FetZilla Power Output
Paul, Greg and I have done extensive Spice modelling and now have a real indication of power output.
This is a single ended voltage gain block and as such will always have an asymmetrical clip. This slightly lengthens the usual SS PP distortion profile, and tends to produce more even than odd at least at clip onset. Using 36V rails (25-0-25Vac trafo) we think it's around +28.3Vp on the positive half cycle at 1KHz into 8R. Negative half cycle clips at just under 2V more.
This means that undistorted power will be exactly 20Vrms (peak x 0.7071). Square this, divide by 8R for power output, and it comes to exactly 50W. This is a very reasonable power output for a medium sized room with 87dB/watt/metre speakers, and more than enough for a moderate sized apartment in a city. Of course there will be headbangers who want more, but for most, and particularly for middle aged people and older, this is more than sufficient for most music, even Hotel California.
The most linear region of operation for the lateral output fets chosen is 1A to 5A. With 28Vp, we would achieve nominally 3.5A into 8R speakers, and max 5A into a reactive load, so this accords very well with strong, linear power output. FETs have a much broader SOAR, so with a 200V rating you would never blow them with a difficult load unless of course it was a short.
Hope this explains things,
Hugh
Paul, Greg and I have done extensive Spice modelling and now have a real indication of power output.
This is a single ended voltage gain block and as such will always have an asymmetrical clip. This slightly lengthens the usual SS PP distortion profile, and tends to produce more even than odd at least at clip onset. Using 36V rails (25-0-25Vac trafo) we think it's around +28.3Vp on the positive half cycle at 1KHz into 8R. Negative half cycle clips at just under 2V more.
This means that undistorted power will be exactly 20Vrms (peak x 0.7071). Square this, divide by 8R for power output, and it comes to exactly 50W. This is a very reasonable power output for a medium sized room with 87dB/watt/metre speakers, and more than enough for a moderate sized apartment in a city. Of course there will be headbangers who want more, but for most, and particularly for middle aged people and older, this is more than sufficient for most music, even Hotel California.
The most linear region of operation for the lateral output fets chosen is 1A to 5A. With 28Vp, we would achieve nominally 3.5A into 8R speakers, and max 5A into a reactive load, so this accords very well with strong, linear power output. FETs have a much broader SOAR, so with a 200V rating you would never blow them with a difficult load unless of course it was a short.
Hope this explains things,
Hugh
FETzilla PCB Group Buy
Keep 'em rolling, now at 32 boards so far:
2 JoMo Adelaide SA Australia
2 Ian Finch Coffs Harbour NSW Australia
2 Gennaji Hyderabad India
2 Ken Lewis LA USA
2 Ron Russell Kent UK
2 John Kenny Dublin Ireland
2 Francis Morrin Dublin Ireland
2 Vitalica Bucharest Romania
2 Erik Deinum Groningen Netherlands
2 Keith Correa ? India
2 Igor Polyakov California (city?) USA
2 Steve (aka SRH) Whangarei New Zealand
2 George (aka JKC) Calgary Canada
2 Anthony Mills Gold Coast Australia
2 Dinesh (aka Chlorofille) Christchurch New Zealand
2 Colin S. (?) (city?) NSW Australia
Acting on advice from Paul, I have added a 1K5 resistor to the drain circuit of the input stage to prevent damage to the VAS gate during switch-on transients. It does not affect loop gain, but does reduce the dissipation in the input device, no bad thing. Now down to just under 80mW with 36V rails, about right for a 400mW package.
One of the two LEDs (the green one) used as voltage reference for the input stage bias generator is now off the board and doubles as the front panel 'on' indicator. It can also be mounted on the pcb if desired.
There is now ground plane separation between 1st and 2nd stages and the high excursion output stage. This should improve intermodulation performance.
