Audio amplifier output stage comparison and optimization

Abstract

In this article I compare some audio amplifier output stage configurations with each other based on Spice simulation. The most common output stages are emitter follower output stages, either as dual or triple emitter follower configurations. Diamond buffer output stages are used in operational amplifiers and headphone amplifiers a lot, but I have not seen this circuit used for power amplifiers often and wonder why.

I tend to swim against the (main-) stream and this is why not following the trend of using a simple emitter follower output stage seems appealing to me. The diamond buffer arrangement has some benefits in theory, which seem worth exploring. This is why I compare the dual and triple emitter follower output stages with variants of diamond buffers.

I follow an iterative approach investigating and optimizing the different output stages by stepping various parameters and observe the effect on circuit performance.

Circuit simulation is only a crude approximation and results depend on model accuracy a lot. This means that the investigation here is somewhat fictional, but may help to observe some trends and gain a better understanding nonetheless.

Definitions and abbreviations

There is some confusing terminology around some of the output stage configurations discussed in this article.

What I refer as folded (pre-) driver is that a PNP type transistor is used to drive the positive part of the next stage. The folded (pre-) driver works against a current source. The (pre-) drivers collector can then either be connected to the opposite power supply rail or be connected to the output node of the next stage, which bootstraps the folded driver stage.

Folded configurations are commonly also referred to as diamond buffers.

A dual emitter follower with folded drivers is a diamond buffer and a triple emitter follower with folded pre-drivers is a diamond buffered triple. In theory, it would be possible to also fold the drivers in a triple emitter follower, but this is not discussed here.

Some abbreviations that may be used in this article:

  • EF2 = dual emitter follower
  • EF3 = triple emitter follower
  • diamond buffer = dual emitter follower with folded drivers
  • DBT = diamond buffered triple emitter follower = triple emitter follower with folded pre-drivers

Scope of the investigation

The first four investigations focus on the effect of the input shunt network applied to following output stage configurations:

  • dual emitter follower
  • triple emitter follower
  • dual emitter follower with folded drivers
  • triple emitter follower with folded pre-drivers

Further investigation covers:

  • improvement of the dual emitter follower with folded drivers performance and stability
  • improvement of the triple emitter follower stability
  • improvement of the triple emitter follower with folded pre-drivers performance and stability

Output stages schematics

All output stages are set up with roughly 100mA standing current in the driver stage and 1A in each power transistor. I case of triples, the pre-driver idle current is 10mA. Given a +/- 30V supply, this results in a powerful class A output stage for 8Ω loads. The purpose of class A operated output stages for this investigation is to exclude any crossover distortion that would appear in output stages biased into class AB, but this also hides generation of crossover distortion. Performance in class AB operation is an entirely different topic.

Note: The schematics do not include a model of the components interconnections, like small inductors representing component terminals and wiring inductance. A simulation setup without any real life interconnection elements like inductors would make the investigations even more unrealistic. I set up two different schematics in simulation: One with ideal interconnections and one that has some small inductors added for a more realistic simulation setup. The inductors vary between 10nH and 40nH and are my estimate for a tight, but realistic component placement assuming 10nH/cm inductance. In reality, the situation would be far more complex with coupled inductance and also stray capacitance between connections, but this would be difficult to model and the model also depends on the exact physical arrangement of components and connections a lot.

Note that the complimentary bias spreaders might cause excessive DC voltage drift in reality when being connected the way I did it for simulation.

Analysis setup

Series resistance of the input voltage source for the stability analysis is stepped with 10Ω, 100Ω, 1kΩ and 10kΩ to see how this affects stability and performance of the output stages. It may happen that the voltage amplification stages output impedance varies with frequency or other parameters. While stepping the input impedance up to 10kΩ is somewhat unrealistic, this exaggerates the results and helps to see trends far outside the usual range. Sometimes plots for higher impedance may be omitted for increased clarity. In any case, plots for 10Ω and 100Ω are present with higher impedance plots missing.

Note that the shunt compensation network at the input is far from perfect, but illustrates the effect. In order to optimize compensation, the voltage source impedance needs to be considered. All output stages have the same input shunt compensation network applied.

