 50Hz and has no "shelf". To get maximum possible feedback strength at audio frequencies, Kb should be kept as low as practical by way of selecting low attenuation resistor R4, but large enough to provide acceptable bias accuracy. In this example, crossover frequency is about 3.6Hz. It means that in fact, small signal frequency response of the amplifier is flat down to 3.6Hz. Thus the amplifier would "struggle" to faithfully reproduce infra-low frequencies, which is unnecessary and undesirable as can cause overloading. Though R9C5 with 16Hz corner helps to some extent, still topology Fig. 14 should not be used if a source might contain infra-low frequency content, for example, vinyl record player pickup preamplifier or an AM detector with swinging carrier level.

Despite low crossover, bias feedback suppression at 20Hz is only about 22dB (compared to 52dB for Fig. 11). At 20Hz, near clipping, such amplifier would have about 2% harmonic distortion. This circuit is presented rather as an example and not suggested for practical implementation.

 

In conclusion, topology shown in Fig. 10 is recommended for ultimate Hi-Fi applications, where distortion and noise level must be kept to minimum. Circuit in Fig. 13 is the best where high input impedance is necessary, e.g., when upgrading vintage radios. R1C1 corner frequency hould match capability of the output transformer. In some cheap radios a transformer is so undersized and inductance is so small, that it is not capable of reproducing anything lower than 150Hz. In such a case, all feedback time constants need to be shifted accordingly.

 

In reality, however, neither of the cicuits (Fig. 10, 13, 14) will work -- they will violently oscillate at high frequencies due to cumulative phase lag caused by the op-amp, tube plate load capacitance and transformer leakage inductance. Therefore, a non-trivial high frequency stability problem lays ahead.

 

12. High-frequency feedback loop stability

As pointed out above, a simple single loop (Fig. 16) will not be stable. Combined phase lag of the error amplifier A1, plate loading by primary winding capacitance and leakage inductance reaches 270 degrees, and even a phase-correction capacitor C2 will not help. (Note that in this and following schematic diagrams, bias emulation/stabilisation circuitry is not detailed, but shown as a single block.)

             Fig. 16. Single negative feedback loop, which is unstable and unusable.

First of all, the transformer -- a root of all evil -- should be taken out of the loop at high frequencies, as proposed in Fig. 17. Here two feedback loops are created. The main one (green) operates over the audio frequencies range and is responsible for low distortion performance. The second loop (red) which is supposed to stabilise the amplifier, does not embrace the output transformer and the load. In other words, the "red" feedback maintains low distortion at the plate of the tube, not directly at the load. Provided the transformer does not add too much distortion (transformer distortion will be covered later), such solution should give reasonably good results.

            Fig. 17. Taking the output transformer out of the main feedback loop. (This circuit is for discussion, not recommended for implementation).

In theory, such solution (Fig. 17) shall work. Tube plate winding capacitance Cp loading creates a -90 degrees phase lag, but the feedback compensation capacitor C2 together with R1 gives +90 degrees phase advance. As a result, only -90 degrees error amplifier (op-amp) phase lag is left in the loop, which seems perfect. In practice, however, such topology has certain inconveniences. Winding capacitance, represented in a common transformer equivalent circuit (Fig. 18) by a lumped capacitance Cp, usually is not known and not specified.

      Fig. 18. Lumped parameter equivalent curcuit of a small output transformrer.

To assess Cp, impedance of the primay (secondary -- open circuit) was experimentally measured for two sample transformers in the frequency range from 20Hz to 20MHz. A small transformer (Fig. 19A) from AWA model 467MA Australian radio is bitumen potted into 50 x 54 x 40mm steel can with 58mm mounting holes pitch, designed for 6M5 or 6BV7 tubes. It has a simple non-interleaved construction with the secondary wound over the primary. A larger transformer is a generic 3.5K/8R/4R transformer usually sold as a part of DIY kit of a single-ended class A stereo amplifiers (Fig. 19B) with EL34, 807 or ГУ-50 (GU-50, FU-50) output tubes. It has interleaved winding, where the secondary is sandwiched between the primary sections.

            

      Fig. 19. Example of a "small" transformer (A, left) and a "larger" transformer (B, right), referred to below.

Fig. 20 shows primary impedance versus frequency for these two transformers.

Fig. 19. Primary impedance of a small 2W mantel radio 7K : 3R transformer (blue curve) and a larger 9W 3.5K : 8R/4R transformer (red curve).

At low frequencies the impedance linearly increases depending on the magnetising inductance Lm value, reaches parallel resonance peak (reaches hundreds of kilohms!), then starts to fall due to winding capacitance Cp. The small transformer can effectively work only above 150...200Hz, while the large one seems to be capable of handling 20Hz. Equivalent winding capacitance Cp of the small transformer is about 120pF up to several mehahertz, above which there is some dip probably caused by some obscure resonance. The larger transformer has a larger Cp about 700pF, which is not surprising due to a much larger physical size of that transformer. However, its impedance plot is riddled with peaks and troughs most likely caused by different sections of windings resonating at different frequencies and sometimes acting as loosely coupled LC tanks. Even more interesting is that at higher frequencies, effective winding capacitance of the large transformer reduces to about 150pF -- red and blue curves are getting closer. This phenomenon can be understood considering that actually Cp is not lumped as in Fig. 18, but rather distributed (Fig. 21).

 Fig. 21. Equivalent circuit of a transformer with distributed winding capacitance and leakage inductance.

At high frequencies only a small portion of Cp gets "connected" to the primary terminals, the rest being isolated by the distributed winging inductance Lp. Thus, instead of 700pF, the plate of V1 sees only a small portion of this capacitance and some lossy inductance, similar to a transmission line, possessing an active (resistive) impedance of several hundreds ohms. However, this impedance is not consistent and not predictable, which makes loop gain calculations at design stage impossible.

Another drawback associated with Fig. 17 is that loop gain depends on the audio signal source impedance. For instance, if the input is open circuit, loop gain raises by a factor of 15. Even worse, unavoidable wiring capacitance to ground Ci (including input capacitance of the op-amp) undermines phase advance and thus limits the unity gain loop frequency and amount of negative feedback available.

Yet another inconvenience is that compensation capacitor C2 affects both audio high frequency roll-off and the loop gain. C2 value in Fig. 17 is the transformer turns ratio down of what C2 would have been in Fig. 16. With C2 = 1.5pF roll-off frequency is about 27kHz. C2 reduction would reduce stability margin at crossover (which will be elaborated upon later). Further, low value, high accuracy, high voltage (2kV recommended) quality (C0G, NP0, mica) capacitors are not common and expensive.

 

From the above discussion it follows that in Fig. 17 the only way to control the loop gain and unity gain frequency is gain-bandwidth product of the error amplifier. This is impractical, as the op-amps with external compensation (like in a good old LM301) are not common these days. Therefore, Fig. 17 topology is not recommended for implementation and was given mainly for discussion purposes.

A better practical topology which allows to control loop gain and audio bandwidth separately is shown below in Fig. 22.

          Fig. 22. High-frequency feedback taken of a capacitive divider.

Several improvements are made. Firstly, the valve plate is loaded by a relatively large capacitance C3. It provides a heavy, but consistent and predictable -20dB/decade gain roll-off, almost unaffected by the transformer parasitics, as C3C4R3 divider impedance in the megahertz range is far smaller than the transformer primary impedance (Fig. 19). Secondly, C3 and C4 form a voltage divider. If, for instance, divider ratio is chosen the same as the transformer turns ratio (25:1 in this example), then, ideally, voltage at point "H" equals voltage at the load "L". Thus, audio bandwidth (roll-off) is controlled by C2 in the same way, as in a conventional feedback Fig. 16. Voltage swing at point "H" 25 times smaller than at the valve plate, so C2 can be rated at a smaller voltage.

Finally, R3 is fundamentally important. Above a certain "corner" frequency Fc determined by R3C4 time constant, about 430kHz in this example, gain from "G" to "H" becomes constant (rather than falling -6dB/octave). In other words, at high frequencies the tube does not introduce phase shift from "G" to "H". Value of R3 is chosen substantially smaller than impedance of the transformer primary (Fig. 19), so the gain is independent of a transformer used.

Similarly, due to a relatively large C2 value, gain from "H" to "F" reaches unity, plateaues above 400kHz and is not much affected by the stray capacitance Ci. Thus, in the megahertz range there is no phase shift from "G" to "F", and the only source of phase shift in the loop is the error amplifier. In other words, while in Fig. 17 topology phase lag of the tube shall be compensated by the feedback phase advance, in the Fig. 22 circuit there is no phase shift at all. That makes loop calculations and design very straightforward.

The following design factors should be considered:

A) Loop unity gain frequency Fo = Foa * Gm * R3, where                       (4)

       Foa -- unity gain frequency of the error amplifier;

       Gm -- valve transconductance.

B) Loop unity gain frequency Fo shall not be "too high" -- definitely not higher than Foa, and also low enough so that parasitics, such as transformer primary effective capacitance, grid stopper (not shown), Miller effect of the valve, strays, etc. do not create considerable phase lag at Fo.

C) On the other hand, Fo shall not be "too low" -- it shall be at least three times above the "corner" frequency Fc, which, in this example, is around 430kHz.

            Fc = 1 / (2 * pi * R3 * C4)                                                                (5)

Note that the Fig. 22 topology is conditionally stable: below Fc the combined loop phase lag is as large as -180 degrees (tube and op-amp together). Above the Fc phase lag settles at -90 degrees (op-amp alone). To ensure stability, loop gain at Fc shall be well above unity or, in other words, Fo shall be several times higher than Fc.

D) R3 value plays a crucial role in reconciling and trading off the above design factors as it is the main instrument to control Fo. Too high R3 may cause instability (factor (B)) due to spurious phase lag caused by primary winding capacitance, grid stopper resistor (not shown), Miller effect of the tube, etc. Too low R3 raises the risk of conditional instability (factor (C)), because Fc is inversely proportional to R3 and Fo is proportional to R3. As a result, when lowering R3, Fc and Fo "move" toward each other, and conditional stability may be breached. From empirical experience, a reasonable R3 range is from 5 Ohms to 50 Ohms.

E) While Fo and consequently R3 affect stability, Foa affects the closed loop distortion factor (HD) of the amplifier at a certain harmonic frequency F:

      HD (F) = THDg * ( Vg / Vin ) * ( 1/ Kea (F) ), where                            (6)

THDg -- distortion factor of the signal at control grid of the tube;

Vg -- control grid voltage;

Vin -- respective audio input voltage to the amplifier;

F -- frequency of a certain harmonic in question (not fundamental test frequency);

Kea (F) -- gain on the error amplifier at the frequency F.

For the most common first order roll-off op-amp, internally compensated for unity gain stability, simply:

      Kea = GBW / F, where                                                                             (7)

GBW -- gain-bandwidth product of the op-amp.

For a higher order roll-off error amplifier Kea (F) is even higher. A larger the Foa or GBW results in a lower THD. Therefore the error amplifier design should be aimed at achieving as GBW or Foa as practical.