Board attached,
Hugh
Keep 'em rolling, now at 32 boards so far:
2 JoMo Adelaide SA Australia
2 Ian Finch Coffs Harbour NSW Australia
2 Gennaji Hyderabad India
2 Ken Lewis LA USA
2 Ron Russell Kent UK
2 John Kenny Dublin Ireland
2 Francis Morrin Dublin Ireland
2 Vitalica Bucharest Romania
2 Erik Deinum Groningen Netherlands
2 Keith Correa ? India
2 Igor Polyakov California (city?) USA
2 Steve (aka SRH) Whangarei New Zealand
2 George (aka JKC) Calgary Canada
2 Anthony Mills Gold Coast Australia
2 Dinesh (aka Chlorofille) Christchurch New Zealand
2 Colin S. (?) (city?) NSW Australia
Acting on advice from Paul, I have added a 1K5 resistor to the drain circuit of the input stage to prevent damage to the VAS gate during switch-on transients. It does not affect loop gain, but does reduce the dissipation in the input device, no bad thing. Now down to just under 80mW with 36V rails, about right for a 400mW package.
One of the two LEDs (the green one) used as voltage reference for the input stage bias generator is now off the board and doubles as the front panel 'on' indicator. It can also be mounted on the pcb if desired.
There is now ground plane separation between 1st and 2nd stages and the high excursion output stage. This should improve intermodulation performance.
Board attached,
Hugh
Attachments
Last edited:
Andrej,
Yes, one 300x75 mm heatsink per channel, each rated to 0.4C/W. Each channel (one board) will dissipate around 25W, so that would raise the temperature 10C above ambient at idle, more when pushed hard. This is the same heatsinking I use for the NAKSA 100, you are correct.
I would think 4R loads would push this amp. It would work OK, but strain it at high volume. I would think 6R should be the minimum at highish volume. In this connection it's not dissimilar to the AKSA/Lifeforce 55.
At 350mA idle current with an 8R load, the first half watt would be pure Class A. At 750mA idle current (54W dissipation into the heatsink, 22C temp rise above ambient at idle), we get a full 2.25 watts of Class A. This is surprisingly loud in fact and is essentially a Class A power amplifier.
Thank you for your interest,
Hugh
Yes, one 300x75 mm heatsink per channel, each rated to 0.4C/W. Each channel (one board) will dissipate around 25W, so that would raise the temperature 10C above ambient at idle, more when pushed hard. This is the same heatsinking I use for the NAKSA 100, you are correct.
I would think 4R loads would push this amp. It would work OK, but strain it at high volume. I would think 6R should be the minimum at highish volume. In this connection it's not dissimilar to the AKSA/Lifeforce 55.
At 350mA idle current with an 8R load, the first half watt would be pure Class A. At 750mA idle current (54W dissipation into the heatsink, 22C temp rise above ambient at idle), we get a full 2.25 watts of Class A. This is surprisingly loud in fact and is essentially a Class A power amplifier.
Thank you for your interest,
Hugh
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Done, Chris, thanks for the interest!
Do we have a mutual acquaintance, Ian McP?
Keep 'em rolling, now up to 34 boards. Check the graphic from #44, just been updated.
2 JoMo Adelaide SA Australia
2 Ian Finch Coffs Harbour NSW Australia
2 Gennaji Hyderabad India
2 Ken Lewis LA USA
2 Ron Russell Kent UK
2 John Kenny Dublin Ireland
2 Francis Morrin Dublin Ireland
2 Vitalica Bucharest Romania
2 Erik Deinum Groningen Netherlands
2 Keith Correa ? India
2 Igor Polyakov California (city?) USA
2 Steve (aka SRH) Whangarei New Zealand
2 George (aka JKC) Calgary Canada
2 Anthony Mills Gold Coast Australia
2 Dinesh (aka Chlorofille) Christchurch New Zealand
2 Colin S. (?) (city?) NSW Australia
2 Chris Powell (?) Hong Kong China
Cheers,
Hugh
Do we have a mutual acquaintance, Ian McP?
Keep 'em rolling, now up to 34 boards. Check the graphic from #44, just been updated.
2 JoMo Adelaide SA Australia
2 Ian Finch Coffs Harbour NSW Australia
2 Gennaji Hyderabad India
2 Ken Lewis LA USA
2 Ron Russell Kent UK
2 John Kenny Dublin Ireland
2 Francis Morrin Dublin Ireland
2 Vitalica Bucharest Romania
2 Erik Deinum Groningen Netherlands
2 Keith Correa ? India
2 Igor Polyakov California (city?) USA
2 Steve (aka SRH) Whangarei New Zealand
2 George (aka JKC) Calgary Canada
2 Anthony Mills Gold Coast Australia
2 Dinesh (aka Chlorofille) Christchurch New Zealand
2 Colin S. (?) (city?) NSW Australia
2 Chris Powell (?) Hong Kong China
Cheers,
Hugh
HI Danny,
You're in!! Now at 36 boards. Check the graphic from #44 for the PCB update.
