sziklai bjt push-pull biasing and thermal stability

[exe]

Hi there,

I wanted to create a thermally stable sziklai push-pull output for my power supply. The problem is make it thermally stable. There a a few approaches to that, I experimented with two:
1. thermal coupling of biasing circuitry (rubber diode/Vbe multiplier)
2. Adding emitter resistor to driving transistors to counter-act bjt heating

The problem with the first approach (which seems to be very common) is that it's very hard to make it working reliably. A common solution to that is to add emitter resistors at the output. But they produce quite a bit of heat. Like, commonly it's in the range of 0.1...0.3 Ohm, which is, at 2A output in my dense board is already a lot of heat, and they also increase output impedance and make transient response slower. It's also difficuilt for me to make Vbe multiplier to really "follow" the drift of driving transistors. It kinda helps to use matched pairs of transistors (see the pic).

So, I tried another approach: driver's emitter resistors are ridiculously large to make it stable. In order to make it working they are bypassed by a capacitor. It seems to be working fine. Looks like a good approach to me. What do you think of this approach? Any potential downsides?

[magic]

Does it have to be push-pull, does it have to be Sziklai?

Output impedance is still limited, up to some kHz. I guess U2 will take care of it, so meh. No point going less than resistance of PCB.
They need to be quite ridiculously large indeed, because they are outside the pair's feedback loop and their resistance is "divided by β of the power devices", I hope you see what I mean.

Complementary Sziklai pairs like these can be prone to cross-conduction at high frequencies due to charge storage effectively keeping both sides turned on. This includes oscillation.

[moffy]

The main advantage when I used the Sziklai pairs was that I didn't need a complimentary PNP power output transistor just the PNP driver for the bottom pair all the rest could be NPN's. They do make biasing the pseudo darlington output easier, with just 2 Vbe instead of 4. And as Magic stated the 100 ohm emitter resistors get effectively divided by the beta of the power transistor, but without the dissipation so that is a gain. Didn't know about the propensity for oscillation, Magic, do you think the 150 ohm driver collector resistors will help mitigate that?

[T3sl4co1l]

You put the emitter resistors in the wrong place!

Intuition: the first transistor should sense what the second (power) transistor is doing.  So, the final's collector current should flow through the emitter resistor.  We have:

Tim

[magic]

I now see another problem with this scheme. As the outputs heat up, their Vbe decreases and so does the current through BE bypass resistors. More of the driver's current flows into the base.

Potentially solvable by further increase of the ridiculously high resistance. Also, mind that β of the outputs increases with temperature. Potentially solvable by stronger negative TC of the bias spreader.

At this point it must be said in favor of the traditional bias technique that it does not require thermal tracking with the outputs, only with the drivers.

[T3sl4co1l]

Not significant; if it's going unstable from a 30% variation in bias current, it sure as hell isn't going to behave over the, whatever, 30000% variation including load range.

The main thing I've noticed about the configuration is maybe needing a bit of miller C across the driver, or ferrite bead on one or both bases.  The loop gain between the two transistors can be quite high, oscillating near fT of one or the other, from not much stray inductance around them.

Tim

[exe]

You put the emitter resistors in the wrong place!

Intuition: the first transistor should sense what the second (power) transistor is doing.  So, the final's collector current should flow through the emitter resistor.  We have:

Tim

That emitter resistors provide negative feedback to slow down sziklai a little bit to prevent oscillation. Afaik, they can be replaced ferrite beads.

[exe]

Does it have to be push-pull, does it have to be Sziklai?

Why sziklai: because it's easier to avoid thermal runaway. Why push-pull: it helps with transient response and discharging output caps after an overshoot, and it lets the power supply to also work as an electronic load.

Output impedance is still limited, up to some kHz

Ah, you mean because of shunting caps? Yeah, that's true. I was thinking if I can use some high-K caps and have, say, 10u capacitance or something in 0603 size. The DC voltage across caps is very small anyway.

They need to be quite ridiculously large indeed, because they are outside the pair's feedback loop and their resistance is "divided by β of the power devices", I hope you see what I mean.

