A collection of amp-output Stability Networks

Hello there all,
I thought that it might be interesting to 'collect' in one Thread the myriad of amplifier-output Stability Networks.
I would love to see variations of these networks AND a general discussion of the subject 🙂
 
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Depending on what you want, you could argue that C is useless or that C is essential. It's essential when you want to use this to keep RF signals picked up by the loudspeaker cable out of the amplifier. It is useless (in theory anyway) when you want to make the real part of the output admittance positive at all frequencies to ensure small-signal stability with any passive load, as the capacitor only changes the imaginary part of the output admittance.
 
The LR network in series with the load prevents the impedance (as seen by the amplifier) from becoming too low at ultrasonic frequencies. The RC network that shunts the output prevents the impedance from becoming too high at ultrasonic frequencies. Depending on the amplifier, one or both may not be needed.
Ed
 
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The RC is always recommended to go on the amplifier side of the output inductor//resistor network. It’s there primarily to prevent HF instability of the OPS. It’s has to go before the inductor because at HF the inductor isolates the amp from the load, and if the RC network were placed on the speaker side of the inductor, would render the RC network ineffective. BTW, Self talks about this as well.

The output coil prevents the OPS pole from migrating downward in frequency with the attendant phase shift with capacitive loads which would result in loop instability.

The RC network prevents local OPS instability.

There have been a few papers over the years about terminating the speaker cable at the loudspeaker end to damp overshoot, ringing which are always present due to the amplifier output inductance + speaker cable inductance and cable capacitance.
 
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The RC is always recommended to go on the amplifier side of the output inductor//resistor network. It’s there primarily to prevent HF instability of the OPS. It’s has to go before the inductor because at HF the inductor isolates the amp from the load, and if the RC network were placed on the speaker side of the inductor, would render the RC network ineffective.
I don't think there is any evidence that HF could be inject from the amp's output node.
The output stages, such as EF2, CFP, have very low output impedance even without NFB. Putting RC directly at the output node does nothing as the RC has relative high impedance than the output impedance of the amp, even at high frequency.

I believe the correct form is that @MarcelvdG mentioned in #5.

Assuming the speaker is resistive only, and it is 10 Ohm, also the R is also 10 Ohm, the impedance looking from the output stage is constant 10 Ohm regardless the frequency. That's what a Zobel network should do. However, the main purpose here is not to do impedance matching. Impedance matching with all kinds of speakers is not practical. The main purpose here is to isolate any potential capacitive load.

Regarding C is useless or not. It depends on whether the amp could be stable without any load. Some vintage amps require to be loaded at high frequency to be stable. If so, the C is required.
 
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Here's Matthew Polk's issued patent on a speaker cable RC terminator, installed at the far (non amplifier) end of the cable.

Also attached is Nelson Pass's article on the same topic, from Speaker Builder magazine.
 

Attachments

Terminating the cable + speaker lumped reactive load is a separate issue from a Zobel placed before the output coupling inductor designed to improve the stability of the OPS.

There are two stability issues here. Loop stability is aided by isolating excessive load capacitance which causes the OPS HF pole to migrate downwards in frequency with the attendant phase shift the output coil takes care of ghis.

The Zobel addresses local OPS HF instability. It is relatively easy to get an emitter follower to oscillate, and especially EF2 and EF3 configurations.
 
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There have been a few papers over the years about terminating the speaker cable at the loudspeaker end to damp overshoot, ringing which are always present due to the amplifier output inductance + speaker cable inductance and cable capacitance.

I've had decent results with conjugate networks on subwoofers (haven't yet tried mids or highs). This one seemed to add definition between bass guitar and kick drum, along with giving more sense of the beater on the drum. Think of it as being less "thooom" and more "thwamp". I'll write the thing up eventually, but for now note the load phase angle has gone from +-60 degrees to +-10 degrees, showing a reduced reactive component, which could have bearing when actual cables are used. Without baffing at the math, at a first glance EDPR would be improved, a useful point for class-AB amps where output transistor SOA is a consideration.

Test records: Rush Moving Pictures, Donald Fagen The Nightfly, Tori Amos Under The Pink.

Please ignore the kank at 160 Hz, that's a cabinet issue under scrutiny. The impedance peaks out at 45 ohms at around 38 Hz.

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