2 JoMo Adelaide SA Australia
2 Ian Finch Coffs Harbour NSW Australia
2 Gennaji Hyderabad India
2 Ken Lewis LA USA
2 Ron Russell Kent UK
2 John Kenny Dublin Ireland
2 Francis Morrin Dublin Ireland
2 Vitalica Bucharest Romania
2 Erik Deinum Groningen Netherlands
2 Keith Correa ? India
2 Igor Polyakov California (city?) USA
2 Steve (aka SRH) Whangarei New Zealand
2 George (aka JKC) Calgary Canada
2 Anthony Mills Gold Coast Australia
2 Dinesh (aka Chlorofille) Christchurch New Zealand
2 Colin S. (?) (city?) NSW Australia
2 Chris Powell (?) Hong Kong China
2 Danny (?) Lierde Belgium
Cheers,
Hugh
You're in!! Now at 36 boards. Check the graphic from #44 for the PCB update.
2 JoMo Adelaide SA Australia
2 Ian Finch Coffs Harbour NSW Australia
2 Gennaji Hyderabad India
2 Ken Lewis LA USA
2 Ron Russell Kent UK
2 John Kenny Dublin Ireland
2 Francis Morrin Dublin Ireland
2 Vitalica Bucharest Romania
2 Erik Deinum Groningen Netherlands
2 Keith Correa ? India
2 Igor Polyakov California (city?) USA
2 Steve (aka SRH) Whangarei New Zealand
2 George (aka JKC) Calgary Canada
2 Anthony Mills Gold Coast Australia
2 Dinesh (aka Chlorofille) Christchurch New Zealand
2 Colin S. (?) (city?) NSW Australia
2 Chris Powell (?) Hong Kong China
2 Danny (?) Lierde Belgium
Cheers,
Hugh
Hugh
Let me stop lurking around your products and jump in with four boards.
What is the possibility that the critical parts can be supplied with the boards- matched etc? In my experience many great project have died a slow death when you cannot source the correct parts or are possibly buying fakes.
Jozua
Cape Town
South Africa
Let me stop lurking around your products and jump in with four boards.
What is the possibility that the critical parts can be supplied with the boards- matched etc? In my experience many great project have died a slow death when you cannot source the correct parts or are possibly buying fakes.
Jozua
Cape Town
South Africa
HI Sonnya, Jozua,
Added to the list, thank you for both for your interest, we are now at 42 boards, a very good effort for a budding project:
2 JoMo Adelaide SA Australia
2 Ian Finch Coffs Harbour NSW Australia
2 Gennaji Hyderabad India
2 Ken Lewis LA USA
2 Ron Russell Kent UK
2 John Kenny Dublin Ireland
2 Francis Morrin Dublin Ireland
2 Vitalica Bucharest Romania
2 Erik Deinum Groningen Netherlands
2 Keith Correa ? India
2 Igor Polyakov California (city?) USA
2 Steve (aka SRH) Whangarei New Zealand
2 George (aka JKC) Calgary Canada
2 Anthony Mills Gold Coast Australia
2 Dinesh (aka Chlorofille) Christchurch New Zealand
2 Colin S. (?) (city?) NSW Australia
2 Chris Powell (?) Hong Kong China
2 Danny (?) Lierde Belgium
2 Sonnya (?) City (?) Denmark
4 Jozua Cape Town South Africa
Joz, I think your point is a very good one. Parts, particularly jfets and small mosfets, are hard to find. I think we could supply:
1. 2SK170BL input jfet
2. ZVP2110G VAS mosfet
3. DN2530 bootstrap mosfet (TO92)
4. Lag comp and phase lead silver micas
This would leave only the output lateral fets and the passives, which I think is probably about how you'd want it? The only concern I have is packaging; the envelope would then be more than two thicknesses of pcbs, a bit on the lumpy side, and this would attract much higher shipping. However, it at least ensures that the parts chasing is minimised, and the components would all be guaranteed genuine as they'd come from Mouser/Digikey.
