Hi,
Solid State Amplifier stability
I was wondering if anyone here could share their knowledge on Audio Amplifier design; in particular the design of Zobel (aka boucherot cell – not sure why this term is used as this guy seemed more concerned with Power Systems and their stability) and series Parallel RL networks that are used to ensure amplifier stability.
I’m a student studying Electrical Engineering and I’ve got a project that looks at techniques to stabilise solid-state amplifiers. I decided to focuses on the design of Zobel Networks (series RC network across the output) and the use and specification of the series-parallel RL network; the network that is typically placed between the output and the speaker terminals of the amplifier.
I’ve read Self’s latest book on Audio Amplifier design and also glanced at others such as Randy Sloane's books.
Other than offering empirical advice, none provided a ‘scientific’ method or approach to selecting the right values, nor in particular the kinds of components to use. Comments like “…is about right…” is not really that helpful and don’t stand-up to scrutiny in the Academic environment that I’m in.
Sure, there are general comments like use a film capacitor and an air-cored inductor but, there are many different types of capacitor, and many different ways to make an air cored inductor that affect the Q and other characteristics.
I just wondered if someone here might have some insight on designing these kinds of stabilising network and could offer that advice.
It would be really interesting to understand the processes that are used to design and than test and verify that the selected components are right or suitable?
For my project I’ve got to right up the purpose and effects of these networks, a discussion on the tradeoffs with designs (e.g. impact on performance and what down-sides might exist or appear) and then the processes that are used to arrive at the right values.
If I get a chance I might even do some lab work….
From surfing around the web and looking at schematics of commercial amplifiers, there are a load of variations and around how these networks are applied.
Thanks in advance.
Paul.
Solid State Amplifier stability
I was wondering if anyone here could share their knowledge on Audio Amplifier design; in particular the design of Zobel (aka boucherot cell – not sure why this term is used as this guy seemed more concerned with Power Systems and their stability) and series Parallel RL networks that are used to ensure amplifier stability.
I’m a student studying Electrical Engineering and I’ve got a project that looks at techniques to stabilise solid-state amplifiers. I decided to focuses on the design of Zobel Networks (series RC network across the output) and the use and specification of the series-parallel RL network; the network that is typically placed between the output and the speaker terminals of the amplifier.
I’ve read Self’s latest book on Audio Amplifier design and also glanced at others such as Randy Sloane's books.
Other than offering empirical advice, none provided a ‘scientific’ method or approach to selecting the right values, nor in particular the kinds of components to use. Comments like “…is about right…” is not really that helpful and don’t stand-up to scrutiny in the Academic environment that I’m in.
Sure, there are general comments like use a film capacitor and an air-cored inductor but, there are many different types of capacitor, and many different ways to make an air cored inductor that affect the Q and other characteristics.
I just wondered if someone here might have some insight on designing these kinds of stabilising network and could offer that advice.
It would be really interesting to understand the processes that are used to design and than test and verify that the selected components are right or suitable?
For my project I’ve got to right up the purpose and effects of these networks, a discussion on the tradeoffs with designs (e.g. impact on performance and what down-sides might exist or appear) and then the processes that are used to arrive at the right values.
If I get a chance I might even do some lab work….
From surfing around the web and looking at schematics of commercial amplifiers, there are a load of variations and around how these networks are applied.
Thanks in advance.
Paul.
There was a thread here not so long ago where this was discussed. Something that was shown was that you can make the output LR combination to not have a big input impedance peak with capacitive loads and then the series R-C on the input is used to counter the rising impedance of the LR network and provide a somewhat defined load at the critical frequencies around 1MHz.
With good component selection you get an impedance that varies very little between open load, shorted load and any capacitive load.
With good component selection you get an impedance that varies very little between open load, shorted load and any capacitive load.
Here's a big thread on the zobel...
http://www.diyaudio.com/forums/showthread.php?s=&threadid=120748&perpage=25&pagenumber=1
many different opinions..
And the math (for Academia)..
http://users.ece.gatech.edu/~mleach/ece4445/downloads/zobel.pdf
Very difficult thesis because most depends on the physical world
(the loudspeaker) I think self generalized it because it would of
added 200 pages to his book.
OS
http://www.diyaudio.com/forums/showthread.php?s=&threadid=120748&perpage=25&pagenumber=1
many different opinions..
And the math (for Academia)..
http://users.ece.gatech.edu/~mleach/ece4445/downloads/zobel.pdf
Very difficult thesis because most depends on the physical world
(the loudspeaker) I think self generalized it because it would of
added 200 pages to his book.
OS
Hi AndrewT,
Thanks for the info - I'll try and track that info down.
Hi megajocke,
Thanks also for your advice.
I too read a bunch of posts here on the use of the Zobel network and the series-parallel R-L network on the output.