F) Obviously, a valve with higher transconduction Gm (higher sensitivity) is preferred, as it is easier to drive and Vg is smaller, hence, according to (6), lower THD can be obtained.

G) Division coefficient C3/(C3+C4) does not have to be exactly equal to the transformer ratio. It can be different provided that C2 is adjusted accordingly. However, a smaller division coefficient, say 1:2, would require a smaller C4, and corner frequency would increase, as per (5), putting the amplifier at risk of instability (factor (D)), particularly if source impedance is high -- open circuit or connected to a volume control. On the other hand, too high division will require a larger C2, which might result in high frequency audio noise accentuation (blue noise).

 

Taking all the above factors into account, let us check the "health" and performance of the circuit shown in Fig. 22. We assume that the output tube is EL84 with Gm = 10mA/V. It requires about -16...18V for cutoff, and therefore can be driven directly by an operational amplifier. Positive supply rail of this op-amp can be about +5...8V, negative -25...-30V to keep full supply voltage under 36V. The best for that purpose (at least by the year 2020 standards) would be a JFET op-amp OPA828 which has low noise, low offset (for perfect bias emulation), fast slew rate up to 150V/us and high GBW: Foa = 45MHz.

According to (4), we will get Fo = 6.75MHz, which is far above Fc = 430kHz, but lower than Foa = 45MHz, so stability condition (C) is well satisfied.

Due to a small R3 = 15 Ohm, even assuming the worst unrealistic case -- lumped primary winding capacitance of 300pF -- the respective associated pole will be at 34MHz, far above Fo. Thus, no stability problems are to be expected here either. So far so good.

To drive EL84 to full power, almost near clipping, about 13V of peak-to-peak voltage might be required, so Vg = 13V. We can expect grid distortion (Fig. 1) of about 25% in this case. Audio input Vin = 1V peak-to-peak will be required for such full power output.

From (6) and (7) combined we can expect distortion HD near clipping of the order of 0.15% for 10kHz fundamental and 0.015% for 1kHz fundamental. These figures are quite approximate as the exact composition of various harmonics is not known, probably the second and the third harmonic are prevalent. These THD figures look exceptionally good for a "valve" amplifier, almost too good to be true, but they are real. It is particularly good that distortion quickly diminishes with the output level reduction below clipping. Anyone can replicate the Fig. 22 circuit (do not forget to insert a grid stopper of about 100R) and see for oneself. To reduce THD further, to meet the target of <0.01% extra 26...30dB of loop gain would be required. Since JFET op-amps with 1GHz GBW and +/-18V supply do not (yet in 2020) exist, it will be shown below how to achieve such GBW with a composite amplifier.

 

From the above discussions it is clear that taming a hybrid amplifier at DC, infra-low frequencies and in the megahertz range is not overly difficult. However, unfortunately, it is not the end of all the problems. Next issue to tackle is stability at crossover frequency (30...70kHz range).

 

13. Transformer distortion and crossover frequency

With the dual feedback topology (Fig. 22), distortion generated in the output transformer can not be fully controlled by the feedback, as some amount of the feedback (green line) bypasses the transformer. At the crossover frequency Fcr, where impedance of C2 equals R2, transformer distortion is suppressed only by about 30%. At a lower audio frequency F, when C2 impedance increases compared to R2, transformer distortion suppression also improves, reaching Fcr / F ratio. Thus, to achive a significant transformer distortion reduction, crossover frequency should be higher. On the other hand, high Fcr may cause instability problems. To find a trade-off and choose a reasonable Fcr, one needs to know how much distortion an output transformer actualy produces. Distortion in a transformer is caused by non-linearity of its inductive "ingredients" (Fig. 23).

       Fig. 23. Transformer equivalent circuit showing non-linear inductances.

Magnetising inductance Lm is non-linear of course as the thransformer is wound on an iron core. However, at high frequencies its distortion is insignificant because magnetic flux deviation is minusclule, impedance is very high (megaohms), AC current is small (below 100uA) and voltage across Lm is tightly controlled anyway due to relatively low primary resistance Rp. Non-linearity of Lm manifests mainly at low frequencies, but, as was explained earlier in section 9, low frequency distortion is well suppressed, as the low frequency crossover (0.3Hz, refer to Fig. 11) is way below the audio range.

At high frequencies, leakage inductances Lp and Ls cause most of the distortion. It might sound counter-intuitive at first, as usually leakage inductances are viewed as "air" inductances, not involving a magnetic core. Unfortunately it is not completely true. Leakage flux, seeking a path of minimum resistance (lowest magnetic reluctance) tend to find "shortcuts" through ferromagnetic objects, like transformer steel mounting bracket(s), steel bolts, steel bobbin covers, steel chassis, etc. These fixtures are usually made of construction steel, which has high hysteresis loss and creates odd harmonic flux and hence voltage distortion, mostly the third harmonic. Stainless steel is even worse in this respect.

Tests showed that a generic output transformer, like shown in Fig. 19B, creates as much as 0.05...0.25% at 10...20kHz at nominal load. Obviously without load, there will be no distortion as zero current flows through the leakage inductances. Measured distortion levels were not consistent across the transformer samples. Tighter and more neatly wound coils result in lower distortion. It suggests that minimising leakage inductance is the most important in the first place. The second most important factor is having as little as possible steel fixtures in close proximity to the windings. Removing winding covers reduces distortion 5...10 times. However, an "open" transformer might look not aesthetic or be not safe. Ideally a transformer should be enclosed or covered by non-magnetic materials (aluminium, copper, plastic). If such redesign is impractical, a simple but effective modification can be recommended -- pad the insides of steel bobbin covers by several layers of aluminium "cooking" foil (Fig. 24) or a layer of a thicker foil as used for cooking trays.

     Fig. 24. Transformer side covers padded with aluminium foil for distortion reduction.

The foil should embrace the winding as close as possible. Eddy currents in highly conductive foil repel magnetic field from penetrating the steel caps, thus reducing associated distortion 5...10 times -- to about 0.01%. The foil, squeezing the leakage magnetic field, also reduces the leakage inductiance, which in turn improves stability, as will be explained later. Copper foil would probably work better, but readily available aluminium was found quite adequate.

The following measures should be considered at the amplifier design and buid stage:

- if possible, obtain a transformer with low leakage inductance;

- use non-magnetic fixtures or open transformer design, if it is safe;

- enclose the transformer in an aluminium can;

- avoid using stainless steel parts and chassis; stainless steel is harder magnetically and generates more distortion than ordinary steel;

- if chassis has to be stainless steel, then elevate the transformer over it and/or put a thick aluminium plate-spacer under the transformer;

- if some power sacifice is acceptable, use load resistance higher than nominal.

These measures can help reduce transformer distortion at 20kHz below 0.01%. Distortion level rapidly falls (proportional to frequency squared or even steeper) due to falling impedance of the leakage inductance and audio feedback path (green) taking over the high-frequency path (red). At mid-audio frequencies (0.5...3kHz), which human ear is the most sensitive to, output transformer distortion becomes virtually unmeasurable.

Usually an output transformer has several taps on the secondary. Experiments proved that the best (for stability and frequency response flatness) is to take feedback from only one output -- from the full (highest impedance) secondary winding. On that output the transformer distortion gets suppressed to some extent. But on the other tap(s) the output transformer distortion is not controlled. Therefore, if an amplifier is intended to work into any speaker impedance, particular attention should be given to the distortion reduction measures listed above.

 

Crossover frequency Fcr does not necessarily have to equal --3dB roll-off frequency of the amplifier. For more flexibility in shaping and/or equalising frequency response, Fcr and amplifier bandwidth can be controlled independently by R2C2 and R4C5 circuits respectively (Fig. 25). For both circuits operating independently, impedances of R2C2 should be chosen one-two decimal orders smaller than of R4C5.

  Fig. 25. Separate control of crossover frequency (R2C2) and --3dB roll-off frequency (R4C5).

For example, in Fig. 25, the roll-off is set below 20kHz, so that it partly cancells out possible peaking at 30...35kHz, thus making overall frequency response reasonably flat up to 20kHz. To further attenuate peaking and to get a steeper roll-off above 20kHz, a T-bridge can be used (Fig. 26). As a side effect, a small rise of +0.5...+1dB can appear around 5...10kHz.

                            Fig. 26. Roll-off control by means of a T-bridge.

More on operation and application of the T-bridge can be found here and here. Values of the T-bridge components shown are very approximate and always require optimisation and selection on test, depending on the transformer used.

 

14. Stability of a system with multiple poles

To apply an extra-heavy feedback and achieve extra-low distortion, the aim is to have as much as possible open loop gain in the audio range, and at the same time to have the loop gain rapidly falling at higher frequencies to get a manageable unity gain frequency Fo. A simple single dominant pole -20dB/decade may not be sufficient to achieve the above goal. Therefore, multiple gain stages can be used with respective multipole open loop transfer function. It has already been shown, that a curcuit in Fig. 22, 25, 26 has two poles -- one comes from the operational amplifer, another one -- from the capacitive tube load C3. Such double-pole topology is capable of reducing THD down to 0.01%...0.1%. Further THD reduction will require more gain stages and consequently more poles. An example in Fig. 27 illustrates a two-stage error amplifier with three poles.

                 Fig. 27. Two-stage error amplifier.

           

 Fig. 28. Open loop frequency response (Bode plot) of a triple-pole amplifier. 

Open loop frequency response (gain from point "F" to "H" in Fig. 27) of such system is shown schemtically in Fig. 28. At certain sections it has a very steep fall up to -60dB/decade, and phase lag reaches quite "scary" -270 degrees. However, the zeros RzCz at 280kHz and R3C4 at Fc = 420kHz which slow the fall of the curve back to the benign -20dB/dec slope (green line in Fig. 28) around unity gain crossing. Thus at unity gain crossing Fo (point "g" in Fig.28) phase lag is about 90 degrees, and should the loop be closed, the system will remain stable. This is in line with Nyquist stability criterion, which requires that, for stability, an amplitude-phase gain vector (phasor, Fig. 29) shall not encircle point (-1, 0) clockwise.

         Fig. 29. Open loop gain phasor of a triple-pole amplifier (Fig. 27). 

Reference labels "a" to "i" provide correspondence between Bode plot Fig. 28 and Nyquist phasor Fig. 29. At at two certin frequencies, where the phasor curve intersects the horisontal axis, phase shift equals exactly -180 degrees, making feedback purely positive, rather than negative, and yet the system will not oscillate. Without maths it is difficult to comprehend intuitively. Perhaps it can be said, as a joke, that the system "can not decide", at which of the two frequencies to oscillate and remains stable. It is like unto a parable of a donkey standing right in the middle between equally delicious stacks of straw, unable to make up his mind which one to partake from and eventually starved to death.