There are two simulation setups for each output stages: One with ideal connections and components and another more realistic one with some inductance of the interconnection and capacitors that have reasonable ESR and ESL.

The square wave signal level or the simulation is 25V, which is close to the 30V power supply rails. Transistors CBC increases dramatically at lower VBC so this large signal analysis better illustrates real life conditions. On the other hand side, overshoot is clipped by the power supply rails and appears lower. With the overshoot causing clipping, behavior of recovery from clipping can be observed as well. At the end of the square wave test pattern, where the signal returns to zero Volt, the actual overshoot can be observed without being limited by clipping.

Dual emitter follower

schematic

The dual emitter follower is simple and reliable. Current gain is rather low so the voltage amplification is heavily loaded, which results in higher distortion. A VBE multiplier is required to sense and adjust both the driver and the power transistors temperature. In some cases it might be feasible to run the driver transistors on small separate radiators and sense the driver transistor temperature individually or not at all.

AC analysis

square wave response

conclusion

The dual emitter follower shows only slight gain peaking in the AC analysis, which is considerably higher with the more realistic setup. Square wave response shows overshoot and slight ringing with source impedance up to 100Ω. The shunt network at the input has only negligible effect on both AC and square wave response.

I would have expected the dual emitter follower to be more stable, but the situation might be different with a more commonly found class AB bias.

Triple emitter follower

schematic

The triple emitter follower has much higher current gain than a dual emitter follower, but AC behavior and DC operating point are very difficult to stabilize. The VBE multiplier needs to compensate thermal drift of all three emitter followers. My guess is that the DC bias operating point of this arrangement is very difficult to stabilize.

AC analysis

square wave response

conclusion

The triple emitter follower is outright unstable without the input shunt network. This is all too obvious from both AC and square wave response. In the AC response, very high gain peaks at any source impedance together with abrupt loss of phase margin indicate terrible stability, which is confirmed by sustained oscillation following square wave excitation.

The input shunt network shows a lot of stabilization in both the AC and square wave response. The ringing following the square wave edges is dampened, but pronounced overshoot remains.

Dual emitter follower with folded drivers

schematic

The dual emitter follower with folded driver seems very elegant because the driver transistors compensate the DC bias of the power transistors. Both driver and power transistors need to be on the same radiator. With the driver transistors connected bootstrapped to the ouput node like shown here, the driver transistors VCE is very low and almost constant, which results in keeping all VCE dependent parameters of the transistors nearly constant as well. Apart from the extra set of constant current sources, the design is rather minimalist.

The DC bias of the dual emitter follower diamond buffer is set by the driver transistors emitter series resistors an / or the driver transistors base series resistors. Using cascoded current sources, the cascode transistors can be put on the main radiator without affecting the CCS current. This arrangement is unsuitable for setting the typical class AB operation bias current. This driver only works with the power transistors being run in class A operation.

My experience with this output stage configuration in reality is that bias current seems pretty stable.

AC analysis

square wave response

conclusion

From the AC response of the ideal circuit, it appears as if the dual emitter follower with folded drivers was pretty stable both without and also with the input shunt network. The situation looks entirely different once a bare minimum of interconnection inductance is added to the setup. Now the gain peaks grow considerably while the phase margin drops to the bottom.

Addition of the input shunt network perfectly stabilizes the Ac response of the ideal setup, but not the more realistic one.

The square wave response reveals misbehavior beyond what could be assumed by the AC response. Not only are rise and fall time surprisingly long, but the output signal also shows a strong tendency to stick at the supply voltage rails after clipping by overshoot. The more realistic setup furthermore shows sustained ringing.

An interesting detail here is the shape of the ringing: The ringing has more triangular shape than sinusoid.

The wave forms indicate that this arrangement is inherently unstable and different mechanisms need to be addressed in order to achieve acceptable performance and stability. Improvement is discussed in a different investigation later on.