Cheers,
Hugh
Added to the list, thank you for both for your interest, we are now at 42 boards, a very good effort for a budding project:
2 JoMo Adelaide SA Australia
2 Ian Finch Coffs Harbour NSW Australia
2 Gennaji Hyderabad India
2 Ken Lewis LA USA
2 Ron Russell Kent UK
2 John Kenny Dublin Ireland
2 Francis Morrin Dublin Ireland
2 Vitalica Bucharest Romania
2 Erik Deinum Groningen Netherlands
2 Keith Correa ? India
2 Igor Polyakov California (city?) USA
2 Steve (aka SRH) Whangarei New Zealand
2 George (aka JKC) Calgary Canada
2 Anthony Mills Gold Coast Australia
2 Dinesh (aka Chlorofille) Christchurch New Zealand
2 Colin S. (?) (city?) NSW Australia
2 Chris Powell (?) Hong Kong China
2 Danny (?) Lierde Belgium
2 Sonnya (?) City (?) Denmark
4 Jozua Cape Town South Africa
Joz, I think your point is a very good one. Parts, particularly jfets and small mosfets, are hard to find. I think we could supply:
1. 2SK170BL input jfet
2. ZVP2110G VAS mosfet
3. DN2530 bootstrap mosfet (TO92)
4. Lag comp and phase lead silver micas
This would leave only the output lateral fets and the passives, which I think is probably about how you'd want it? The only concern I have is packaging; the envelope would then be more than two thicknesses of pcbs, a bit on the lumpy side, and this would attract much higher shipping. However, it at least ensures that the parts chasing is minimised, and the components would all be guaranteed genuine as they'd come from Mouser/Digikey.
Cheers,
Hugh
Last edited:
Hugh
Yes I am interested in the additional parts for four boards
1. 2SK170BL input jfet
2. ZVP2110G VAS mosfet
3. DN2530 bootstrap mosfet (TO92)
4. Lag comp and phase lead silver micas
Nothing spoils a project than having to wait 2-3 weeks for parts to arrive and then having to wait another 2-3 weeks if more parts are required.
With so little components would there be any benefit in going for exotic parts g. special resistors or Mundorf caps ?
Two proposals:
1. The switch-on thumb is some concern to me- how about adding a speaker relay section to the pcb?
2. How about publishing a parts list with the critical (exotic) parts identified?
Thanks
Jozua
PS. I am hoping this amp will be a better option that Carlos DX amp ?
Yes I am interested in the additional parts for four boards
1. 2SK170BL input jfet
2. ZVP2110G VAS mosfet
3. DN2530 bootstrap mosfet (TO92)
4. Lag comp and phase lead silver micas
Nothing spoils a project than having to wait 2-3 weeks for parts to arrive and then having to wait another 2-3 weeks if more parts are required.
With so little components would there be any benefit in going for exotic parts g. special resistors or Mundorf caps ?
Two proposals:
1. The switch-on thumb is some concern to me- how about adding a speaker relay section to the pcb?
2. How about publishing a parts list with the critical (exotic) parts identified?
Thanks
Jozua
PS. I am hoping this amp will be a better option that Carlos DX amp ?
Hi Jozua,
You raise good points, however, let me explain the switch on thump issue in some depth.
Most amps have a thump at switch on. It's an inevitable aspect of transitions in the operating state, but it has surprisingly large tolerance.
First up, the thump affects only the speaker driver, which responds to the slow AC - almost DC - voltage across its voice coil.
If the amp is carefully designed, these thumps are infrasonic, and take about 200mS to settle. This is about five Hertz and not audible as a note, rather, as a gentle thump. In most instances, and particularly in this case, the sound is on the same level as a robust toggle switch, and is not easily heard. Greg has verified this, and Paul and I have done extensive LTSpice modelling to assess the size of this spike, which generally is always smaller in reality than Spice believes.
Question: Why not use a relay to disconnect the speaker until it settles?
