How to calculate Zobel Network/Boucherot Cell for Solid State Power Amplifiers

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tiefbassuebertr

tiefbassuebertr

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Joined 2005
tiefbassuebertragung.de
#1
Most commercial and diy power amplifiers uses on it's outputs values inside of a small range:
The resistor values goes usually between 2R7 and 15R (mostly 10R or 4R7 according the most amplifier books the value of DC resistance of most speakers for home audio) and the capacitor values goes between 47nF and 220nF (mostly 100nF)

But sometimes there are to observe very strong deviations.

Linn's early version LK2 (LK-280) e. g. uses only a 100nF capacitor without resistor at its output. Later versions additional use a network consist of a 330nF capacitor and a resistor of only 0R47 (470mR).

Maybe this is necessary by the use of a sziklai darlington (CFP Pair) in the output buffer, but I don't know this exactly.

Are there a calculation basis, where this is comprehensibly ?

Thank you for comments and advices to appropriate websites.

Under the follow threads there are no advices therefore, because the aim is mostly an appropriate zobel network for certainly loudspeaker drivers:
Boucherot cell (Zobel network) values
How to calculate Zobel/Boucherot Circuit
No Boucherot cell?
Amp Stability techniques: Zobel et al.
DIY option for spectral amps?
Confuse... When to use a Zobel network ?
Zobel network
Zobel network - resistor wattage
zobel network in MOSFET power amplifiers
Zobel calculation, help needed!

https://elektroniktutor.de/analogtechnik/zobel.html
http://www.jobst-audio.de/tools-frequenzweiche/zobel-glied
 
#2
The only calculation is to make sure the Zobel has no significant effect in the choosen bandwidth of the amplifiern and a low impedance at frequencies out of band.

It doesn't really prevent oscillation.
The idea is to dump an oscillation in case it occurs. The zobel doesn' t solve anything about unstable amplifiers.

Selected values are more copies from older designs and trial and error. Type of capacitor is important about effective low impedance at high frequencies.
 
#3
Have you read chapter 14 ("Output Networks and Load Effects") of Douglas Self's book APAD 6th ed?

At this point I felt some experiments were called for, and so I removed the Zobel from a Blameless amplifier ... With a pure 8 ohm resistive load, the THD performance and stability were unchanged. However, when a 0.47 mH inductor was added in series, to roughly simulate a single-unit loudspeaker, there was evidence of local VHF instability in the output stage; there was certainly no Nyquist instability of the global NFB loop.​

Self goes on to discuss his experimental results when varying the Zobel network's component values, and finds that there is an optimum. As you move away from the optimum, behavior gets worse and worse.

It seems to me that if you want to perform similar experiments in simulation rather than in the hardware lab, first you must find a way to make your simulated amplifier's output stage exhibit VHF instability when driving (0.47mH in series with 8 ohms). Then you can install a simulated Zobel network and monkey around with its component values.

_
 
#4
mchambin said:
It doesn't really prevent oscillation.
The idea is to dump an oscillation in case it occurs. The zobel doesn' t solve anything about unstable amplifiers.
Click to expand...
Yes it does. No. Yes it does.

The Zobel network is intended to ensure that the output stage sees a broadly resistive load at RF frequencies. A capacitive load may induce oscillation, either parasitic oscillation in the output stage (as the output is usually some sort of follower, and followers do not like capacitive loading at high frequencies) or loop instability. Hence the Zobel resistor must be low enough in value to swamp any likely capacitive load, possibly from the speaker cables. The capacitor must be high enough in value that at RF frequencies it is negligible when compared with the resistor, and low enough in value that it does not impose much load at audio frequencies.
 
#5
A. N. Thiele published a nice alternative decades ago: a first-order series filter with the loudspeaker at the low-pass branch.

That is, from the amplifier's output you first have an LR parallel network and then a capacitor straight to ground. The loudspeaker is in parallel with the capacitor. When the capacitor has a very low parasitic inductance, it shunts any RF picked up by the loudspeaker cable before it can do any harm.

For this network, R is chosen equal to the nominal impedance of the loudspeaker, L as high as you consider acceptable for the output impedance at 20 kHz and C = L/R^2.
 