I'm not sure which amplifier you had in mind that has a critical 1MHz frequency. Several amplifiers I recently played around with, one all FET, had a natural oscillation frequency of 80MHz. This amp burst into oscillation with a 1.3nF cap on the output and the RL network removed – I did try other values but this value seemed to give the best peaked response.
The other amplifier, a BJT design from Randy Sloane seemed to have a natural oscillation frequency around 10-15MHz. The range of frequency dropped as the amplifier output stage got hotter. With the R-L network removed placing a 100nF or larger cap across the output worked.
Another National GAINCLONE IC based design with a natural oscillation frequency of around 2.7-3.0 MHz. This was probably the most sensitive design – as soon as I removed the R-L network and excited the input with an impulse this circuit took off.
In all cases I excited the amplifiers with a step impulse of 0.01s pulse duration that varied between 0.2V IC, 0.65V for the BJT and 1.0V peak for the MOSFET design.
The FET amplifier has a series-parallel R-L combinations of 7.1uH and 25 Ohm. The BJT design has a the same network topology but with values of 0.7uH and 1 ohm. On the other hand the National Semiconductor design uses a 2.2uH and 5 ohm design.
All amplifiers had a Zobel network installed, in the case of the FET amplifier this had too networks, one either side of the series-parallel R-L combinations. For testing purposes I removed one side of the resistors from the circuit, effectively isolating these networks from the output stage of each amplifier.
I guess I can say that there isn’t one fit or necessarily one solution. Hence, my initial questions…
I really don't think that the selection of these parts or the 'right' or 'best' fit is obvious with empirical rules of thumb?
Thanks.
Paul.
Thanks for the info - I'll try and track that info down.
Hi megajocke,
Thanks also for your advice.
I too read a bunch of posts here on the use of the Zobel network and the series-parallel R-L network on the output.
I'm not sure which amplifier you had in mind that has a critical 1MHz frequency. Several amplifiers I recently played around with, one all FET, had a natural oscillation frequency of 80MHz. This amp burst into oscillation with a 1.3nF cap on the output and the RL network removed – I did try other values but this value seemed to give the best peaked response.
The other amplifier, a BJT design from Randy Sloane seemed to have a natural oscillation frequency around 10-15MHz. The range of frequency dropped as the amplifier output stage got hotter. With the R-L network removed placing a 100nF or larger cap across the output worked.
Another National GAINCLONE IC based design with a natural oscillation frequency of around 2.7-3.0 MHz. This was probably the most sensitive design – as soon as I removed the R-L network and excited the input with an impulse this circuit took off.
In all cases I excited the amplifiers with a step impulse of 0.01s pulse duration that varied between 0.2V IC, 0.65V for the BJT and 1.0V peak for the MOSFET design.
The FET amplifier has a series-parallel R-L combinations of 7.1uH and 25 Ohm. The BJT design has a the same network topology but with values of 0.7uH and 1 ohm. On the other hand the National Semiconductor design uses a 2.2uH and 5 ohm design.
All amplifiers had a Zobel network installed, in the case of the FET amplifier this had too networks, one either side of the series-parallel R-L combinations. For testing purposes I removed one side of the resistors from the circuit, effectively isolating these networks from the output stage of each amplifier.
I guess I can say that there isn’t one fit or necessarily one solution. Hence, my initial questions…
I really don't think that the selection of these parts or the 'right' or 'best' fit is obvious with empirical rules of thumb?
Thanks.
Paul.
Here is the thread I was thinking of:
http://www.diyaudio.com/forums/showthread.php?s=&threadid=125679
I was thinking of the unity gain crossover that often is around 1MHz and you'd want a pretty defined load there to make the loop stable. 80MHz sounds like local output stage oscillation. If you have a series RC on the amp side of a parallell LR you can (and probably should) design it so that impedance as seen by the amp doesn't depend much on load in the 1MHz region. Capacitive loads will resonate with the L and the parallell R has to be chosen to dampen this resonance.
If it is designed like this the impedance at >10MHz where you can get local oscillations will be practically load independent.
I wonder if a low inductance resistor is really needed in the RC-network, an emitter follower shouldn't do anything stupid with lightly inductive loads.
http://www.diyaudio.com/forums/showthread.php?s=&threadid=125679
I was thinking of the unity gain crossover that often is around 1MHz and you'd want a pretty defined load there to make the loop stable. 80MHz sounds like local output stage oscillation. If you have a series RC on the amp side of a parallell LR you can (and probably should) design it so that impedance as seen by the amp doesn't depend much on load in the 1MHz region. Capacitive loads will resonate with the L and the parallell R has to be chosen to dampen this resonance.
If it is designed like this the impedance at >10MHz where you can get local oscillations will be practically load independent.