Triple emitter follower with folded pre-drivers

schematic

The main advantage of the diamond buffered triple over the standard triple emitter follower is that the pre-diver and driver transistors thermal drift cancel each other with those devices being thermally connected to each other. The VBE multiplier only needs to track the thermal drift of the power transistors.

According to my experience, DC bias seems to be stable in reality with bias set for class AB operation.

Another advantage is that the pre-drivers VCE is very low and held nearly constant, which reduces all kinds of VCE related nonlinearity. The constant CBC presents a predictable load to the voltage amplification stage during signal excursions near the power supply rails, where the CBC of an emitter follower would rise dramatically. This may help lowering distortion and increasing slew rate in theory.

AC analysis

square wave response

conclusion

The triple emitter follower output stage shows even more instability than the normal triple emitter follower. This is evident from both the AC response with gain peaks up to 30dB and sustained ringing in the square wave plots.

The input shunt network, that has showed good effect with the triple emitter follower, seems not to improve anything here. The waveforms with the network in place even look worse. The nice sinusoidal ringing is gone and replaced by highly distorted triangular waves. This is a similarity with the dual emitter follower using folded drivers investigated earlier. Also, the sticking to the rails observed with the folded dual emitter follower is present here with the triple. Both seem to suffer from the same mechanisms that cause sticking to the rails and abnormal ringing with triangular shape.

Dual emitter follower with folded drivers improvement

As shown earlier, the dual emitter follower with folded drivers has inherent shortcomings, that need to be addressed. Both AC and square wave response are worse than the normal dual emitter follower. Below schematic shows some worthwhile improvements:

schematic

The resistor between the output node and the joined collectors of the driver transistor suppresses HF feedback bewteen the two stages. The mechanism here is exactly the same like with the diamond buffered triple, where two such resistors are required. The additional filter capacitor may be used, but seems not necessary. The effect of the filter resistor is that the sustained ringing on top of the square waves observed earlier is eliminated.

The large capacitor between the drivers emitters enables push-pull operation of the driver stage. This partially overcomes the current limit of the driver stage and thus allows faster operation. The effect is steeper slopes in the square wave response.

AC analysis

square wave response

conclusion

The Ac response has not changed and this was also not expected. The square waves show much faster fall time now, without overshoot or sticking to the power supply rails. At higher source impedance there is still a hint of the ugly ringing, but with reasonably low source impedance, the square waves look nice.

Triple emitter follower improvement

While the triple emitter follower is praised for excellent performance all the time, almost nobody really explains how to stabilize this beast. The diamond buffered triple has far worse stability issues than the normal triple emitter follower. As shown before, some shunt compensation at the input of the output stage does improve the situation, but there is further room for improvement.

Since shunt compensation ahead of the first stage has helped, it is somewhat obvious to apply this to the second stage as well. Here, it is advisable to shunt to the collector instead since this also mitigates the base-collector capacitance, which is dependent on VCB. So this R-C shunt to the collector both acts as a snubber to reduce any ringing of CCB and both swamps CCB, which makes the behavior more predictable. This is one of the main factors to get the triple emitter follower more stable on paper. In many designs, the series resistor is omitted, but I believe that the loss introduced by the resistor is an advantage. If the series resistor of the snubber is too large, this defeats the purpose of the shunts. A value of 10Ω seems just right.

Adding shunt compensation ahead of the driver stage comes with a serious drawback: The output stage is no longer capable to reproduce proper square waves. This can be remedied by putting a speedup capacitor between the pre-drivers emitters. This capacitors now allows push-pull operation of the pre-drivers, which enables quick charge removal from the shunt capacitors. The speedup capacitor needs to be larger than the shunt capacitors by some orders of magnitude.

Also, R-C low pass filters between the power transistors and the (pre-) driver transistors seem a very good idea to avoid feedback through the power supply rails.