Yeah, well, almost. I thought they need to be big because the current that flows through them is small (3-5mA), so to create a meaningful drop on them (30-50mV) it needs to be this big.

[exe]

Huh, found an "interesting" problem with the capacitor configuration: during startup, capacitors shunt those resistors so that voltage across them is zero, as if resistors are not there. With biasing adjusted for a steady condition this creates a shot-through.

I can only think of this solution: bias voltage should rise gradually to let capacitors charge. I added a small capacitor:


(500n is actually a bit too small, making peak shot-through current of 440mA).

[T3sl4co1l]

What capacitors?  On the emitter resistors? Just nix 'em.

That emitter resistors provide negative feedback to slow down sziklai a little bit to prevent oscillation. Afaik, they can be replaced ferrite beads.

The finals could have emitter resistors to limit transconductance; FBs in the same place will not be effective because of DC bias (saturation).  But this does little, because current gain quickly dominates at high currents (read: final's r_pi << R_BE).  So current feedback is the only applicable case up there.

If r_pi is much larger, though, it could be fine over the whole operating range.  I don't know why you'd be using say a Darlington here, but in the event you would, then emitter degeneration can be designed to cover the whole range.

Some audio amps are made that way; I guess because just so much current gain was needed, and one or two rounds of Sziklai pairing saves on saturation voltage.

Tim

[magic]

I once came up with this "folded Sziklai pair" arrangement as a way of getting LDO output with TL431 or similar regulator. It wasn't built in the end so no warranty but IIRC it simulated OK at least

R1 supplies bias to the chip while shielding it from Vin ripple, it could be omitted if not needed. The stage is unity gain with local feedback and it can source and sink, although sinking is weaker. Darlington upgrade seems an obvious possibility. Quiescent current is well defined: I(R2)-I(R3)-Ib(Q3).

edit
I suppose D1 could also be the BE junction of a power NPN for more sinking.

[exe]

What capacitors?  On the emitter resistors? Just nix 'em.

Wait, they are essential . I was wrong about voltage drop across them. With 4mA quiscent current and 100 Ohms they develop 400mV each. That's why the whole thing become very thermally stable: lots of negative feedback. Please see the simulation results where I step the load 10mA -> 2A -> 10mA.

Though I found another problem: during rapid load change those capacitors cause some shot-through when transitioning from high load to light load, up to 1A in simulation. So I reduced those caps to 1u and emitter resistors to 10 Ohm. This limits peak shot-through current to 0.5A for about 0.5us. I think I can live with that .

[magic]

That's why the whole thing become very thermally stable: lots of negative feedback.

Only driver currents are stable, there is no compensation for Vbe and β drift of the outputs.

Try adding temp=150 to them.

[exe]

Only driver currents are stable, there is no compensation for Vbe and β drift of the outputs.

Try adding temp=150 to them.

Well, for output bjts the temperature change 20C => 150C gives jump from 10mA to 200mA in LTSpice. Much more than I expected. Dang . Push-pull outputs are very hard to bias.

Still, I'm not going to let outputs to heat up that much.

[mikerj]

Do you even need to bias the output stage into class AB for a power supply? 

[Mechatrommer]

i think should also be applicable to Sziklai... thermally couple Q5 with power output...
https://www.quora.com/How-can-thermal-runaway-be-eliminated-in-class-B-amplifiers/answer/Ian-Hendry-11?ch=10&oid=108468631&share=3492f79f&target_type=answer

[exe]

Do you even need to bias the output stage into class AB for a power supply?

Of course,  otherwise there'll be too much cross-over distortion .

Jokes aside, it helps a lot with stability. Imagine output overshoots a little bit. How to sink current? If not biased into AB, the the opamp would need to go 1.4V down to make output stage sinking, and then 1.4 again. This creates oscillation.

i think should also be applicable to Sziklai... thermally couple Q5 with power output...
https://www.quora.com/How-can-thermal-runaway-be-eliminated-in-class-B-amplifiers/answer/Ian-Hendry-11?ch=10&oid=108468631&share=3492f79f&target_type=answer

Yeah, well... I think for "proper" biasing, the bias circuitry should take into account both temperature of driving transistors, and output transistors.

