Zero Phase margin but high stability, mystery or miracle?

[Kokoriantz]

This is my ultimate linear amplifier before I switch to class abD. I wanted it to be simplest possible with less than 10° phase shift at 20khz in open loop, class AB but no crossover distortion, double zero in THD. I came up with this circuit, 2 stage MOSFET amplifier. It has 125khz open loop bandwidth with 55db loop gain.
I simulated with Tina and Ltspice with in built models for Tina and Cordell models with Ltspice. In both I have same response but different adjustments. Both models get crossover cleaned at 200ma bias without degenerating sources. As the graph shows it has zero PM, idem in Tina. As this is transconductance output, the gain increases by current by over 6 folds, this makes the graph meaningless. This why I worked by square wave transients as it reflects better the stability at different output currents. And the transients are excellent despite the must oscillating feedback.
On Tina I show the transient of 15Vp 10khz start without input RC, if any oscillation exist, it shows clearly, and there is non. How this is possible? again an illusion?       

[mawyatt]

Your signal injection point isn't in the correct place, its shown shunt across the output. Usually in simulations you place the floating voltage source in series with the feedback path (eliminated the need for decoupling) and measure the voltage on either side of the voltage source to ground reference and then take the ratio for the Open Loop Response.

From the transient response looks as if you have a well damped amplifier, with plenty of gain and phase margin.

Best,

[mag_therm]

For the large value ( < 1 uF) electrolytics in signal and bypass, it would be useful to include
capacitor loss angle ( tan delta) or "esr" and series inductance ( from self resonant frequency or "srf") as lumped components in the model.
You can obtain data and explanation  on these from some of the main electrolytic provider's datasheets.
(tan delta is temperature and frequency dependent)
Audio amplifiers normally have intentional -3dB at about 42 Hz and 15 ~ 20 kHz.

With  that high gain up into  200 kHz? the circuit pcb may need some compartments, and maybe neutralization components.

[Kokoriantz]

Same same.

[Kokoriantz]

For sure, the PCB needs to be compartmented, I tried just 1pF from base or emitter of the driver to the input of the feedback and the amp is an oscillator.
I don't like much the bypass capacitor in the feedback, I would prefer a servo instead but as I decided to be simplest possible I will do with.   

[Kokoriantz]

I simplified the circuit to see better the mystery. The LTP+EF response alone I simmed  on Tina shown bellow, it exceeds 1Mhz. When in circuit, in open loop it gets the same first pole of the output. It is also in the precedent version.
This circuit on Tina shows 100v/us slew rate with better damped transients.

[Kokoriantz]

As I added a bootstrap to the EFs, I increased the impedance of the emitters so I applied Schade feedback which decreased the loop gain by 12db but smashed the distortion to 0.0002%/0.0005% 1W/60W. The PM now is no more zero, it is -3.5° yet robust stability. The scope graphs are shown without input RC to show also the extraordinary slew rate.
   

[Kokoriantz]

I was wrong with the measurement, I forgot to cancel the output inductor. Here is without, it is +4.3°.
Sorry about that.

[Kokoriantz]

I understand better what is going on with the stability of this amp. The closed loop bode plot shows a clear resonance should take place on the pulses, but the scope shows nothing. If I observe the error on the input differential, instead of having a saturation due to slew rate saturation of the output all the length of the pulse rise, I get very short period of saturation then oscillations occur while rising. As the frequency of resonance is about 15Mhz, it gets damped when the pulse gradually reaches its maxima without overshoot. 

[Kokoriantz]

I pushed the circuit to its limit with 60db NFB and only 2.5° Phase margin. It is perfectly stable.
By feeding the emitters with other branch of the differentials, the ac base to emitters is decreased hence the bootstrap increases further the open loop gain.
This configuration with less Schade feedback has more third order harmonics but of opposite phase that act as dynamic expander, however the THD+N is 0.001%-0.002%
I modeled on LTspice, unfotunatly the 2n4401/3 are too high Hfe, giving 70db gain and oscillating.
The Tina models have 360 and 330 which is more than the max datasheet 300. I bought a pair of each and measured 250-270. 