The issue of 'protection' is hugely discussed but involves quite a bit of additional complexity. A suitable relay would have capacity to pass tiny currents without impedance or diodic effects, but very heavy currents when someone hits the bass guitar hard. It turns out these requirements are particularly onerous, and to my knowledge only Omron and Amplimo have products specifically designed for this task. They both use small gold contacts which initially close, then much larger tungsten/berrylium contacts closing a short time later.
A control circuit, with tailored delays - 200mS on switch on and immediate deactivation when the amp is turned off - is required. While you are about it, you might as well put in DC protection, which senses any current over a volt or two and deactivates the relay to protect the speakers. These measures are expensive, and while they are not too complicated, they increase component count by perhaps 30%.
Let's examine the 'damage' done by these transition thumps. Let's assume a worst case 8V for 100mS. Now, if we use a driver of nominal 8R impedance, it normally has a DC resistance around 6.8R. This means that an 8V spike will generate a max current through it of around 1.2A. This corresponds to Iexp2R watts, or just under 10 watts, but the duration will be less than 200mS, and in truth this is only the peak dissipation, held for only a few short milliseconds since the spike peak is of exceptionally short duration. The dissipation for the entire 200mS switching transistion probably averages about 1W.
Even the smallest drivers have a continuous dissipation in excess of 10 watts. The most sensitive speakers are full rangers of high sensistivity, and even the Fostex 208 sigma is rated to 37 watts continuous. So, 10 watts is mere bagatelle, simply warming the coil for its task ahead.
Further if the sound emitted is not actually a note, but an infrasonic, slow moving spike, then the sound serves usefully to inform the listener that the amp is on and all is well.
For a 200W amplifier, the situation may be different. This spike could be tens of volts, and the potential damage, particularly to small drivers, could be very real. This is not the case here with a 50 watt amplifier using only 36 volt rails.
The original intent here, and Lineup will correct me if I'm wrong, is to design a very simple, elegant amplifier with minimal components. There is always the temptation to make things more complicated than required; but this defeats the purpose of the exercise for the DIYer who wants something simple and easy to get going. There is a strong drive to preserve the 'simpler is better' ethic here.
I would say, therefore, that an output relay - which some say affects the sound quality by the way - is not necessary in this application. However, if you would like one, you should consider giving it DC sense as well. The module should be offboard, with the relay a special component specifically designed for audio switching, and it will require its own power supply, of course.
When I originally published my proposed pcb design I mentioned that SWF, whose design this is, was in Europe on holiday. He won't be back for another eight days or so, ash clouds permitting, and since he is doing the listening tests and development, I won't be stealing any thunder and publishing the parts list until he has signed off. After all, he's built it, I'm only the layout handmaiden. This is simply courtesy, but it will require patience from interested folk here. That's cool for me, I'm pretty old, but for the young ones, it won't be over until the fat lady sings!
I am sorry for delays, as it happens I'm in another city attending to difficult family matters, and I'm not much use on building or listening tests either.
I hope this puts my view on the matter, that you follow the arguments, and that I haven't put Greg's nose out of joint. He is the guru here because his assessment and energy is behind the evolution of Lineup's outstanding idea, and I defer to him, and of course to Mikelm as well.
Thanks for your indulgence,
Cheers,
Hugh
You raise good points, however, let me explain the switch on thump issue in some depth.
Most amps have a thump at switch on. It's an inevitable aspect of transitions in the operating state, but it has surprisingly large tolerance.
First up, the thump affects only the speaker driver, which responds to the slow AC - almost DC - voltage across its voice coil.
If the amp is carefully designed, these thumps are infrasonic, and take about 200mS to settle. This is about five Hertz and not audible as a note, rather, as a gentle thump. In most instances, and particularly in this case, the sound is on the same level as a robust toggle switch, and is not easily heard. Greg has verified this, and Paul and I have done extensive LTSpice modelling to assess the size of this spike, which generally is always smaller in reality than Spice believes.
Question: Why not use a relay to disconnect the speaker until it settles?
The issue of 'protection' is hugely discussed but involves quite a bit of additional complexity. A suitable relay would have capacity to pass tiny currents without impedance or diodic effects, but very heavy currents when someone hits the bass guitar hard. It turns out these requirements are particularly onerous, and to my knowledge only Omron and Amplimo have products specifically designed for this task. They both use small gold contacts which initially close, then much larger tungsten/berrylium contacts closing a short time later.