However, jokes aside, this multi-pole system is conditionally stable. It might oscillate if loop gain falls.Then the Bode plot (Fig. 28) will move down (shown in red) and will be crossing the "0dB" unity gain level at -40dB/decade slope at -180 degree phase lag, creating oscillation condition. Referring to phasor (Fig. 29), loop gain reduction will cause the phasor "shrinking" radially in all directions. As a result, "c-f-g" stretch of the phasor can end up on the right hand side of the (-1, 0) point, thus encircling it, which, according to Nyquist criterion, indicates instability of the closed loop.

In a multi-pole conditionally stable amplifier loop gain must be well controlled. If loop gain becomes too high, the system might oscillate at very high frequencies due to parasitic poles and delays (section "h-i" in Fig. 28) which might "rise" above the 0dB line. If loop gain becomes too low, a conditionally stable system might also oscillate at some medium frequencies (about 300kHz in the above example). For that reason, it is quite normal if a hybrid amplifier gives out a brief burst of oscillation when the output power tube is beginning to warm up. Such behaviour is quite acceptable and would not damage the speakers, as the oscillation condition is quickly passing and power is small while the tube is "cold". For good conditional stability margin, frequencies of the zeros (for example, point "F" in Fig. 28 at Fc = 420kHz) should be chosen at least three times (better 5...10 times) below the unity gain frequency (point "g").

An unquenchable oscillation in a conditionally stable system may start after overloading. Signal clipping obviously is equivalent to the effective loop gain loss and also introduces extra recovery delays. Both factors together may create a condition for oscillation. Techniques for making such oscillations soft, self-quenching, will be discussed later.

Finally, an amplifier may lose stability at the crossover frequency due to potential loop gain dips, notches and even phase reversals due to the two feedback paths -- main (green) and high frequency (red) in Fig. 22 -- working together. Similar to low-frequency crossover, care must be taken to avoid summation of out phase signal components.

 

15. Stability at high-frequency crossover

To analyse combined effect of both fedback paths, an equivalent schematic in Fig. 30 will be used.

                Fig. 30. Simplified schematic for crossover amplitude-phase study.

It is similar to Fig. 22, but the transformer is shown with lumped net leakage inductance Ls referred to secondary winding. Voltage net Vt is not physically accessible. Capacitive divider C3C4 has the same division ratio as the transformer, so Vt = Vh. Since the crossover analysis covers the range from about 500Hz to 200kHz, R3 and C1 practically have no effect and can be neglected. Closed loop amplifier gain in this example is set to approximately (R1 + R2) / R1 = 4 (not 15...16 as in Fig. 22). It is done to make the phasor plot more manageable, and does not qualitatively affect the results.

Before attempting to plot the overall phasor of an open loop, it is helpful to study a partial phasor of the load/feedback sub-circuit only -- from Vt to Vf. Fig. 31 shows Vf  phasor for purely resistive load Rload.

Fig. 31. Partial feedback Vf phasor showing contribution of main resistive and HF capacitive branches.

At low-medium audio frequencies, while impedance of Ls is negligible, Vload = Vt =Vh. With frequency increasing and Ls impedance becoming considerable, Vload vector (green) acquires phase lag and loses magnitude, following a semi-circle (thin green). It can be shown (applying Thevenin's equivalent generator principle) that Vf is combined of two components. One of them is a scaled portion a*Vload (green), where a = R1 / (R1 + R2). It is basically in phase with Vload and follows a smaller semi-circle. The other component is related to a current flowing through C2 and therefore exhibits phase advance. This "effect of C2" red vector, based at a*Vload, also follows a semi-circle, its diameter stretching from a*Vload to Vh. Sum of the green and red components is the resultant Vh vector (phasor), shown by bold dark blue curve.

It can be seen that around crossover frequency, phasor Vh comes close to zero, in other words, Vf becomes rather small. Remembering that closed loop amplifier gain equals |Vload| / |Vf|, we can see that amplifier gain would peak at the crossover. It is not surprising, considering that the "green" feedback path has a large phase lag due to the leakage inductance, while the competing "green" path has almost +90 degreees phase advance due to capacitor C2. These two signals tend to almost cancel each other, similar to what was discussed above in section 10 and illustrated by Fig. 12. In time domain it points out to a "ringing" transient response.

To assess stability of the whole amplifier, a full open loop gain phasor should be inspected for compliance with Nyquist criterion. To plot the full phasor, a partial feedback subcircuit complex phasor vector Vf (Fig. 31) shall be multiplied by the gain of the remaining amplification stages (Fig. 29). In this sense multiplication means vector lengths multiplied and their arguments (phases) added. The result is presented in Fig. 32.

              Fig. 32. Full open loop gain phasor in case of resistive load.

Though section "d-e" of the phasor curve runs closer to the origin, the amplifier will be stable, as the phasor still does not encircle (-1, 0) point. Conditional stability even improves due to phase advance in the hundreds kilohertz range.

If Zload has a capacitive component, resonant peaking of Vload occurs and phase lag reaches --180 degrees (Fig. 33).

         Fig. 33. Feedback phasor for capacitive load conditions.

As the load impedance becomes more capacitive and resonance Q-factor raises, feedback phasor Vf comes closer to the origin (green), which points to marginal stability, severe peaking and "ringing" of the closed loop amplifier. Further Q-factor increase results in the feedback phase reversal -- Vf phasor circles the origin at the "back" (red). Full Nyquist open loop gain phasor plot in this case would look something like shown in Fig. 34.

             Fig. 34. Open loop gain phasor for capacitive load.

Feedback transfer phasor of Vf encircling the origin in Fig. 33 translates into open loop gain phasor (Fig. 34) also encircling clockwise the origin and consequently the (-1, 0) point. It means, according to Nyquist criterion, that the amplifier with feedback will be unstable under such load. So, for assessing stability at crossover, instead of Nyquist criterion a simpler partial feedback phasor Vf analysis can be applied -- if Vf phasor (for example, in Fig. 33) does not encircle the origin, then the amplifier will be stable, otherwise it will oscillate close to the load resonance frequency, determined by leakage inductance and load capacitance.

The above analysis shows that an amplifier will always be stable with a resistive load, let alone with slightly inductive one. It is usually the case with an electrodynamic speakers, so a simple double-path RC crossover, as in Fig. 22, 25 or 26, is adequate. If the load is purely capacitive, such system will be unstable. If a load is somewhat capacitive, then the amplifier might be stable (with ringing transient response) or unstable -- it depends on the Q-factor of the resonance. The most effective way to improve tolerance to capacitive loading is to reduce leakage inductance as much as possible, so that load resonance frequency is significantly higher than the crossover frequency Fcr. In this case, the Vf phasor would resemble Fig. 35 with the loop pushed away from the origin, and the system will be stable.

Fig. 35. Feedback phasor when load resonance frequency is well above the crossover frequency.

As shown in Fig. 36 as an example, to further improve capacitive loading tolerance, phase correction via a capacitor C6 and load damping circuit R6C7 can be added.

                             Fig. 36. Phase correction and load resonance damping.

Resistor R5 creates a zero in megahertz region, which helps high frequency stability and also attenuates RF injection, which might be caused by mobile phones and picked up by the speaker cable.

The above measures result in quite adequate stability margin and capacive loading resilience. Fig. 37 illustrates transient response of an amplifier with quite "poor" output transformer -- leakage inductance 40uH -- under various load conditions.

        

    A)  No load, peaking 3.5% at 40kHz.                    B)  Load = 0.22uF, peaking 12% at 36kHz.

         

          C) Load = 8R, overshoot 10%.                       D) Load = 8R || 1uF, peaking 35% at 23kHz.

                                         E) Load = 8R || 1.5uF, peaking 46% at 21kHz.

                                   Fig. 37. Transient response at different load conditions.

From Fig. 37A it can be seen, that the damping circuit itself causes some minor peaking, but it allows the amplifier to tolerate up to 0.3uF of pure capacitive loading -- just in case. With resistive load the transient is quite clean with 10% overshoot which indicates flat frequency response to around 30kHz. The amplifier tolerates a capacitor up to 1.8uF in parallel with resistive load. Not every conventional tube amplifier with 20dB of feednack can boast such resilience! It is an "overkill" as dynamnic speakers, even with complicated crossover circuitry, never present highly capacitive impedance.

 

16. Direct load drive

Output transformer bypass technique discussed above, bypass not only the transformer, but the load as well. That results is the transformer distortion and amplifier frequency / transient response are not fully controlled by the feedback at high audio frequencies. A question may arise: is it possible to drive the load directly by the tube at high frequencies, thus bypassing the transformer, but still keeping the load in the loop (Fig. 38)?

          Fig. 38. Concept of bypassing output transformer via C3, but not the load.

This concept indeed has some merits -- frequency and transient response at the load (Zload) would be perfectly controlled by the feedback, with a very low output impedance. However this topology has certain shortcomings worth discussing. Firstly, for high-frequency stability at high frequencies (megahertz range) Zload shall be stable and consistent -- about 10...33R, as recommended above. In fact, Zload should work as R3 (as in Fig. 22, 25, 26, 27, 30, 36). Therefore, connecting a random speaker as a load in Fig. 38 will not be possible. Secondly, and most importantly, due to the inevitable leakage inductance of the transformer, load drive current flowing through the "green" path, will have almost -90 degrees phase lag in respect of the plate voltage, while the capacitive drive current through C3 ("red" path) would have almost +90 phase advance. Needless to say, at some (crossover) frequency, typically in the range og 50...200kHz, when these currents become equal in magnitude, they will almost cancel each other, creating a deep notch in the loop gain, similar to what was illustrated in Fig. 12 in the context of the low-frequency crossover. This will result, at best, in severe transient ringing of the plate voltage (though transient at the load would look perfect!), poor marginal conditional stability. At worst, if some extra phase lag develops in the transformer, for example, by the primary winding resistance and winding capacitance, loop gain Nyquist phasor will encircle the origin, and the amplifier will lose stability.

For the direct load drive concept to work better, some modifications should be considered (Fig. 39). In this example, a quite "poor" 5K/8R output transformer is assumed with leakage inductance Ls as large as 40uH.

                Fig. 39. Crossover stabilisation for direct load drive feedback topology.

Firstly, R3C4 circuit decouples provides consistent loading at the feedback pickup point in the mehahertz range, as the load is decoupled by L2. R6 is intended to suppress possible resonances -- to keep "L" loading predominantly resistive. Secondly, some phase advance is introduced into the main "green" signal path around crossover frequency (which is 110kHz in this example). Funny enough it is achieved by artificially increasing leakage inductance, by adding L1, with subsequent introduction of some active impedance component by R4. Indeed, a sadly well known principle "from which we get sick, with the same we get treated" is at work. With L1 = Ls, the best achievable phase advance is +19.5 degrees when R4 is 58% of L4 impedance at the crossover frequency. Similarly, phase lag is introduced in the "red" direct drive path by splitting a capacitor in two -- C3 and C4 -- and adding resistor R5 in parallel with one of them. With C4 = C3, phase lag is also -19.5 degrees when R5 is 58% of C5 impedance. (If C3 > C4, phase lag can be increased, but more audio power will be dissipated in R5.) Now, due to the combined advance/lag phase correction, "red" and "green" signals add with about 141 degrees phase shift, and do not completely cancel each other out at crossover. The amplifier in Fig. 39 can work, producing well controlled output, though ringing and peaking at the plate of the output tube may still be present.