[T3sl4co1l]

The whole point of the arrangement is the outputs' Vbe is factored out.  To be exact, it's reduced by a factor related to the driver Early effect.  Which will be pretty tiny, and also the output voltage range utterly dominates over that variation (to be specific: Vce(driver) = Vout - Vbe(output) - Vee).

Jokes aside, it helps a lot with stability. Imagine output overshoots a little bit. How to sink current? If not biased into AB, the the opamp would need to go 1.4V down to make output stage sinking, and then 1.4 again. This creates oscillation.

I mean.. the choice isn't class C or AB, I don't know where you're getting that from...  It's a sliding scale between AB and C.

What's commonly called "class B" is usually just something convenient for the devices, like zero-(voltage-)biased triodes that happen to run at low Ia at chosen B+; or transistors with complementary bias diodes (and no extra slop taken up by resistors or Vbe-mult.) so they're just on the threshold; or etc.  It's not that there's NO conduction at idle, that's impossible, we don't have ideal on/off* amplifying devices.  Strictly speaking, everything is a little bit class AB: even the no-bias complementary emitter follower draws leakage current.

*In the sense that any output current is "on", i.e. where the current is proportional to (or at least one-to-one dependent upon) the input.  But "off" is off, current ~= 0.  A ReLU function for example.

A more specific definition of class AB is biasing such that gain of each device at idle is a bit less than half the gain at peak output: therefore as one cuts off and the other turns on harder, total gain remains fairly stable and distortion is minimized.  This isn't exactly easy to do with BJTs (gm ~ Ic so you're basically looking at 50% class A) but is feasible with emitter degeneration (limits gm for large signals), or FETs or tubes (where the square or 3/2 power law limits gm), and then a lower idle point can be chosen.

And Vbe is far from the only way this circuit can be biased.  It can be done in piecewise fashion, like with a resistor from input to output: then the op-amp drives the output directly, for small currents, but activates the (class B/C) output stage for larger currents.  Loop gain depends on load, which might not be desirable for compensation purposes, but it trades off with precision at low currents and low idle current.

Not to mention class G or H or whatever kinds of schemes -- of which the traditional tap-changer PSU is a crude model.  A proper realization does the changing ~instantaneously so the output tracks input perfectly even at high rate of change.  Obviously, the ~10s ms of relay plus charging supply caps can't be done seamlessly; granted, the momentary loss of output tracking might not be noticeable in a mere PSU.

Tim

[langwadt]

http://www.douglas-self.com/ampins/dipa/dipa.htm section 5.3

[Mechatrommer]

i think should also be applicable to Sziklai... thermally couple Q5 with power output...
https://www.quora.com/How-can-thermal-runaway-be-eliminated-in-class-B-amplifiers/answer/Ian-Hendry-11?ch=10&oid=108468631&share=3492f79f&target_type=answer

Yeah, well... I think for "proper" biasing, the bias circuitry should take into account both temperature of driving transistors, and output transistors.

thats why Q5 is thermally coupled to output darlington. your proposal is similar to my eye (thermally coupled) except you are using extra PNP in driver stage. i'm currently playing with darlington class AB, and i burnt like 3 pairs of big TO-247 darlington already in 2 nights due to thermal runaway (my mistake not putting heatsink before bias adjustment). now i'm experimenting with NTC thermistor as bjt/npn bias voltage divider (similar to the given link), i believe the thermistor could not track output (darlingtons pair) Vbe (bias level) very well but currently and hopefully i want to avoid thermal runaway like the other nights, at least thats what i understand as "thermally stable". i havent seen a method for driver (bias circuit) that tracks closely or exactly the darlington's Vbe changes with temperature. i believe different bjt/darlington will have different Vbe-vs-temperature profile, thermal coupling "latency" is another issue. tracking this closely and matching in Vbias circuit will need some ingenuity imho. i'll be happy if you can prove me wrong (on circuit, not on simulator).