#7
Stray RF pickup on the speaker cable is another issue, although the Zobel may help with that too. It is generally reckoned that RF pickup can be made worse if the cable resonates, and the way to deal with this is a CR 'Zobel' at the speaker end with the resistor equal to the cable RF characteristic impedance (not the speaker impedance).
 
#8
To calculate something meaningful, you must know:
The cause of the oscillation, there are many of very different natures, including unexplained.
The caracteristics of the load, woofer, tweeter, 2 way 3 way loud speaker, speaker câbles.
The layout parasitics. Capacitances Inductances Mutual inductances Capacitive couplings.
You need a meaningful model. Output stages are not linear because of high amplitude signals ( Class aB stage is far from linear at crossover and terribly far at clipping ), an 8 ohm rated loud speaker impedance is far from an 8 ohm resistor, it is inductive/capacitive and non linear.
 
#10
DF96 said:
Class AB is, when correctly biased, quite linear at crossover. That is the criterion for correct bias!
Click to expand...

I design my own amps so there is no setup procedure that comes with it for biasing.

So I apply a small sine wave and monitor output on a scope.
I turn up bias until crossover distortion goes.

However this doesn't quite work.
If I turn up the sine wave the crossover distortion can sometimes start to reappear. So I need to apply more bias.

As for Zobel values I would have thought for more inductance in the speaker then more capacitance is needed to counteract it in the Zobel.
 
#12
DF96 said:
Stray RF pickup on the speaker cable is another issue, although the Zobel may help with that too. It is generally reckoned that RF pickup can be made worse if the cable resonates, and the way to deal with this is a CR 'Zobel' at the speaker end with the resistor equal to the cable RF characteristic impedance (not the speaker impedance).
Click to expand...

Or wisely pick a better suited cable for the task. 🙂 (At least within domestic audio)

Belt and suspender is both a series LR and shunt RC, as has been mentioned. And given the location of the circuit, we just need these filter elements to be an effective load before the amplifier's loop gain closes towards unity and well above audio bandwidth as to not affect performance.
 
#13
The capacitance in a Zobel network is not there to "counteract" speaker inductance. It is there to remove the Zobel resistor from the load at audio frequencies.

If you have significant gm-doubling then you have too much quiescent current. I realise that some people deliberately choose this (so-called 'first watt' bias).
 
#14
DF96 said:
Yes it does. No. Yes it does.

The Zobel network is intended to ensure that the output stage sees a broadly resistive load at RF frequencies. A capacitive load may induce oscillation, either parasitic oscillation in the output stage (as the output is usually some sort of follower, and followers do not like capacitive loading at high frequencies) or loop instability. Hence the Zobel resistor must be low enough in value to swamp any likely capacitive load, possibly from the speaker cables. The capacitor must be high enough in value that at RF frequencies it is negligible when compared with the resistor, and low enough in value that it does not impose much load at audio frequencies.
Click to expand...
On Linn's LK2 there are more (at least 3) versions of PCAS003 board than described in the service manual on page 2 - go to attachement and under
http://www.acousticpsychos.com/Files/Linn-LK2-pwr-sm.pdf
1) the here not showed version use a 10nF cer. cap in series to a 10Ω resistor - usuall in use also in other brands and models. Additional there two RC networks in use (27Ω 1nF) between base and collector of each output power devices (TIP35C/36C , sometimes BD249C/250C) - go to the attached image in post #11 under
http://www.diyaudio.com/forums/solid-state/134993-help-linn-lk2-schematic-2.html#post5400949
Also this network is sometimes to find in other power amp devices.
2) also not showed is a version with only a capacitor (100nF polyester) between output and GND without serial resistor and without the RC networks (27Ω 1nF) between base and collector of each output power devices.
3) showed version on page 2: like previous version, but with additional RC Network 330nF/0,47Ω at the output (second picture)

The most interesting question for me is to know the reason, why only a 100nF capacitor is in use (i. e. without additional resistor in serial mode). In such cases there is a shorting present at the output above a certainly frequency value (maybe to protect the tweeter in case of occur from unwanted oscillation ?) and why the resistor value for the additional RC-network in the third version is only 0,47Ω and not 4R7 or 10R as usually to find.

Such steps from 2) and 3) I have never seen before resp. in other power amps - actually therefore the question in post #1

Maybe the use of Linn's speaker cables K20 resp. K400 requires these steps.
 
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