A major drawback of Fig. 39 circuit is that too much inductance (Ls + L1 + L2) is inserted between the signal source and the load. The amplifier is unlikely to be able to deliver full power at 20kHz. Inductor L2, which is outside of the feedback loop, must be a low distortion one -- with no ferromagnetic core and positioned at least a diameter or length, whichever is greater, distance away from any steel parts, in the first place, the chassis. Note that if an amplifier is intended to work into a fixed load with inductive impedance component of the oeder of tens of microhenry, e.g., a full-range speaker in a mantel radio, L2R6 can be omitted.

In conclusion, due to the limitations and extra complexity, the direct load drive method is not strongly recommended for implementation, but rather has been studied for completeness.

 

17. Error amplifier

The main gain stage or the error amplifier shall conform to certain requirements, as outlined in section 12.

(a) Sufficient unity gain Foa is needed to achieve reasonably high unity gain of the whole amplifier Fo. Assuming Fo about 5...10MHz and the fact that the output tube has less than unity gain Gm*R3 (Fig. 22 and equation (4)), Foa should be around 25...100MHz.

(b) Gain as high as practical below the corner (zero) frequency Fc (equation (5)) in order to have a formidable loop gain at audio frequencies and hence ultra-low distortion. Therefore, more than a single pole in the transfer function may be beneficial.

(c) High slew rate -- typically above 20V/us --  to ensure effortless tube drive close to cut-off with "pointy" grid voltage waveform (Fig. 2) and at the maximum audio frequency of 20kHz.

(d) Output voltage swing, sufficiently large to drive low sensitivity tubes to cut-off.

(e) Low input current (nanoamps) and low offset voltage for the accurate bias emulation and DC stabilisation (section 7).

(f) Low noise, not exceeding the thermal (Nyquist) noise of the input and feedback resistor R1 (Fig. 10, 13, etc.) -- preferably under 10nV/SQRT(Hz).

(g) Fast recovery after overload condition to avoid extra phase lags and condition stability loss. 

(h) Protection of the tube control grid from excessive grid currents and excessive negative grid voltage.

Several topologies can be considered to satisfy the above criteria.

 

17.1. Single operational amplifier with high sensitivity tubes

If ultimate extra-low distortion figures are not critical and 0.01..0.1% at full power is acceptable, then, as suggested in section 12, a single quality op-amp, e.g., OPA828 can be used. The tubes must be of high transconductance "high sensitivity type", so that the op-amp could drive them. The best of class is Russian 6П15П with 12W maximum plate dissipation, Gm = 15mA/V and Vg1 cut-off voltage of only -7V (Vg2 = 150V). Obviously, the smaller the drive voltage, the less absolute distortion voltage will be referred to the error amplifier input. Other good tubes are 6CH6, EL84 and some less powerful as 6AG7 (6П9), 6M5, ECL86 or even more exotic N78. In any case, it is desirable to run the valve at somewhat elevated plate voltage and reduced screen voltage in order to reduce cut-off voltage. If more output power is needed, several tubes can be connected in parallel. In this case, to equalise current sharing between them, they need to be matched and/or have individual cathode resistors. The later will degenerate transconductance and nullify the whole low drive advantage of the high Gm tubes. Therefore, these cathode equalisation resistors should be shunted by capacitors, as commonly done with self-bias. The larger the cathode resistors, the more bias will be applied by the conventional self-bias and less will need to be emulated. Taking this approach to the extreme, the whole bias can be made automatic with no emulation, thus the small current sensing resistor R7, as well as R6 (Fig. 13) can be omitted, as shown in Fig. 40.

                   Fig. 40. Parallel connection of the output power tubes with self-bias.

Operational amplifier A1 maintains zero DC bias at its output, as all the biasing is automatic. Each tube has its own grid stopper (R8, R9) to be soldered physically close to the sockets, as well as grid current limiter (R12C5, R13C6). The tubes run at the maximum plate voltage and reduced screen voltage. Cathode capacitors C7, C8 require special attention. Huge values, reaching thousands microfarad (as seen in some designs) are not only stressful for the tubes (during warm-up), but in this case will be detrimental in respect of low-frequency transients. Time constants shall be nowhere near the crossover frequency (refer to section 10). At the crossover frequency, which is typically of the order of fractions of Hertz, these capacitors shall be virtually ineffective -- not to introduce an undesirable phase advance. Otherwise, risk of getting a dip (Fig. 12) and undulations increases. Therefore C7, C8 must be reasonably sized -- 47...220uF -- so that at the lowest audio frequency (20Hz) their impedance is about 20...50% of 1/Gm. Also they should be shunted by 1uF ceramic capacitors (not shown in Fig. 40).

 

17.2. Cascaded error amplifier

To drive lower sensitivity output tubes, an additional amplifier is required, similar to Fig. 27. It should be able to provide enough voltage swing up to 50...60Vpp, slew rate of at least 20V/us, little phase lag around the loop unity fain frequency Fo = 2...10MHz and provide a zero at Fc = 0.25...1MHz (Fig. 28). A simple common base gain stage solution is suggested in Fig. 41.

                      Fig. 41. Common base driver stage with pull-down load resistor.

As large output swing is no longer needed from the op-amp, a faster and lower voltage one can be selected, e.g., AD8033 with GBW as high as 80MHz. Zener ZD1 (slightly biased to breakdown in order to avoid slew rate distortion due to charging its capacitance) and diode D1 are added to limit negative grid voltage excursions and protect the tube. Quiescent bias of 1...1.5mA for Q1 is usually sufficient to achieve adequate slew rate. Capacitor C1 with R3 and R4, effectively connected in parallel for AC, provides integration effect to form a required zero at Fc (at about 600kHz in this example). The larger Fc -- the higher is the loop gain and lesser distortion, but the higher the risk of conditional instability. At the frequencies above Fc, collector and base of Q1 are virtually linked together via C1, and Q1 introduces negligible phase shift. This also helps under overload conditions -- such amplifier softly recovers from overloading and does not fall into continuous oscillation.

Further improvement of this topology is illustrated by Fig. 41.

           Fig. 42. Common base driver stage with a current source and additional pole.

A current source ZD2Q2 instead of a pull-down resistor R2 and an additional pole-zero pair C2R5, helps increase gain of the transistor stage alone to above 45dB at 20kHz. Hence the loop gain of the whole hybrid amplifier amounts to 95dB at 20kHz, and even more at lower audio frequences. Surely, such strong feedback can keep THD well below noise level.

A minor inconvenience of the circuits in Fig. 41 and Fig. 42, which can not outweigh advantages of efficiency, stability and simplicity, is that choice of operational amplifiers is quite narrow. It must have very high bandwidth, low noise, small offset, small input current (JFET or CMOS) and low noise. AD8033 is probably the best, followed by OPA828.

Overload indication is possible by taking signal from the output of A1 to a window comparator, similar as to what shown in Fig. 44, but with larger window, as under normal operation, AC voltage at A1 output may reach hundreds of millivolts.

 

17.3. Error amplifier with parallel channel

In this configuration, a fast, high slew rate stage A2 (Fig. 43) does the bulk of amplification work.

            Fig. 43. Error amplifier with a parallel low frequency channel.

Amplifier A2 is not a precision amplifier though and is not suitable for adequate bias emulation. Therefore at an additional precision amplifier A1 assists A2 in the audio range and DC. (Such approach is not new and dates back to the era of chopper-stabilised amplifiers.) A1 and A2 are not just cascaded or daisy-chained as in Fig. 27, 30, 41, 42, but work in parallel, as A2 input is connected directly to the input summing junction "F". Obviously, A1 does not contribute to the overall gain above its unity gain frequency Fo1, but below Fo1 amplifiers A1 and A2 are effectively cascaded with their gains multiplied. In other words, unity gain frequency of A1 becomes a corner (zero) frequency Fc (Fig. 28). As a result, very high loop gain and extremely low distortion may be achieved in audio range.

For stability reasons Fc shall not be too high, typically under 1MHz. The "problem" is that these days it is almost impossible to get a commercial JFET or CMOS precision low noise operational amplifier with such low unity gain frequency. All the manufacturers are competing and striving to make unity gain of their products as high as possible. Operational amplifiers with external compensation, like an old LM301, where you can set any required unity gain bandwidth by an external capacitor, are not common either. Modern extra low current CMOS op-amps do have bandwidth in the required range, but they are too noisy for quality audio. As a result, most likely one can get an operational amplifier with Fo1 higher than required.

Reducing bandwidth by applying integration (Fig. 43B) is not a good idea, as R1 adds noise and effectively shunts the summing junction "F", reducing loop gain for A2. It is far more practical to introduce a resistive divider R1R2 at the output of A1 (Fig. 43C) to deliberately reduce its gain and Fo1. Even further, capacitor C1 turns gain degeneration on from above 70kHz, creating an additional pole-zero pair at 70kHz / 300kHz respectively, while in the audio range A1 operates at full gain thus maximising the system loop gain.

An example of practical implementation is shown in Fig. 44.

  Fig. 44. Error amplifier with parallel low frequency channel, "pole knocking" and overload indication.

High speed main gain stage uses a differential pair Q2Q3 with a current mirror Q4Q5. Its gain typically is above 20000, gain bandwidth and slew rate being proportional to bias current. Assuming total input capacitance of an output tube, wiring and collector junction capacitances of Q3 and Q5 is about 30pF, bias current of about 1.5mA can reach 20V/us, which is sufficient for driving almost any power tube. Under these conditions, gain-bandwidth of the stage will be about 250MHz, which is more than enough. Gain denerating resistor R10 can be inserted to reduce the excessive gain (in case high frequency oscillations occur). Note that increasing of the bias current (in attempt to further rise the slew rate) is not recommended, as DC gain can be adversely affected by thermal processes in the transistors and Early effect. Low capacitance "video" transistors, like BF420 / BF421 can be used in this and other similar circuits.

Voltage shifting dividers R5R4C3 and R11R12C5 are requred to keep Q3 away from saturation, even if the tube occasinlly runs into mild grid current operation (class A2). Since Q3 operates virtually in common base configuration in respect of high frequency signal, impedance in its base circuit shall be kept low, which explains an emitter follower Q6.

Input source follower based on a quality high transconductance JFET Q1 is obviously required to ensure no loading of the summing junction "F".