Adding some small R-C shunts to the power transistors from base to collector seem to helpful taming local resonance by transistors base to collector capacitance and interconnection inductance. The schematiuc of the triple emitter follower with folded pre-drivers shows such snubbers at the power transistors.

schematic

AC analysis

square wave response

conclusion

Increasing the shunt capacitors at the driver transistors lowers the gain peak in the AC analysis. This effect is far less evident once interconnection inductance is added for the more realistic simulation. The gain peak at 9MHz is persistent regardless of the shunt capacitors value. With the capacitor increased to 3nF, a gain dip in the lower MHz range can be observed, but the gain peak at 9MHz remains. This shows that the 9MHz gain peak cannot be entirely eradicated by the driver shunt capacitance in reality. A value of more than 1n5 does not seem to improve stability, but cuts into performance instead.

The square wave response shows overshoot regardless of the driver shunt capacitors size. The overshoot look better controlled than with any driver shunt capacitance, but still indicates some instability.

There is still need for further improvement. Maybe the lazy omission of the small snubber networks for the power transistors makes a difference, but on the other hand side the improved triple emitter follower with folded drivers has those in place and also shows this gain peak which cannot be removed by the drivers shunt capacitors. Since the gain peak is persistent in the more realistic setup only, the unavoidable interconnection inductance is involved in establishing the peak and this would need to be addressed in a different way.

Diamond buffered triple EF improvement

improved schematic

Below is an example of a diamond buffered triple emitter follower with some improvements added:

An important part of the improvement is the addition of two 100Ω resistors added in series with each pre-drivers collector in order to suppress feedback from the drivers via base to collector capacitance of the pre-drivers. Those resistors are usually not shown in any schematic, with rare exceptions. Those resistors are essential to stabilize the diamond buffer arrangement unless CBC of the pre-drivers is very low.

Further additions in the improved schematic are shunts from the drivers base to the drivers collector terminals. They have the same purpose like shown for the improved triple emitter follower: Control the gain peak of the output stage at high frequency. The effect of the capacitors value stepped from 470pF to 1n5 is shown in the AC analysis.

The speedup capacitor allows push-pull operation of the pre-drivers and allow fast charge removal from the shunt capacitors at the drivers base.

Another addition to the schematic are small shunt networks from each power transistors base to collector terminal (47pF and 100Ω in the schematic). The idea behind is the same like for the shunts at the driver transistors base. However, they do not seem to have much effect and probably require further tweaking to become effective. The base to collector capacitance of the MJL3281A may reach up to 6nF at V>sub>BC of 2V and the MJL1302A even reaches 9nF. With four transistors in parallel, this is a massive capacitance to deal with.

Looking at the step response of a R-L-C filter with R=2R2, L=50nH and C=9nF, Q is 1.1 and the step response shows overshoot. With L=100nH, Q becomes 1.5 and overshoot increases in magnitude. Corner frequency of this low pass filter is only slightly above 5MHz. 50nH equals 50mm of wire and 100nH equals 100mm likewise, which is well within the range of realistic PCB design. My experience is that the snubber required to tame R-L-C resonant networks may be substantial. Probably the snubbers capacitance would need to be increased and the snubbers resistance to be decreased. This may tame the resonance, but also slows down the output stage.

AC response

square wave response

interim conclusion

Plots for 1kΩ and 10kΩ output impedance of the signal source driving the output stage were omitted, both because this is pretty unrealistic and also because the plots look ridiculous and distract from the more realistic plots. Note that the plots for high impedance feeding the triple emitter follower output stage look much better. The improvements added to the DBT do not suffice to improve the DBT enough.

Stability and performance strongly depend on the output impedance of the voltage amplification feeding the DBT. Performance is only acceptable for lowest source impedance and stability gets worse with lower source impedance in turn. This is further aggrieved by increasing the shunt capacitance at the drivers base.

Increasing the shunt capacitor ahead of the driver transistors lowers the gain peak in the frequency response and also reduces overshoot and ringing in the time domain. However, even 3nF of capacitance cannot fully stabilize the DBT once real world interconnection inductance is added. The gain peak at roughly 8MHz is flattened considerably by the shunt capacitor at the driver base to driver collector, but this is far less evident in the more realistic setup.

From AC analysis point of view, it appears feasible to slightly increase the source impedance in order to find a balance between performance and stability. With 3nF shunts for the drivers, the BDT discussed here is already pretty slow and this does not seem a good way forward. Since the output impedance of the signal source forms a low pass filter with the input shunt capacitor, this is just pre-filtering.