[Kokoriantz]

I adjusted by Schade feedbacks to get exactly zero PM with 54db NFB. I added a Zoble the get extra 20° PM. I added 50pf capacitors on the bases of EFs to have 200khz loop bandwidth. Here is the result with 1us pulse with and without Zoble and with input RC, showing output and error signals. 

[Kokoriantz]

Anyone who thinks phase margin is good will change his mind with this experiment.
I replaced the Zoble 100n/2ohm to 10n/22ohm to reduce the PM from 20° to 3° and I get better damped error. No doubt this amp enjoys near zero PM. 

[analityk]

Using ordinary resistance to set idle current for power transistor should not work in real life. Circuit with LM also should be replaced by transistor. I mean the speed of this reg isn't so fast and it can introduce some amounts of noise and instability especially if it doesn't have any capacitor (without it feedback loop make panic, and opamp inside LM can fall in oscillation) but any capacitance between gates is real pain. Another question is lacking of source/drain resistors. MOS's can work like switches but in linear region the can thermal runaway.

[Kokoriantz]

Thank you for giving some interest with this circuit.
I have added the LM317 in current mode in the first post as I was using current mirrors, since I got rid of them, there is no need to bias with it. See the last posted circuit.
I used many times both MOSFETs and BJTs without degenerative resistors by applying a thermal sensor upon the power transistor. Here it is an NTC 10k 3950K as washer is bolted along one of the  outputs, the parallel resistor of NTC, adjusts the required drift /°C which is about 5.5mv/°C.
For now this amp requires a regulated power supply as the bias depends highly upon it(30ma/V), I already received SMPS 300W +/-36v, I will see first if such low phase margin really works, if bias is drifting too much by PS, I will add CCS to LTPs.

[analityk]

Try something like this:
https://obrazki.elektroda.pl/8586082500_1620039648.png

[Kokoriantz]

I simulated the circuit indicated above. At 20khz it has 52db NFB for 140° phase shift. This is not good, with 90° you need 60db to have high definition. Mine has 20° shift with 62db NFB.
The slew rate is too low, it has very high shout through see scope with 10khz square wave.
With 1khz 33W, it gave 0.014%THD.
I biased 175ms each output transistor.

[dietert1]

Sorry, those 10 pF capacitors in the feedback path of audio amplifiers are horrible design. They make a capacitive divider with the input stage input capacitance, which isn't a real capacitor. Better put a good 1 or 2 nF capacitor onto the feedback side of the input stage and then calculate according to design gain what the 10 pF cap should become to make the feedback divider flat at higher frequencies. This change can avoid surprise when building the first prototypes.
BTW, a similar cap on the signal input side is useful against EMI.

Regards, Dieter

[Kokoriantz]

This capacitor 5pF in parallel with the feedback resistor, is called Lead capacitor and used since the early feedback tube amplifiers.
It leads the phase to be before the the 0db crossing to offer higher phase margin. If that frequency is too high as is the case 15Mhz, it doesn't require series resistor as the output impedance which is in series is high enough. 

[dietert1]

I know that many amplifiers have this design problem. That 10 pF may help, but there is a better solution and it is simple enough.
Do you understand frequency compensation of a scope probe? There is a resistive divider parallel to a capacitive divider. Why would somebody want to adjust for correct probe compensation? How does it affect the representation of a 1 KHz test signal? Does it only affect the signal transitions?

Regards, Dieter

[analityk]

Instead AD847 I was use OPA189, I think opamp is most important things here. Secondly I place two transistors current source between two gates not between gates and outputs. Third the compensation loop is for compensation, you can and even should make some test and adjustments. And for 100W output power one pair of power fet should be enough. This is twice lower gate capacity and Miller effect.

[Kokoriantz]

I changed the input stage to be inverter current feedback amp. When I joined the collectors of common based transistors to the emitters of the drivers, I got an oscillator in open loop very nice rail to rail square waves of 15us. When I close the loop I get perfectly stable amplifier exempt of oscillations.     

[Kokoriantz]

The input stage is acting as a stand alone multi vibrator. I don't understand yet how it work. At the input I have also pulses.