Parallel channel gain reduction divider R3R15C6 operates as described in respect of Fig. 43, reducing unity gain frequency of A1 from 3MHz to about 700kHz. Diode limiter D1D2 deserve a special explanation. It is so called "pole-knocking" circuit, preventing hard oscillation condition in a conditionally (un)stable system. Under overload condition, the diodes clamp the error correction voltage developed by A1 at Q6 base to about 100...200mV (considering attenuation of the divider R3R15), while voltage at the summing junction "F", applied to the main gain stage can be substantially higher than that. Thus, the slow, phase lagging op-amp A1 gets effectively taken out of the loop, and the main wideband agile stage is left to look after overload recovery process. In other words, the diode limiter "knocks out" poles, rather than zeros, from the transfer function.

This topolgy lends itself to overload indication. Under normal operation, due to high gain of the main stage, A1 output AC voltage is quite small -- literally a few millivolts. During overload, large spikes manifest at A1 output, which trigger a window comparator A2, which discharges C2, turns Q7 and consequently, the indication LED LED1 ON. Relatively large relaxation time constant R7C2 extends LED ON time, so that even shortest, overload event will not go unnoticed.

 

17.4. Error amplifier with local feedback

In this approach (Fig. 45), preamp A1 is cascaded with the main gain stage, but the later provides current negative feedback around the tube only, turning the tube into a linear ("ideal") voltage controlled current source with mutual conductance of 1/R7 (45mA/V in this example).

                 Fig. 45. Linearising of power output tube by a local negative feedback.

Due to extremeny high gain of Q1-Q4 configuration (typically above 10000) and current recycling via C7 (as explained in section 5), such "super tube" becomes linear -- from voltage input at "D" to current output at "A" -- to 0.01%. Global negative feedback by op-amp A1 further reduces distortion, thus making it practically unmeasurable. As the gain stage here is subject to common mode, its "long-tail" current supply should be stable, and it is taken from a high voltage source via a large R4. Divider R9R11 allows several volts of headroom for Q4. A simpler single-ended stage, similar to Fig. 42, can work in this topology too.

Several design guidelines must be taken into consideration.

Firstly, you may have noticed that the local feedback current sensing resistor R7 in this circuit is larger than in other implementations. This is important in order to maintain sufficient bandwidth of the local feedback -- at least 3...4 times wider than the overall global feedback. In respect of the local loop, the valve represents a cathode follower with a small gain, which equals R7 * Gm. So to keep this gain high enough, it is recommended to choose a larger R7. On the other hand, R7 should be as low as possible to reduce output voltage swing and slew rate requirements for the op-amp A1. As a trade-off, R7 can be chosen as follows:

R7 = (0.1...0.2) / Gm,                                                                (8)

where Gm is mutual conductance of the tube.

Under these conditions, the voltage controlled current source transfer function will remain "flat" up to 15...20MHz and at the same time AC voltage at "C" and "D" will be small enough -- a few volts maybe.

Secondly, voltage gain from "D" to "H" at high frequencies (around Fo) shall be slightly under unity. In other words

R3 = (0.5...0.8) * R7.                                                                 (9)

Obviously, in this case

Fo = (0.5...0.8) * Fo1,                                                                (10)

where Fo1 -- gain-bandwidth product of A1.

Keeping Fo slightly below Fo1 is recommended for stability, as phase lag of an operational amplifier is guaranteed to behave well below its unity gain frequency. It is reasonable to select Fo = 3...8MHz, so any JFET low noise op-amp with gain-bandwidth Fo1 of about 4...10MHz will work fine as A1. JFET operational amplifiers with such bandwidth are quite common. If a faster op-amp is to be employed as A1 (such as AD8033 with GBW = 80MHz), then the bandwidth can be degenerated to the requred Fo1 by an optional R5C5 circuit. In this case complying with (9) and (10) becomes particularly important to ensure open loop gain goes below 0dB above Fo.  Table 2 summarises a typical line-up of the relevant frequencies.

Description	Relevant components	Frequency	Notes
HF crossover	R2, C2	20...50kHz
HF "corner", Fc	R3, C4	250...500kHz	Refer to section 12.
Global NFB unity gain, Fo	A1, R5, C5, Gm, R7	3...8MHz
GBW of A1 stage, Fo1	A1, R5, C5	4...10MHz
Local NFB unity gain	R4, Cgk, Gm, R7	20...25MHz	Long tail current through R4 has effect.
Main gain stage	R4, Cgk	150...200MHz	Cgk includes collector capacitances of Q2, Q4.

                   Table 2. Typical frequencies order for the nested feedback topology.

Given that A1 output voltage swing is relatively large (about 2...4V) compared to Fig. 42 (100mV) or Fig. 44 (5...10mV), op-amp A1 shall be specified for audio applications, otherwise a generic slow op-amp might itself create even more distortion than the linearised power stage. Operational amplifiers OPA1678, OPA604, MUSES03 and similar ones are the good candidates.

Secondly, under overload condition, A1 does not take direct control over driving the tube (unlike in Fig. 41, 42 where the gain stage is bypassed by a capacitor or T-bridge). Therefore, as there is no inherent "pole knocking" feature in this circuit, adding any extra pole-zero pairs in the global feedback would not be possible. However, they are unlikely to be needed, as the distortion is already negligible.

Thirdly, it is not so easy to arrange overload protection indication, as signal at "D" is quite large under normal conditions, and a window comparator thresholds would have to be accurately adjusted.

Note that (for this and all other error amplifier implementations) it is not advisable to take overload detection signal straight from the summing junction "F", as it might be susceptible to noise injection and "back door" stray distortion penetration (compare section 3).

Lastly, in Fig. 45 the local feedback does a great job linearising the power tube as a current source, but, unlike in the other topologies, does not encompass the output transformer and the load (speaker). Only the global feedback is in position to compensate distortion in the transformer and the load, but since the global feedback is weaker, it is less efficient in this respect. Ramifications of that as well as function of R13 and C8, shown in red in Fig. 45, will be covered later.

 

17.5. Comparison and discussion

Table 3 gives a summary of the loop gain performance for the topologies outlined above. It is assumed that sensitivity (input voltage to reach full power output) of a hypothetical amplifier is 350mV (500mV amplitude). Loop gain values are estimated at 20kHz, which is a worst case, and distortion products at 20kHz are not audible anyway. At 1kHz loop gain would be at least 26 dB higher, and distortion lower.

Reference	Comments	Loop gain at 20kHz	Advantages / Drawbacks
Fig. 40	6П15П, OPA828	43dB	Simplest, high distortion (0.15% @ 20kHz), requires high-Gm low cut-off tubes.
Fig. 41	EL34, AD8033	72dB	Simple, limited op-amp choice.
Fig. 42	EL34, AD8033	89dB	Simple. limited op-amp choice.
Fig. 44	GU-50 (ГУ-50), TL081	89dB	Easy overload indication, complexity, limited op-amp choice.
Fig. 45	EL34, OPA1678 (Fo1 = 5MHz)	Local = 64dB, Global = 33dB, Total = 97dB	Highest gain, complexity, inconvenient overload indication, limited suppression of load nonlinearity.

                  Table 3. Loop gain comparison, advantages and disadvantages.

Looking at the table 2, it is difficult to find an absolute winner. Each topology has its own cons and pros. For a simple low power amplifier, perhaps a simple single op-amp topology (Fig. 40) could be recommended. For high power amplifiers, simplicity of Fig. 42 circuit seems appealing. Circuit in Fig. 44 would be more suited for driving lower sensitivity tubes, like GU-50 or 807, due to the four-transistor high balanced slew rate push-pull driver stages with the current mirror. In reality, even with the rectangular input signal to the amplifier, slew rate limitating never occurs in any of the above described topologies, as the crossover capacitor (C2 in Fig. 16, 17, 22, 25, 26, 30, 36, 38, 39, 45) naturally limits the slew rate, turning rectangular input into triangular output waveforn. A few decibels variation in loop gain is of little significance either, as with the loop gain of the order of 90dB, distortion is inaudible anyway. Thus, both topologies -- Fig. 44 and Fig. 44 -- are equally strong candidates for a zero-distortion amplifier.

 

17.6. Nested feedback topology advantages

The circuit in Fig. 45 with nested feedback deserves special discussion. The output tube is well linearised by 64dB local feedback to perfection, while the load and the transformer are under a weaker global feedback, 33dB in this example. Therefore, load nonlinearity is not compensated so well as in other topologies. Or in other words, output impedance of this circuit is not so close to zero. Nonlinearity of the load will result in both voltage and current slightly distorted. However, it is debatable whether it is a problem or a benefit.

For example, mechanical non-linearity of a speaker translates into its electrical impedance non-linearity. If we supply undistorted voltage to a speaker, then the current will be distorted, and vice versa. Which is better? Possibly, clean speaker voltage is better than clean current, as current distortion might be a result of self compensation of the magnetic field non-unifirmity, but this is not a definitive answer. What if "pushing hard" the voltage makes mechanical distortion even more harsh and audible? Taking this situation to the extreme -- is it better to power a speaker from a zero impedance voltage source or from an infinite impedance current source. Everyone knows that, to damp mechanical resonance, at low frequencies it is far better to feed a speaker from a zero impedance voltage source. But the answer is not so straightforward for midrange and highs. It might be that the best is to drive a speaker from a source with active impedance so that electro-mechanical resonances and "ringing" in the drivers and crossover filters are damped better.

Answers to the above questions might be subjective and heavily depend on the particular speakers used. Experimentation with output impedance and listening tests will give the best useful answers. And the circuit in Fig. 45 perfectly lends itself to such experiments. By changing the global loop gain in A1 stage, output impedance of the whole amplifier can be controlled, while at the same time the amplifier itself will remain almost distortionless due to a profound linearisation of the output tube by the local feedback. "Almost" means that the transformer distortions are not ironed out together with the valve, but compounded with the speaker distortion. However, magnetics related transformer distortions at high frequencies are relatively small, most likely smaller than those of a speaker driver which has a solid steel core.

Circuit R13C8, marked red in Fig. 45, can be used to control A1 feedback. R13 reduces the global loop gain at mid and high frequencies, while C8 ensures the feedback is still strong enough (and output impedance is low enough) as low bass -- to damp mechanical resonance of a speaker and suppress magnetisation non-linearity related distortion of the transformer. These components might be made adjustable or switchable for experimentation and listening tests. For example, with R13 = 10K, as shown in Fig. 45, global loop gain is about 6dB. With 6dB of global feedback and the tube itself acting as a current source, output impedance would approximately equal the nominal speaker specification (usually either 4 or 8 Ohms, depending on a transformer tapping.) Therefore with 6dB global feedback, the amplifier will be "half way" between being a voltage source and a current source. At low frequencies a speaker will be driven from a low impedance voltage source, while in midrange and treble it will be effectively driven trough a 8 (or 4) Ohm series resistor. Again, it is not clear how that will affect sonic perception. If a speaker is a full-range single driver, then it can be speculated that midrange (where speaker impedance is the lowest) would be subdued, while bass and highs would be emphasised and perhaps sound brighter. It might benefit instrumental music, but not necessarily the vocals. With mutlti-range speakers the answer is not predictable at all, as the crossover filters design will mostly affect the outcome.