According to my experinece in reality so far, the DBT OPS is borderline stable when built like shown on the schematic and driver shunt capacitors of 3nF, which is far higher than I'm comfortable with.

perfect schematic

Since all improvement achieved so far did not yield satisfactory performance and stability, I focused on the last stage of the triple, the power emitter follower. I added provisions for snubbers here on my PCBs and installed 100Ω and 47pF. Both values were inspired by Bob Cordell's HexFET output stage and he claims that the addition enables to use lower gate series resistance and still have a stable output stage. I did not question the exact component values and just added them as placeholders hoping they would do more good than harm.

The detail simulation of the power emitter follower stage showed that the snubbers are useless for my BJT output stage with the component values copied from the HexFET design.

Once I investigated the power emitter follower on its own, I found out that those snubbers are very useful for removing the gain peak that was still there after all iterations so far. As expected, the shunt resistor needs to be lower and the shunt capacitor needs to be higher. I came to the conclusion that 33Ω and 1nF are a good balance. In turn, the driver shunt capacitors can be reduced to 1nF. This sharpens the corners of the square wave response a bit. For more safety margin, 1n5 capacitors are more than sufficient.

Increasing the shunt capacitors in the power transistor stage causes issues with slew rate and brings a tendency to stick to the rails on clipping as observed earlier with the shunt capacitors for the drivers. The solution is the same again: A small speedup capacitor across the emitter resistor.

perfect AC response

For the Ac analysis, thesetup was: Signal output impedance is held constant at 10Ω, the driver shunt resistor is 1nF, the power transistor shunt resistor is 33Ω and shunt capacitor stepped 50pF, 500pF, 1nF, 1n5 and 3nF.

By increasing the size of the power transistors shunt capacitor, the gain peak can be flattened until the gain curve shows no peak anymore, but a smooth roll-off. The phase penalty of large capacitors is not too dramatic, but I would prefer to keep the capacitance as low as possible.

perfect square wave response

For the square wave response, the same setup was used like for the AC analysis: Signal output impedance is held constant at 10Ω, the driver shunt resistor is 1nF, the power transistor shunt resistor is 33Ω and shunt capacitor stepped 50pF, 500pF, 1nF, 1n5 and 3nF.

Surprisingly, the power transistors shunt capacitors size does not show much effect on the rise and fall time of the square wave response. Overshoot and ringing is well controlled.

final conclusion

The missing link was the shunt network for the power transistors. Once this is optimized, the diamond buffered triple seems to perform very well.

Emitter follower stability in general

Here is what I know, learned and collected during my research:

Once the signal approaches the supply rails, the transistors CBC increases dramatically. This substantially changes the behavior of the transistor and presents a very different load to the previous stage. In emitter follower applications, the CBE is bootstrapped by the output node and is of less concern.

In output stages biased into class AB, the current through the transistors changes with signal amplitude and rises once the signal swings closer to the power supply rails. This may cause transistors FT to drop.

Wiring inductance easily forms oscillator circuits with parasitic transistors capacitance. Resistors help to spoil the Q-factor and this is one reason why series resistors at the base (or gate) are important. However, for BJTs, the base resistor should not be larger than ten times the emitter resistor value.

Emitter followers are destabilized by any capacitive loading at the output. This is why there is an inductor at the output of any serious amplifier: To mitigate capacitive loading of the output stage.

Emitter followers output impedance increases with frequency, but they don't like to be driven by a high impedance. Thus, chaining emitter follower stages inherently leads to problems.

Also, the output resistance of the voltage amplification that feeds the signal into the output stage may vary with frequency and other factors. This is why I stepped the output resistance of this stage in simulation to see how stable the output stages are when being driven with varying input resistance.

Emitter follower stages are impedance converters. A single emitter follower turns resistive input impedance to inductive output impedance. A dual emitter follower turns the resistive input impedance to inductive2, which is unstable. Placing a capacitor at the input converts the input impedance to capacitive and returns the output impedance to inductive1.