I wonder if a low inductance resistor is really needed in the RC-network, an emitter follower shouldn't do anything stupid with lightly inductive loads.
Try to find information on power factor correction. A zobel network is supposed to make the load look resistive at all times, so there is no phase lag between voltages and currents.
A single zobel could be quite useless and you often find historical values of 10 ohms in series with 100 nF.
A single loudspeaker should be inductive, so is the cable feeding it, this inductor is a constant unless you remove windings from the speaker or adjust the cable length. The capacitance in the zobel is intended to counter the inductive reactance and make the load appear purely resistive and therefore you get maximum power transfer.
A single zobel could be quite useless and you often find historical values of 10 ohms in series with 100 nF.
A single loudspeaker should be inductive, so is the cable feeding it, this inductor is a constant unless you remove windings from the speaker or adjust the cable length. The capacitance in the zobel is intended to counter the inductive reactance and make the load appear purely resistive and therefore you get maximum power transfer.
Gents:
1. In the power application, capacitors are used to introduce a phase shift in the AC current waveform. Rotating machinery, for example, loads the powerlines inductively. Power delivered is the product of voltage times the current times the phase shift. This is the basis for power factor...a pf of 1 is zero phase shift.
It is important to the power companies, because the transmission network must support the current of the load, but if the current is not in phase, the amount of billable power will be low.
Insertion of capacitors brings the power factor that the power company sees closer to 1. It does so by using capacitive reactance..it introduces a 90 degree current vector in the phasor diagram..180 degrees opposite of the inductance vector..
(Don't make me come over there and draw diagrams... )
2. For amplifiers with negative feedback, the stability is determined by the amount of phase shift in the gain plot. If the phase of the output exceeds 180 degrees before the 1/b line is hit, the feedback will be positive.
Capacitors loading the output cause the phase shift to be worse.
If the amplifier gain plot crosses the 1/b line faster than 12 db/octave, it will be unstable.
Figure 9.6 of this link:
http://www.analogzone.com/acqt1211.pdf
Or page 53 of the IC opamp cookbook, third edition. Jung, 1991.
Cheers, John
1. In the power application, capacitors are used to introduce a phase shift in the AC current waveform. Rotating machinery, for example, loads the powerlines inductively. Power delivered is the product of voltage times the current times the phase shift. This is the basis for power factor...a pf of 1 is zero phase shift.
It is important to the power companies, because the transmission network must support the current of the load, but if the current is not in phase, the amount of billable power will be low.
Insertion of capacitors brings the power factor that the power company sees closer to 1. It does so by using capacitive reactance..it introduces a 90 degree current vector in the phasor diagram..180 degrees opposite of the inductance vector..
(Don't make me come over there and draw diagrams...
)2. For amplifiers with negative feedback, the stability is determined by the amount of phase shift in the gain plot. If the phase of the output exceeds 180 degrees before the 1/b line is hit, the feedback will be positive.
Capacitors loading the output cause the phase shift to be worse.
If the amplifier gain plot crosses the 1/b line faster than 12 db/octave, it will be unstable.
Figure 9.6 of this link:
http://www.analogzone.com/acqt1211.pdf
Or page 53 of the IC opamp cookbook, third edition. Jung, 1991.
Cheers, John
I'm aware that to get the maximum power transfer out of a linear two-terminal network the load impedance must equal the complex conjugate of the source impedance.
But this has no applicability to audio amps where load impedances are bridged rather than matched. If you tried to match the load to the amplifier output impedance you would have connected a 10 milliohm speaker! The power is limited by non-linearD) effects such as transistors exploding or overheating in audio amps.
It is possible though to use a zobel and/or capacitor to counter the inductive rise of the speaker, making them look resistive decreasing reflected power into amp, maybe this is what you are thinking of. It decreases amp dissipation a little (practically nothing as it's the high frequencies where there aren't much power in the music).
But this has no applicability to audio amps where load impedances are bridged rather than matched. If you tried to match the load to the amplifier output impedance you would have connected a 10 milliohm speaker! The power is limited by non-linear
D) effects such as transistors exploding or overheating in audio amps.It is possible though to use a zobel and/or capacitor to counter the inductive rise of the speaker, making them look resistive decreasing reflected power into amp, maybe this is what you are thinking of. It decreases amp dissipation a little (practically nothing as it's the high frequencies where there aren't much power in the music).
chev350 said:
pffft...academic environment....
Just guess..the better you are, the better your guess...
Go for a book like Jung, read on loop stability with negative feedback..he's very good at writing the basic theme.
A basic issue with power amp stability is the need for speed (high gain bandwidth product), negative feedback, and the virtual lack of control the designer has on what is connected to his amp.
Any time the load can cause the gain/phase of the amp to exceed 180 degrees shift, the amp will oscillate.