The author of this article has not experimented himself with feedback depth effect on sound coloration for this nested feedback topology. I suppose not many people have ventured in this field, as most of the amplifiers have quite low output impedance by design. Therefore it is left for an enthusiast to play with it, rersearch and perhaps open a new page of science (or call it "witchcraft" if you wish) -- something like "Sound coloration control by frequency dependent amplifier output impedance"... 

 

18. Output power optimisation

Power tubes in the extra-heavy feedback amplifiers can be driven virtually all the way from cut-off to saturation, as distortion becomes a non issue. Thus output power before clipping is 30...50% higher compared to a conventional class A amplifier. Three parameters, namely: (a) current cut-off, (b) control grid current, (c) plate current saturation set limits to maximum output power. Observation of control grid wave form near clipping is a convenient way of optimising plate load and tube quiescent operating point. To get maximum output power, it is desirable that all three or at least two limiting conditions are reached at the same time. Otherwise, potential of the tube will not be fully utilised. Three following pictures illustrate the concept.

Fig. 46. Control grid voltage waveform -- plate load resistance is low, early cut-off.

In Fig. 46 negative grid voltage excursions are exaggerated and pointy, which indicates that the tube is very close to cut-off. At the same time, positive lobes are nicely shaped and are nowhere near zero volts level. The picture suggests that the tube has plenty of unused room for the plate current increasing, but no margin for the plate current decreasing. Thus the tube is not fully utilised. To improve the situation, one could:

- increase quiescent plate current and reduce plate voltage supply, if possible, keeping, of course, within permissible plate dissipation and transformer DC current rating;

-  increase plate load by selecting a lower tap of the transformer or connecting a speaker with higher impedance.

 

Fig. 47. Control grid voltage waveform -- plate load resistance is too high, early plate current saturation.

The situation in Fig. 47 is opposite -- the tube is far from cut-off, but the positive peaks of grid voltage are enraged, indicating that the feedback is struggling to squeeze a required peak plate current from the tube. The tube is underused in respect of current. Apparently, plate voltage becomes too low at the peaks (probably down to 40...50V), and the plate current saturates as the electron flow returns to the screen grid. It is unhealthy for the tube, as screen grid dissipation rises. As a side note, scren grid dropping resistors (R1 in Fig. 8, R8 in Fig. 10, 13, 14, R12 in Fig. 45) are not only there for screen grid current recycling, but for the screen grid protection as well. Obviously, plate load impedance is too high. To correct the problem, one could:

- decrease quiescent plate current and increase plate voltage supply, if possible, keeping, of course, within permissible plate dissipation and transformer DC current rating;

-  lower plate load by selecting a higher tap of the transformer or connecting a speaker with lower impedance.

Finally, Fig. 48 illustrates optimum load matching.

Fig. 48. Control grid voltage waveform -- optimum plate load resistance, cut-off and saturation are reached together.

Here, stretching of both positive and negative lobes of the waveform is reached at the same time -- the tube is being exercised all the way from cut-off to saturation, delivering maximum output and still low distortion, due to heavy feedback. For example, 6L6G clone tube with 300V plate supply and 20W quiescent plate dissipation can produce 8.5W of clean audio, while in a conventional amplifier it would have delivered 6.5W at 10...15% distortion. Positive grid voltage peaks in Fig. 48 reach only about --4V, not zero. It is not a problem, just an indication that screen grid voltage is a bit higher than necessary, or that the tube is running in a "light duty" mode at a bit lower current.

Note that if optimum matching (as in Fig. 48) is not possible with a given speaker and given transformer taps, of if maximum power output is not absolutely required, then it is better to lean towards excessive plate load impedance situation (Fig. 47), rather than low plate impedance (Fig. 46). Using a lower tap of the transformer secondary and higher speaker impedance will reduce leakage inductance related distortion (discussed in section 13).

 

19. Noise and hum

Noise and hum have always been enemies of audio amplifiers. Never, even in the most tubey amplifiers, such features as "soft velvet hum", "soothing static with gentle crackling" or "silver-bell microphonics" can be presented as advantages. Designers struggle relentlessly to eliminate or minimise such artefacts.

In the hybrid amplifiers discussed in this article, static (Nyquist) noise is easy to control (refer to section 11). Use as small as possible input resistor (R1 in most of the drawings) and a low-noise JFET operational amplifier. R1 of 4.7...10K would produce about 9...12nV/SQTR(Hz) and with another 10nV/SQRT(Hz) from the op-amp, which add up "geometrically", in a "root of sum of squares" fashion, overall noise can be around 15nV/SQRT(Hz). This is can not be considered "ultra-low" noise, but quite acceptable.

Hum is more diffucult and subtle, as there are various sources, such as:

a) Stray capacitive coupling to AC voltages (poor shielding);

b) Voltage ripple on power supply rails;

c) AC and/or ripple currents flowing through analog or signal ground;

d) Magnetically induced voltages from mains transformer and/or heater wiring;

e) Currents through earthing ground loops;

f) Amplitude envelope demodulation of stray RF interference.

Shielding recipe is quite common (Fig. 49) -- use screened cables for audio input, keep audio wiring and sockets away from mains and high voltage AC circuitry, heater wiring, ensure close narrow-track and compact layout of the summing junction of the front end (shown in red), use a double-sided PCB with ground plane copper under and around the summing junction net. These measures will also help against distortion penetration. To minimise external RF susceptibility (for example, from mobile phones), also shield feedback connection to prevent re-radiation of RF noise onto the sensitive front end, fit a small capacitor C5 on very short leads or soldered directly to chassis across the output, thread the speaker cable through a ferrite sleeve or wrap a turn or two over a ferrite ring. It is important to wrap both wires through the same core, as a common mode choke. Do not fit separate ferrite beads or rings on each speaker wire, as it might cause audio distortion due to magnetic nonlinearity of the ferrites.

  Fig. 49. Hum reduction measures -- shielding, screening, T-bridging of HF feedback.

Supply voltage ripple on the operational amplifier rails is not an issue, as modern op-amps have excellent power supply suppression ratio. Voltage regulation is not needed -- just simple filtering will do. Modulation of the tube plate current by plate and/or screen voltage ripple is of no consequence too, as the extra-heavy feedback would effectively eliminate all hum of that nature. Nevertheless, regulation of screen grid supply is recommended -- not to minimise hum, but rather to reduce stress on the valve during warm-up when supply voltage is typically much higher than under operation conditions.

Still there exists a certain mechanism of ripple penetration from "+B" rail straight into the summing junction -- through the HF feedback path -- divider C3C4 and then via C2. This ripple gets significantly attenuated -- by about -22dB by C3C4 and by another -47dB by R2C2, assuming that crossover frequency is 25kHz and ripple frequency is 100Hz, altogether by -69dB referred to output (speaker). For example, a 1V 100Hz ripple on "+B" bus would translate into just 350uV hum at speaker terminals. Such level of hum would be practically inaudible. For even better hum suppression, resistor R5 can be inserted (Fig. 49). This resistor shunts low frequency hum to ground, while not affecting HF feedback operation. It would add another 30dB to the supply rail ripple reduction. Note that R5 shall not be too small, otherwise it would cause appreciable phase advance at crossover frequency which might adversely affect stability.

 

19.1. Star point topology

Arrange a star point or use chassis as analog ground -- that is the question. In theory and on paper star point is better (Fig. 50). Since a star point ("S") is considered physically small and has zero impedance, then, in theory, currents flowing in or out of it shall not create any potential difference, and hence no noise or hum injection.

              Fig. 50. Star point signal ground style and external noise injection path.

Star point arrangement implies that all grounded or ground referenced circuitry, components and terminals of the amplifier, including input RCA jack and speaker terminals, are not directly connected to chassis, but connected to the star point, which in turn is linled to chassis ("G").

Such topology makes the system vulnerable to external hum and noise. If for example, there is a potential difference between a braid of an input audio lead and the earth terminal at the power point, noise/hum current will begin flowing along a path highlighted red. First of all, such current flowing on the outer shield of audio connections, will re-radiate magnetic field into the under-chassis cavity. Secondly, at each discontinuity of the shielded wiring (for example, sections "a-b", "c-d", "e-S", some portion of common mode noise will be converted into differential mode noise and will get superimposed on the input audio signal. Extermal RF interference follows the same path. Such an amplifier is likely to respond by clicks, crackling or pops to switching of heavy household loads, and by buzz and murmur to mobile phones operating in the vicinity.

To improve immunity to conducted and radiated noise, filtering should be added, as shown in Fig. 51.

                     Fig. 51. External noise filtering for star point ground configuration.

Here, the input audio connector is grounded to chassis through low-inductance bypass capacitors C1 and C2 (about 0.01uF). Solder lugs should be short and wide, C1 and C2 shall have the shortest possible leads, or soldered directly to the chassis, if practical. Ideally, C1 and C2 shall be silver plated washers made of high dielectric constant ceramic material, if such parts commercially exist at all. Similarly, speaker terminals should pass via feed-through capacitors C3, C4. As a result, high frequency noise gets dumped to chassis at the entry, before it can propagate further down the wiring. The noise current travels on the outside surface of the chassis to the earth terminal of the mains filter. No RF noise penetrates into the circuitry. Quality mains EMC suppression filter is of paramount importance in this arrangement. If the mains filter is not able to pass the chassis noise to the power cord, then the currents will try to find other ways, like through the mains transformer interwinding capacitance (Fig. 50), which will negate the benefit of filtering. To better block noise penetration, the input lead and the speaker wiring can be run through (wrapped around) ferrite cores, rings or sleeves. As mentioned above, both speaker wires shall go through the same core together.

These noise reduction measures, illustrated by Fig. 51, protect well from RF interference, but might not be able to fully eliminate audible clicks from high energy lower frequency ground loop voltage spikes, glitches and bursts, because impedance of the filtering capacitors is not that low.

Complexity of mechanical arrangement and still not the 100% cure of the noise problem leads to a question if it is worthwhile at all to rely on the star point topology. Would it not be easier to have the whole chassis as signal ground?

 

19.2. Chassis as signal/analog ground

The greatest advantage of the chassis as signal and analog ground is that all grounded terminals can be directly attached to it, and external RF noise will not penetrate under the chassis. Chassis has very low impedance, but still using as a ground return for the "dirty" AC and ripple currents should be avoided. For that purpose, noisy currents should be contained in one or several local loops. Fig. 52 is an example of that strategy.

                    Fig. 52. Chassis as analog ground with several local star points.

As shown in Fig. 52, reservoir capacitors are not randomly grounded to chassis, but are connected together with "cold" ends of the transformer windings to the respective star points. Star point S2 services high voltage rectifiers. Pulsed current, charging C1 and C3, circulates in a loop and not through the chassis. Star point S2 represents a similar arrangement for the low voltage rectifier, powering an operational amplifier and transistor circuitry. Filter/smoothing/bypass capacitors C2, C5, C6 pass only negligible ripple current, limited by filtering impedances L1, R3, R4 respectively, so these capacitors do not need to be connected to the star points. Moreover, they should be connected directly to chassis shortest way to provide low impedance bypassing for audio and megahertz frequencies. So, here is the rule: reservoir caps go to their star points, bypass/filter caps go to chassis. Needless to say, valve heaters are supplies by twisted wiring, not using chassis as a return. Thus the chassis becomes both a signal ground as well as analog ground for circulating DC and audio AC currents related to the amplification process. Physically these star points are just solder lugs screwed to chassis somewhere not far from the power transformer.