The input shunt network to ground ahead of each output stage configuration thus gyrates the input and output impedance of the first emitter follower and therefore helps to stabilize the dual emitter follower output stages as a whole. For a triple, the attained stabilization is not enough.

Placing a R-C snubber to ground at the output of the preceding voltage amplification stage is good practice in any case since the snubber establishes a reliable load at HF, which helps to stabilize the voltage amplification stage. Typical values of this snubber are 100pF and 10Ω to roughly 100Ω. Together with the varying output impedance of the voltage amplification stage, a low pass filter is formed. This low pass filter limits the bandwidth fed into the output stage, rolling off high frequencies that might excite oscillation. This in turn also means that the output stage bandwidth is restricted by the voltage amplification stage output impedance.

The previously shown stabilization of the triple emitter follower was achieved by slowing down the second stage by adding base to collector capacitance that works in conjunction with the base series resistance. Another way would be to slow down the last stage (by selecting slow transistors for example) and in turn speed up the second stage by paralleling multiple fast transistors, for example like the SC3503 / SA14381 pair instead of the rather slow MJE15032 / MJE15033 pair.

Diamond buffer stability in detail

I experienced difficult to explain stability problems with the diamond buffered triple emitter follower that I built. One of the symptoms was a roughly 200kHz oscillation with triangular shape. This frequency and wave form is unusual for local instability of an output stage and is also uncommon for global feedback loop instability. I did some research and found an interesting discussion on the DIY Audio forum started by Alan, who observed pretty similar instability like I did. Here is the discussion about the unstable diamond triple emitter follower on the DIY Audio forum.

Alan's theory is that there is a positive feedback loop between the pre-driver and driver transistors due to the pre-drivers collectors being connected to the emiters of the driver transistors. The feedback path seems largely influenced by the pre-drivers base to collector capacitance. So in order to minimize this feedback path, pre-drivers with low CBC should be used.

It seems helpful to add resistors with roughly 100Ω in series with the pre-driver transistors collectors to reduce the feedback.

Note that this is true regardless of whether the output stage is a dual emitter follower with folded drivers or a triple emitter follower with folded pre-drivers.

One way to completely cure the issue is to connect the pre-drivers collectors to the opposite supply voltage rails instead of the next EF stage emitters. This unfortunately also removes the bootstrapping of the pre-drivers, which I see as one of the possible major advantages of the diamond arrangement.

According to my own experience, the resistor breaking the feedback is effective when applied to the dual emitter follower, but not effective in the diamond buffered triple. In case of the triple, this even shows in simulation. Nonetheless, it is good practice to include the filter resistors. The exact root cause of the problem is unknown to me and dependent on the actual setup, it may even work with the filter resistors in place.

While the weird oscillation showed in some plots of the simulation earlier, the instability becomes most obvious once the output stages are placed inside the negative feedback loop of the amplifier.

Below are some oscilloscope screenshots of an amplifier built from modules of my modular audio amplifier system. The diamond buffered triple was included in the negative feedback loop of the Cordell style front end, which features feedback Baker clamps and adaptive clipping references to prevent saturation of all stages with any power supply voltage. The output stage with bootstrapped pre-drivers even had the filter resistors in series with the collectors installed, which unfortunately did not show any effect in this setup. The screenshots were taken at 20kHz and different levels of overdrive.

pre-drivers bootstrapped light clipping

pre-drivers rail connected light clipping

pre-drivers bootstrapped heavy clipping

pre-drivers rail connected heavy clipping

Ferrites

Ferrite beads may be an option to further stabilize any output stage if the correct type is chosen and placed at the correct location.

Spice models and specification

The Spice model of a ferrite is simply an inductor with parallel resistance, parallel capacitance and series resistance. Certainly, this is a simplification that excludes a lot of effects a real ferrite has. For example, saturation is not modeled. However, here are the component values of the Würth ferrites used for the investigation:

Parameter 74276031 74276051 7427605 7427606
Inductance [nH] 420 580 990 1200
Parallel resistance [Ω] 80 105 135 130
Series resistance [Ω] 0.003 0.005 0.005 0.005
Parallel capacitance [pF] 0.01 0.01 0.05 0.01

Below are some plots of afore mentioned ferrite beads. The ferrites used for this investigation are WE-WAFB from Würth Elektronik. The plos are derived from REDEXPERT. I find those ferrites especially useful because they roughly have the form factor of low power THT resistors and fit the 10mm pitch I use for such resistors. For serial connection, small ferrite beads may be put around the base series resistor instead.