You have to consider the actual amp transfer function with the worst case loads the unit will see. If you plop a matched z speaker line across a hot amp for example, and the speaker remains inductive through the zero gain frequency of the amp, the speaker wire will be the only load the amp sees...trouble with a capitol T..(a matched Z speaker line will have capacitance out the wazoo... and if the load z is above the line z, the system looks capacitive to the amp.)
It's not just power amps which suffer the problem, the link I posted shows it happens to even the smallest of amps...
Burr Brown, analog devices, linear tech, they all tend to provide app notes which may be of use to you..
Cheers, John
Re: Re: Amp Stability techniques: Zobel et al.
Thanks John you said it in better readable language.
jneutron said:
pffft...academic environment....
Just guess..the better you are, the better your guess...
Go for a book like Jung, read on loop stability with negative feedback..he's very good at writing the basic theme.
A basic issue with power amp stability is the need for speed (high gain bandwidth product), negative feedback, and the virtual lack of control the designer has on what is connected to his amp.
Any time the load can cause the gain/phase of the amp to exceed 180 degrees shift, the amp will oscillate.
You have to consider the actual amp transfer function with the worst case loads the unit will see. If you plop a matched z speaker line across a hot amp for example, and the speaker remains inductive through the zero gain frequency of the amp, the speaker wire will be the only load the amp sees...trouble with a capitol T..(a matched Z speaker line will have capacitance out the wazoo... and if the load z is above the line z, the system looks capacitive to the amp.)
It's not just power amps which suffer the problem, the link I posted shows it happens to even the smallest of amps...
Burr Brown, analog devices, linear tech, they all tend to provide app notes which may be of use to you..
Cheers, John
Thanks John you said it in better readable language.
megajocke said:I'm aware that to get the maximum power transfer out of a linear two-terminal network the load impedance must equal the complex conjugate of the source impedance.
But this has no applicability to audio amps where load impedances are bridged rather than matched. If you tried to match the load to the amplifier output impedance you would have connected a 10 milliohm speaker! The power is limited by non-linear
It is possible though to use a zobel and/or capacitor to counter the inductive rise of the speaker, making them look resistive decreasing reflected power into amp, maybe this is what you are thinking of. It decreases amp dissipation a little (practically nothing as it's the high frequencies where there aren't much power in the music).
I agree with your third paragraph, you got the drift of it. Amplifiers like resistive loads or near resistive loads, then they perform best.
Capacitive loads the current leads the voltage and is bad, Inductive loads is the opposite and it is also bad, so we add this magic network so that the amp thinks it is seeing a resistive load.
Amp stability
Hi all,
Thanks for your advice and input.
Hi jneutron,
Can you suggest a relevant Jung title? I had a quick look at one of the Analog Devices Op Amp Applications Handbook, the one you can download on the AD website... there is certainly some good background material in that book - thanks.
Unfortunately they don't give a strategy or approach for getting to the right values for the Zobel and the series-parallel R-L network.
Yes, they do suggest an R-L combination for an AD815AY but there wasn't any discussion as to how they arrived at the values. In this particular example they didn’t use a series R-C Zobel network either!
Thanks anyhow.
Paul.
Hi all,
Thanks for your advice and input.
Hi jneutron,
Can you suggest a relevant Jung title? I had a quick look at one of the Analog Devices Op Amp Applications Handbook, the one you can download on the AD website... there is certainly some good background material in that book - thanks.
Unfortunately they don't give a strategy or approach for getting to the right values for the Zobel and the series-parallel R-L network.
Yes, they do suggest an R-L combination for an AD815AY but there wasn't any discussion as to how they arrived at the values. In this particular example they didn’t use a series R-C Zobel network either!
Thanks anyhow.
Paul.
Re: Amp stability
Umm, I did.
""IC opamp cookbook""
Walter G Jung
Third edition, eigth printing.
Sams, 1991.
Chapter 1.2, ""The non-ideal Op Amp.""
Page 53 shows the plots and the relationship.
Any good textbook which introduces negative feedback principles will be good to peruse.
For your app, you just need to develop the range of amp transfer functions, then get your phase margins as impacted by various loads.
You might be better off asking guys like Nelson Pass, or John Curl, they do this for a living. I'd certainly ask them..
Cheers, John
chev350 said:
Umm, I did.
""IC opamp cookbook""
Walter G Jung
Third edition, eigth printing.
Sams, 1991.
Chapter 1.2, ""The non-ideal Op Amp.""
Page 53 shows the plots and the relationship.
Any good textbook which introduces negative feedback principles will be good to peruse.
For your app, you just need to develop the range of amp transfer functions, then get your phase margins as impacted by various loads.
You might be better off asking guys like Nelson Pass, or John Curl, they do this for a living. I'd certainly ask them..
Cheers, John
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