Star point S3 represents one speaker terminal physically bolted onto chassis. Active speaker terminal remains the only possible back door for RF interference penetration, so a feed-through capacitor C4 and optional common mode ferrite ring might be used, but not overly critical in a typical EMC-benign environment. If the secondary has several taps, all connections should run through the same ring. Power transformer T1 has some capacitance Cw between its primary windings and the screen winding (layer). Therefore, star point S4 is made to return the AC capacitive noise current to its origin -- mains. So, it is reasonable to use an earth lug of the filter or its mounting screw as star point S4.

The above measures easily render the chassis equipotential in respect of conducted hum and radiated noise, but still there lurks a subtle and dangerous enemy -- magnetic field of the power transformer.

 

19.3. Power transformer magnetic field related hum

Magnetic (leakage inductance) field radiated by the power transformer can induce hum voltages on the wiring and on the chassis directly. The former can be mitigated by placing front end circuitry away from the transformer. The field perpendicular to the chassis is strongly attenuated by the Eddy currents in the chassis and poses little problem. A tangential component of the field can be diverted by using a steel chassis. To further mitigate its influence, sensitive circuitry should be wired in a single plane parallel to the chassis and close to it, in a PCB-like manner, with the wiring "creeping" on the underside chassis surface, rather than making messy "3D" point-to-point connections.

Eddy currents do a good useful job in repelling magnetic field from the underchassis area, but they may pose their own problem. When Eddy currents circulate in a uniform sheet of conductive material, they do not create potential difference across the sheet as such, as both electromotive force and voltage drop inside the material are uniformly distributed. However, if there is any disturbance, discontinuity or non-uniformity in the way of the Eddy current flow -- such as cutouts, holes for valve sockets, joints, patches, etc, -- a potential difference will develop across these "anomalies" and can create groung hum voltage between say RCA audio input connectors and a grounding point of the amplifier front end. To minimise negative effects of the leakage magnetic field, the transformer preferably should be mounted on brackets, without any cutouts, fully above the chassis with the bobbin axis parallel to the chassis (Fig. 53A). If a more common aesthetically appealing mounting (which does require a cutout) is intended, then the transformer should be elevated above the chassis by spacers or stack of nuts (Fig. 53B) -- to minimise protrusion of the windings and field leakage under the chassis.

Fig. 53. (A) Preferred transformer mounting above the chassis, and (B) acceptable -- transformer raised.

The way how power transformer is fitted to chassis is important too. Fig. 54 shows schematically a side view / cross section of a typical transformer installation, similar to Fig. 53B.

  Fig. 54. Installation of a power transformer with insulated mounting screws.

One can easily realise that mounting screws together with top cover plate form a loose single turn, magnetically coupled to the windings. Such turn works in effect as a secondary winding, developing about 150mV of  AC hum between bolt A and bolt B. If such transformer is directly bolted to chassis, then this AC hum voltage will be transfered to the chassis, particularly if the chassis is made of low conductivity material, such as stainless steel. The cutout under the transformer does not help either, further increasing chassis resistance between the mounting bolts. From there the hum voltage spreads all over the chassis and the chassis can no longer be a considered clean equipotential signal reference.

The problem is easily fixed though by insulating all mounting screws, except for one, from the chassis. Thus the single turn loop will be open, and no current will flow through the chassis between the screw. One grounded screw will still provide electrical earthing of the transformer iron for safety and for dumping capacitively coupled noise. Insulation fixtures -- washer(s) and a  bush -- are shown in green in Fig. 54. Heat-shrink tubing over the screw shank and a couple of nylon washers can do the job. It might be practical to insulate all four screws and use a solder lug to ground only one of them to star point S4 (Fig. 52). Transformer mounting on insulation can be recommended for Fig. 53A case as well -- just in case, to prevent loop current conduction from the transformer mounting brackets to chassis.

 

19.4. Rectifier noise

There exists a belief that a vacuum tube rectifier "sounds better" than silicon diodes. Well, rectifier does not sound at all as it is not involved in amplification. However, is is true that a tube full wave rectifier generates less noise. Due to high "internal resistance", softer and smoother turn-on/turn-off, current through a vacuum tube results in smoother, wider and lower amplitude peaks, less high harmonics and no ringing on current cut-off, compared to what happens with a "hard" solid-state diodes. Softer rectifier current translates into softer transformer winding current and consequently milder leakage inductance flux "splashes" around the power transformer, less magnetic radiation onto the chassis and wiring -- in a word, less hum and buzz. A price to pay for a tube rectifier is well known -- large voltage drop and power wasted into heat. From this logic it follows that the larger voltage drop a rectifier tube has, the better it sounds. For example, an old fashioned 5Z3P (5Ц3С) or 274 tube can be expected to "sound better" than much more advanced and efficient low impedance indirectly heated rectifier GZ34 (5AR4).

The above conclusion about sonic superiority of tube rectifiers applies only to crude and primitive DIY-style tube amplifiers, abundant on the market, where hum reduction design rules are neglected. In a well designed amplifier with all discussed above star point, filtering, shielding and transformer grounding precautions, rectifier noise will not be an issue, and solid state rectifiers are recommended. The best is a diode bridge, as such solution results in a better copper/window utilisation in the transformer, higher efficiency, smaller size and less weight. Traditionally, power transformers for tube amplifiers have a center-tapped high voltage winding. In this case, silicon diodes rated at double DC voltage can also be used. However, adequately rated resistors in series with the diodes (R1 and R2 in Fig. 52) or a bridge rectifier are still recommended. Notwithstanding some voltage drop, they will somewhat relieve the transformer by stretching current pulses and reducing dissipation in the transformer. They will also limit in-rush current. To reduce reverse voltage stress on the diodes, it is better to have two individual resistors instead of one common. Further, by adjusting these resistors it is possible to balance the legs of the rectifier, as typically two halves of the winding have different resistances. Shunting the diodes by high voltage 0.01uF capacitors, as common in the radio receivers, will not hurt, but not necessary, as modulation hum is not applicable to audio amplifiers.

 

19.5. Ground loop hum and earthing

In most of the countries exposed metal parts of electric household appliances and devices must be earthed for safety through the earth wire of a power point. This applies to a valve amplifier with metal chassis as well. If star points of several items of audio equipment are directly connected to earth, then the heavy duty earth connections might overpower the audio leads with slimsy screens in acting as signal ground. It is no problem, unless any AC hum voltage is induced, conductively or magnetically, onto the earth wires of the power cords. In the later case, weak audio lead screens might not be able to maintain zero potential between the grounds of the respective pieces of audio equipment and hum will be audible.

To minimise this adverse effect, all the equipment should be plugged by closely bundled together power cords into a single power extension board, which in turn is to be connected by a single cord to a power point. Audio leads shall also be as short as practical and have decent shields with generous amount of copper braiding. Such measures would minimise the area of ground loops and therefore reduce unduced voltages from any magnetic source, such as power transformers of the same equipment. Layout of power cords might need to be empirically optimised for minimum hum.

The above measures will not work, if any piece of incorrectly designed equipment itself generates some AC hum voltage between the earth and signal ground (chassis). It might be caused by conducted emission from the transformer, as explained in section 19.3. Then all the equipment chain will get polluted with hum. In this case the only remedy is to separate signal ground from earth (chassis). In the case of a star point topology (Fig. 50, 51) it can be done by inserting a 10...33 Ohm resistor paralleled by 0.01uF capacitor between points "S" and "G". The noisy earth loop will be practically broken, as resistance of the audio lead shield is far less than the said 10...33R resistor.

However if the whole chassis serves as signal/analog ground, this method is not applicable. The only thing left to do is to disconnect the whole chassis from the earth. In this case the mains suppression filter, including its mounting fixtures, shall be disconnected and isolated from the chassis. In the alternative, the filter can be omitted or substituted by a pair of capacitors (Fig. 55).

       Fig. 55. Diode safety protection if chassis is not earthed.

Now, since the mains circuit becomes open to electromagnetic interference, it should be separated extremely well from the signal circuitry. Of course, the primary side of the power transformer now will be fully open to extermal interference. To minimise noise propagation under the chassis, it is reasonable to lay the primary side wiring, including power ON/OFF switch on the top side of the chassis. The best power transformer to use would be a transformer with split bobbin (Fig. 56A) or separate primary and secondary bobbins (Fig. 56B).

 

Fig. 56. Examples of high-isolation transformers: (A, left) -- split bobbin; (B, right) -- separate bobbins (R-core).

With such high isolation transformer, earthing of the chassis is not really needed, as the risk of electrical breakdown is negligible, and parasitic capacitance between primary and secondary side is small -- hence very low AC current conducted to chassis. For example, in pre-perestroika Soviet Union household wiring did not have any earth conductor at all, all the equipment used to have transformers with good isolation, and there were no issues.

If the power transformer to be used is more "conventional", like in Fig. 19B or Fig. 53B, particularly if obtained from an obscure source, then it is still recommended to provide protection by way of reverse parallel diodes between chassis and earth (Fig. 55). In normal operation, voltage between the chassis and earth is small, below turn on knee of the diodes, and the diodes do not conduct, breaking possible ground loops. In a very unlikely case of a short between active mains conductor and chassis, the diodes will go into conduction limiting chassis-to-earth voltage for safety of a user. Heavy duty three-phase rectifier modules, well suited for D1, can handle surges of hundreds of amperes -- more than enough to trip a hosehold circuit breaker or earth leakage current safety device. Resistor R1 reduces chassis-to-earth hum voltage due to some residual AC leakage through the transformer and helps avoid unpleasant crackling and buzzing sounds while plugging and unplugging input audio lead. Capacitor C3, which should be soldered closely across the diode bridge terminals, is there to shunt possible RF interference from local radio stations, so that the diode protection module does not turn into a "crystal radio" AM detector.

It is recommended, if possible to fit the diode protection circuit to an amplifier, but provide a replaceable link "C-E-D" (Fig. 55), so that the amplifier could work with hard earthing, diode protection or with floating chassis. Ti will be possible then, in a real setup, in situ, select an option which would give acceptable hum results and level of safety.

More explanation is needed in regards to transformer core and screen layer grounding (links "E-S", "C-L" in Fig. 55). Conventionally both are connected to chassis, which is earthed -- no questions. But if the chassis is isolated from earth, is it better to connect the transformer body and a screen winding layer (or foil) to the chassis or to the earth? Unfortunately, there is no definite answer -- it should be determined empirically. Consider Fig. 57.

  Fig. 57. Interwinding capacitance and AC capacitive leakage current testing.