DC saturation

In general, ferrites saturate quickly once DC current is applied so collector and emitter of the power transistors are probably both poor locations to put ferrites in. If base to collector R-C snubbers are used, the ferrite beads should either be placed in series or in parallel with the base resistor in order not to counteract the snubbers, else the ferrite bead may also be put on the transistor terminal directly. The effect of the snubbers stabilizing the emitter follower is so positive that I would at least add provisions in any case.

The Würth tool REDEXPERT allows to apply DC current to the ferrites to see how that impacts the impedance. Else, this should be scope of every good datasheet.

Location

Placing ferrites in series with the driver transistors base seems a very bad location. A good location for ferrites in amplifier output stages seems to be in series with the power transistors base stopper resistor. Even better would be to place the ferrite bead in parallel with a larger value base resistor of maybe 10Ω. This has two advantages: First, the parallel connection ensures low Q of this network. Second, at DC, the base series resistor in almost zero and thus allows better DC bias current sharing of the power transistors.

For MOSFET output stages, I would prefer to put the fettite bead in series with the gate resistor and chose a ferrite with high impedance.

Simulation

Note that only the single emitter follower consisting of the power transistors is investigated here. The results apply to any configuration. Below are some plots showing AC and step response with some ferrite beads in parallel with 10Ω resistors. The base to collector snubber networks consisting of 33Ω and 1nF are also installed.

AC analysis

The effect of the ferrite is to lower the gain peak and drag it to lower frequency. Phase is almost unaffected, which is a bit surprising since the added inductance is substantial. So from small signal AC point of view, the ferrites do no harm.

square wave response

For the square wave response, the single emitter follower was driven with a voltage source with only 1Ω output impedance.

The overshoot and subsequent ringing is reduced by the ferrites with the high inductance ones showing more pronounced effect, but also slower decline of the overshoot. Rise and fall time is almost unaffected. With the ferrites connected in series with the base resistor, the ferrite would affect the rise time. Also, ringing may increase with a series connected ferrite instead in some configurations.

Experience

When I first experimented with ferrites, I put a pair of Würth Elektronik WE-TOF 742701121 in between my diamond driver module and the BJT power transistors module and notices that this greatly reduced the faint ringing I still had after all the improvements detailed in this article. This lead to the conclusion that ferrites may be useful for stabilizing amplifier output stages and I started a more detailed investigation regarding ferrites.

Next I experimented with putting small Kemet B-20L-48B-L in series with the 2R2 base series resistors, but this did not yield considerable improvement. The Kemet ferrite may be somewhat close to the 74276031 from Würth Elektronik.

According to simulation, a parallel connection of ferrite and resistor is the most promising solution.

While the effect of the ferrites in simulation is not very dramatic, the real world effects are likely there. Pending validation on the bench.

Conclusion

Ferrites do have a place in audio and one of the possible applications is stabilization of the output stage. While it is true that ferrites are highly non-linear, so are semiconductors. So combating one nonlinearity with another seems a promising approach. I need to further experiment with my free samples from Würth Elektronik to come to a perfect solution and final conclusions.

Distortion

Assessing distortion in simulation is difficult due to unrealistic transistor models, but the result is probalby good enough for a rough comparison. Below table shows distortion at 1kHz near clipping at 30V supply rails with 8Ω resistor load:

Input resistance Dual emitter follower Triple emitter follower Two stage Diamond buffer Three stage Diamond buffer
10Ω 0.002% 0.002% 0.006% 0.002%
100Ω 0.004% 0.002% 0.008% 0.005%
1kΩ 0.025% 0.003% 0.028% 0.002%
10kΩ 0.194% 0.009% 0.173% 0.005%

Note that the data presented here is based on an outdated simulation setup and the distortion analysis needs to be updated for more current results.