[T3sl4co1l]

now i'm experimenting with NTC thermistor as bjt/npn bias voltage divider (similar to the given link), i believe the thermistor could not track output (darlingtons pair) Vbe (bias level) very well but currently and hopefully i want to avoid thermal runaway like the other nights, at least thats what i understand as "thermally stable".

I made an amp once that just didn't stabilize; it was probably at best neutral, maybe slightly positive tempco.  Nothing special about the design, Vbe mult and Darlington emitter follower as anything else.  I think the main difference was the unusually low current density in the outputs (I had high current BJTs to hand), skewing the tempco unfavorably or something.  Ultimately slapped a 10k NTC across the Vbe transistor (C-B I think?), which along with the other component values, basically meant throttling it off hard (~class B) by 70C or something like that.

Tim

[Mechatrommer]

in my case, i have two AB amp currently built, one is low volt (single split ±15v) rail exactly like the link above. and another one is medium volt (dual split ±15v for control opamp and ±60v for power output) rail copied from https://www.analog.com/media/en/technical-documentation/application-notes/an18f.pdf page AN18-7.. the low volt version is stable at some slight cross conduction at room temp, esp when Vbe npn is coupled to the heatsink, even at 2 ohm load (and release when temp is high enough, i have yet to populate overtemp protection cut-off circuit). but the high voltage version is self destruct on slight cross conduction if i'm late 5 seconds, and thats on idle load. the app note originally using 2 diodes drop biasing, i added one more diode to improve THD (cross over distortion).. self destruct. changed to transistor based biasing, trimpot adjust to slight cross conduct at room temp... quiescent current sky rocketed and self destruct in 5 seconds before i managed to grab my thermal imager, you have to experience it to appreciate what a thermal runaway is all about (cracking power darlingtons like popcorn) and now experimental 7Kohm NTC thermistor in my stock to Vbe npn's C-B, and trimpot adjust on B-E, last night test was a success without heatsink... yes hopefully the higher the temp, the NTC preferably throttle hard so there should be a cross point where equilibrum at some non-destructive temperature. higher than this temp, cut-off harder but THD increases. next step is to adjust for acceptable THD at lower (or "operating") temperature... this is trial and error basis, i dont know the math, even if i do, i dont know the components parameters, so why learn theory that may not reflects reality?

[exe]

I'll try compensate for output transistor temperature with an NTC. Like this one: NTCALUG03A473HC https://lcsc.com/product-detail/NTC-Thermistors_Vishay-Intertech-NTCALUG03A473HC_C144909.html . It can be screwed on top of the power transistor. I'm not sure yet how I'll do it mechanically as the board is very dense. I'm also thinking if I want a single NTC for both power transistors, or one NTC per transistor.

Hopefully it won't be too difficult as, in simulator, the bias voltage tempco is only 0.23mV/C, comparing to ~3.6mV of driving transistors.

[Mechatrommer]

Since the lower part of your power bjt is only to absorb overshoot, that will not take much load hence temp rise should not be an issue. Its the higher part that provides power/load needs heatsink and monitoring.. in my case, the setup is sort of 4 quadrant psu, so both bjt will equally loaded. Cheaper option is shared heatsink and only one vbe bjt/ntc needed to monitor that one heatsink. Mass produced pro grade devices use sort of metal plate bent as clamp/holder screwed to the heatsink to pinch the sensor or whatever component to the heatsink, others use pretensioned metal clip. For temporary/personal setup like mine i just use hotgun glue (easily removable for prototype), or maybe better, heat resistance epoxy/ab glue. Ymmv.

[exe]

This is what I'm gonna try. So, D1 and D2 are thermally coupled with output transistors, while Q1 and Q3 coupled with driving transistors.

I have to admit I've never burned a bjt, or any other component... yet. I'm a bit scary if that happens while normal PSU use as that would put full voltage to the output. So, I want to make sure this is not gonna happen.