Each winding has certain distributed capacitance to the screen or to the core, which can be emulated by a couple of lumped capacitors from each end of the winding to the screen or core respectively. These capacitors are shown in red in Fig. 57. The values of the stray capacitances depend on the transformer construction, insulation material and thickness, etc. and are not known. Besides, different windings have different voltages with different phases, so capacitive currents differ in amplitude and direction -- some add, some subtract and partially cancel each other. If, for example, secondary winding with its higher voltages creates more capacitive leakage AC hum current to the screen, than the screen should be connected to the secondary side, that is to the chassis, and vice versa. But it is impossible to predict theoretically which side of the transformer -- primary or secondary -- would generate more capacitive leakage hum AC currents.

Therefore, before wiring an amplifier up, the following transformer test is recommended (Fig. 57). Secondary winding terminals are connected together to a virtual "chassis" side as they are to be connected. A current sensing resistor of about 100R...1K is fitted between the earth and the chassis node. Primary side is powered from the mains. And with an oscilloscope or an AC millivoltmeter, voltage across R1 is measured which will be proportional to the capacitive leakage current. Then -- exercising extreme care! -- screen and core of the transformer are tried to be connected either to the earth side or chassis side or is left unconnected. Then the above is to be repeated with the primary winding polarity reversed. All combinations and permutations are to be tried aiming to find a configuration which would give the lowest voltage reading across R1. Thus, the best in terms of AC leakage configuration should be recreated when installing this transformer in a real amplifier by setting links "E-S", "C-L" and phasing the primary winding accordingly (Fig. 55).

Instead of performing the above test before assembing the amplifier, it can be done after. Enable the diode protection (Fig. 55) using its R1 as a current sensing element, connect audio input of the amplifier to earth (to earth, not chassis!), and simply listen to the hum through the speakers. Then again, try all combinations of hooking up the screen and core of the transformer to earth, chassis or leaving unconnected, and repeat with the opposite primary polarity, find the combination which gives the least hum.

 

20. Examples of the ultra-low distortion amplifiers implementation

Chassis side photos of  a couple of the hybrid ultra-low distortion amplifier samples are shown in Fig. 58 and Fig. 59.

 Fig. 58. Bottom view of a hybrid amplifier. Output -- GU-50, rectifier -- 1.2kV silicon diodes.

 

 Fig. 59. Bottom view of hybrid amplifier: output -- EL34, rectifier -- 5Z3P.

Both versions of the amplifier are built on a generic "DIY style" chassis and components readily available on the market. Power transformer, output transformers and a choke are identical -- of the same type as shown in Fig. 19B.

One example (Fig. 58) uses GU-50 output tubes, a parallel channel type of the error amplifier (similar to Fig. 44 with selected on test TL081B operational amplifiers) and direct connection of the audio transformer secondary to the output terminals. It can handle up to 0.1uF of pure capacitive load.

The other example (Fig. 59) is based on EL34 tubes, cascaded error amplifier (Fig. 42), has a phase corrector at the output, allowing up to 0.8uF of pure capacitive load. The phase corrector components can be seen mounted on the tag strip. This version also have foil pads under the covers of the output transformers (section 13, Fig. 24).

Both amplifiers have screen grid voltage regulators based on high voltage Zener diodes and MOSFETs. Error amplifiers with their respective voltage rectifiers and filters are laid out on small PCBs. The parallel channel version PCB (Fig. 58) is more involved, as it requires a bipolar supply voltages. Both PCBs include overload indication comparators, indicator LEDs are located next to the octal valve sockets (which were originally intended for 6SL7 tubes, but are vacant in this hybrid amplifier).

Chassis is used as analog/signal ground and it is earthed directly -- for simplicity.

Frequency response is quite flat with --0.2dB fall at 20Hz and --0.5dB fall at 20kHz.

Harmonic distortion was difficult to measure. A quick test on "Audio Precision" instrument, close to clipping, with 80kHz bandwidth, resulted in a flat reading of 0.004%...0.005%, rising to 0.008% at 20Hz and to 0.006% at 15...20kHz. The former is obviously due to low frequency loop gain loss and output transformer magnetisation non-linearity, the later is caused by the leakage inductance non-linearity of the output transformer (section 13), as during these tests the transformer was not fitted with the foil pads. The bulk of 0.005% is AC hum from the ground loop and chassis exposure to the power transformer magnetic field. (Differential pick-up was not used in this test.) Thus, signal-to-noise+THD+hum was recorded at about 86dB all across the audio range.

More distortion tests were performed with a separate audio oscillator and distortion meter HP8903A. The oscillator used was quite basic with a bulb amplitude stabilisation, so it iself was capable of 0.003% above 10kHz. At lower frequencies, its signal distortion was higher due to temperature modulation of the bulb filament. Distortion measurement at 10kHz with 400Hz low cut-off filter and aluminium foil padded transformer read the same 0.004% with no load, and with a 8 Ohm load showed a marginal increase to 0.005% due to the leakage inductance residual non-liearity and some accentuation of the harmonics coming from the test oscillator. Again, the bulk of the figure is residual hum and white noise.

These results indicate that actual distortion created by the amplifier itself, particularly in the audible range, is smaller than 0.003%, particularly at mid-range (1...5kHz). In effect, these tests measured mostly noise, hum and distortion of the test oscillaror, rather than harmonics of the amplifier under test. It is reasonable to assume that distortion is extra-low by design, by virtue of super-strong feedback. It equals to 20...30% (section 2, Fig. 2) divided by the loop gain.

Even at the clipping level, distortion below 0.003% is insignificant and not audible. At more realistic lower comfortable listening levels, distortion virtually disappears, due to single-ended class A operation, unlike in transistor push-pull amplifiers, where relative THD remains constant or even increases at low level.

Output impedance of this amplifier has not been measured. It is very low (by design) at mid-range, but creeps up with frequency, reaching fractions of an Ohm or perhaps about one Ohm or so at 20kHz. It has an inductive component (no surprise) and (surprisingly!) some negative resistance at high frequencies above 10kHz -- connecting an active load results in a slight increase (!) of the output voltage. Magnitude of this effect depends on the output transformer and phase corrector used (section 13), but generally the effect is within 0.5dB magnitude.

 

21. CONCLUSION

Prior to publishing of this article (in 2020), the concept of extra-deep feedback, extra-low distortion tube amplifier design has not been explored. At least, the author of this article in not aware of any references to similar undertakings. Firstly, heavy feedback is commonly considered impossible to implement due to transformer phase shift. Secondly, it was considered impractical, as solid-state linear and even switch-mode (class D) amplifiers, using modern bipolar transistors and MOSFETs, with thoughtful design, could achieve very low distortion, providing flat response, wide bandwidth, low noise and high power -- and at a reasonable cost. Most importantly, extra-low distortion has never been a goal for the tube amplifiers. Instead, obsessive efforts are directed towards trying various circuits and tubes of various makes and brands in attempt finding the "sweetest" combination, giving "fantastic" sound" which "only valves can produce". Mild second order distortion is believed to make the sound "better".

Some hybrid amplifiers are known though. Usually they contain a tube front end, which is believed to create that fantastic tubey mild distortion and sound colouration with push-pull transformerless solid state output -- to get decent power at manageable weight. However, such hybrid topology is not free from crossover distortion in the solid-state output stages.

In comparison, the hybris amplifier concept presented in this article, is different. It aims at getting extra-low distortion by extra-heavy deefback, which made possible due to bypassing of the outupt transformer -- the root of all evil -- at infra-low and ultrasonic frequencies. That method allowed to turn an unstable system into a robust conditionally stable one.

This amplifier does not belong to a "tube" amplifier category, but rather to a transistorised electronics only with a valve as a final power device. This amplifier is more like a reference amplifier -- low noise, low distortion, clear transparent sound, no sound coloration -- nothing added, nothing taken away. Due to the feedback, performance of both channels in a stereo amplifier is completely identical -- no need of matching the tubes, let alone worrying about the brands, black plates versus grey plates, shape of the getters and the like nonsense.

The main difference when compared to common solid-state amplifiers is that it uses single-ended class A output and current recycling (section 5) which minimises "back door" distortion leakage (section 3). Single-ended class A is the only topology which ensures a guaranteed monotonic THD reduction with the output level decreasing (section 4). This is the crucial distinction of this amplifier compared to the solid-state ones, most of which utilise push-pull power stages, and distortion might remain constant or even rise at low levels. Another difference is higher output impedance at high frequencies, compared to a solid-state device.

Formal listening tests have not been performed on this amplifier, so it is not clear if it sounds better, worse or just "different", compared to a reference amplifier. The author of this article compared its sound to a quality solid-state device in an ordinary room setting, and did not perceive any difference. The sound was excellent -- clear and transparent -- as expected. However, a trained and experienced expert listener might well register some difference, consciously or subconsciously. Particularly interesting is frequency dependent output impedance with negative component -- perfect speaker dampling at bass and more loose and even enhancing effect on treble. Such effects have never been "listened into", as none of the common amplifiers possess such a feature.

So it might happen, that this amplifier sonically outperforms a reference solid-state device. On the other hand, it is quite possible that no difference is perceived. (In this respect, the author agrees with the opinion expressed in another article "Why tubes sound better".) Then, why bother with this tricky and relatively low power design? All in all, the answers to these questions are yet to be obtained...

A topology variation with a local feedback (section 17.4) provides a platform for experimentation with frequency dependent output impedance -- to find out whether it affects sonic perception. Currently, output impedance is either extremely low (of the transistor amplifiers) or, on the other extreme, is quite large (valve triode amplifiers without feedback). The topology described in this article can combine both features making output impedance very low at low frequencies and medium at mid-highs.

 

Having read (or skimmed) the article to the end, a disappointed reader might ask: "Where is the full schematic and PCB files?". Well, they are not published, and it is for a reason. This amplifier is not a crude two or three valve technology of the 1940's. It is rather a "delicate", high-precision analogue device, which requires a certain level of radio engineering and particularly analogue "culture" and expertise to build. Lots of clues, techniques, explanations are offered in this article to allow a person more or less skillful in the art to successfully undertake the project. For example, a qualified person would know how to design a PCB properly, would be aware of the temperature modulation related distortion and would be able to choose quality adequately rated feedback resistors. A qualified person would certainly fill in some common bits and pieces missing in the article, such as voltage regulators and power supply. Also, a qualified person would be able to sensibly and purposefully experiment with the device.

However, if a schematics were made available, but a hobbyist lacks skills and/or knowledge, it could result in failures, or substandard disappointing performance.

The ideal solution would be to design and offer a simple kit with a populated PCB and cleas assembly instructions. Once it is available, a notice will be placed in the article.

In the meantime, through the contact page of this site, the author could provide assistance to those who venture on replicating the "zero-distortion" hybrid amplifier. The author would appreciate comments and feedback in respect of the article, language, presentation, typos, etc., as well feedback on the performance of such amplifiers and listening experience. 

Good luck!