However, it is obvious that the triple stage output stages performance is mostly independent from input resistance while the two stage OPS shows a strong dependence. At 10kΩ input resistance, which is an extremely unrealistic case, this goes so far that visible attenuation of the two stage OPS output signal can be observed. This also shows that the input impedance of the three stage OPS is much higher, which is expected.

Conclusion of the simulation results

Comparing the classic dual end triple emitter followers with their equivalents featuring folded driver stages, it becomes clear that the electrical behaviour of the classic circuitry is much better and easier to optimize.

In real world applications, the configurations with folded drivers have much simplified thermal design that in case of a dual EF may either be stable without a VBE multiplier, or in case of a triple, has the benefit that two transistor junctions temperature coefficients cancel each other and only one junction needs compensation by a VBE multiplier. My experience with this is pretty encouraging so far.

The triple emitter follower OPS offer more performance than the dual while showing a lot of potential stability issues. In theory, the diamond buffer arrangement should have improved electrical performance, but this does not show in simulation. I assume that the transistors models used for the investigation are not accurate enough to show this. Lack of modeling the VBC dependent nonlinearity may be the reason that simulation results look better than the results in reality.

When optimizing electrical stability, There is a trade-off between performance and stability. The more stable, the slower the output stages become. A slower output stage included in the global negative feedback loop of an amplifier will in turn require the loop compensation to be adjusted in order to keep the amplifier stable.

All output stages perform best when being driven by a low impedance source. Whether the voltage amplification stage can deliver a constant and predictable output impedance, is another matter. The output impedance is a function of frequency in any case and other factors may have an influence as well.

I had a bias when starting the investigation that there must be something magic and superior to the diamond buffer configuration. The name alone implies something precious. While diamond buffers indeed have compelling properties like improved thermal stability, they also suffer from inherent issues with this topology that need to be addressed and are more challenging to stabilize. Being confronted with those issues in reality was surprising for me and it was difficult to find solutions because it seems that this is not widely known or discussed.

Once I actually built a dual emitter follower OPS with folded drivers and a triple with folded pre-drivers, I noticed stability issues that seemed unlikely to stem from global feedback and went back to simulation in order to isolate the root cause. Together with some research, I found solutions that are not new, but obviously not well known. Apart from not encountering folded drivers too often in schematics of power amplifiers, I did not see the extra components mandatory for stability anywhere in textbooks so far with Bob Cordell's book as exception, where the R-C low pass filter for the dual emitter follower with folded drivers is presented, but the effect not explained in detail.

Another conclusion from simulation is how important it is to include elements of the real assembly like small inductors and ESR / ESL of capacitors. In idealized setups, everything looks much more stable than it likely is in reality. Simulation deviates from reality due to unrealistic component models anyway and omitting even more elements found in reality leads to even further deviation. The effect of real world interconnection elements on performance can be very dramatic, which shows in many plots presented in this investigation.

Performance in reality

I actually built two output stage configurations discussed here, namely the diamond buffer and a diamond buffered triple output stage. Apart from the results shared in this investigation, I discuss detailed conclusions in the respective articles about the driver modules of those output stage configurations:

Folded driver

4x BJT OPS

Diamond driver

4x BJT OPS

References

There is an article on Wikipedia explaining some basics about the diamond buffer.

The basics about output stages are explained in books about amplifier design like from Douglas Self and Bob Cordell. However, none of the books I own answer all of my question in satisfying detail. I found some good bits on the DIY Audio forum, which made me start this investigation. This article also collects and connects some of the knowledge that is scattered on the DIY Audio forum. Probably the most useful website about triple emitter follower stability is the one about the YAP output stage, which is part of the YAP power amplifier project.

John Broskie writes about diamond buffers and improvement of the basic topology in his mighty diamonds article. I find this very helpful.

Samuel Groner briefly mentioned the triple emitter follower with folded pre-drivers in his comments about Douglas Self's amplifier design handbook on page 51.