A control circuit, with tailored delays - 200mS on switch on and immediate deactivation when the amp is turned off - is required. While you are about it, you might as well put in DC protection, which senses any current over a volt or two and deactivates the relay to protect the speakers. These measures are expensive, and while they are not too complicated, they increase component count by perhaps 30%.
Let's examine the 'damage' done by these transition thumps. Let's assume a worst case 8V for 100mS. Now, if we use a driver of nominal 8R impedance, it normally has a DC resistance around 6.8R. This means that an 8V spike will generate a max current through it of around 1.2A. This corresponds to Iexp2R watts, or just under 10 watts, but the duration will be less than 200mS, and in truth this is only the peak dissipation, held for only a few short milliseconds since the spike peak is of exceptionally short duration. The dissipation for the entire 200mS switching transistion probably averages about 1W.
Even the smallest drivers have a continuous dissipation in excess of 10 watts. The most sensitive speakers are full rangers of high sensistivity, and even the Fostex 208 sigma is rated to 37 watts continuous. So, 10 watts is mere bagatelle, simply warming the coil for its task ahead.
Further if the sound emitted is not actually a note, but an infrasonic, slow moving spike, then the sound serves usefully to inform the listener that the amp is on and all is well.
For a 200W amplifier, the situation may be different. This spike could be tens of volts, and the potential damage, particularly to small drivers, could be very real. This is not the case here with a 50 watt amplifier using only 36 volt rails.
The original intent here, and Lineup will correct me if I'm wrong, is to design a very simple, elegant amplifier with minimal components. There is always the temptation to make things more complicated than required; but this defeats the purpose of the exercise for the DIYer who wants something simple and easy to get going. There is a strong drive to preserve the 'simpler is better' ethic here.
I would say, therefore, that an output relay - which some say affects the sound quality by the way - is not necessary in this application. However, if you would like one, you should consider giving it DC sense as well. The module should be offboard, with the relay a special component specifically designed for audio switching, and it will require its own power supply, of course.
When I originally published my proposed pcb design I mentioned that SWF, whose design this is, was in Europe on holiday. He won't be back for another eight days or so, ash clouds permitting, and since he is doing the listening tests and development, I won't be stealing any thunder and publishing the parts list until he has signed off. After all, he's built it, I'm only the layout handmaiden. This is simply courtesy, but it will require patience from interested folk here. That's cool for me, I'm pretty old, but for the young ones, it won't be over until the fat lady sings!
I am sorry for delays, as it happens I'm in another city attending to difficult family matters, and I'm not much use on building or listening tests either.
I hope this puts my view on the matter, that you follow the arguments, and that I haven't put Greg's nose out of joint. He is the guru here because his assessment and energy is behind the evolution of Lineup's outstanding idea, and I defer to him, and of course to Mikelm as well.
Thanks for your indulgence,
Cheers,
Hugh
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Hugh
Thanks for the detailed reply.
I am possibly moving towards an active speaker implementation with a DEQX setup, hence the concern that a thump could be a risk for the tweeters. If need be I will address the issue via a separate relay board.
Basically I just want two identical amps that could give my "old" class A amp serious competition.
Regards.
Jozua
Thanks for the detailed reply.
I am possibly moving towards an active speaker implementation with a DEQX setup, hence the concern that a thump could be a risk for the tweeters. If need be I will address the issue via a separate relay board.
Basically I just want two identical amps that could give my "old" class A amp serious competition.
Regards.
Jozua
Hi Sam,
Welcome to our thread - agree emphatically. A quality cap in series with a tweeter is a great idea, and with a conventional, passive filter, it is the norm anyway.
George,
The caps are both 6,800uF and the linking resistors are 0.15R, with time constant around 14Hz. The idea is to reduce rectifier charge pulses into the cap closest to the amplifier output stage. This in turn removes some of the switching noise in that cap and reduces intermodulation with the voice coil return currents from the speaker.
Anthony,
No problem, you're in, thank you for your interest. I need to do some sums on this, it will increase cost, but it won't be too much. I will likely solder in the VAS as well.
Cheers,
Hugh
Welcome to our thread - agree emphatically. A quality cap in series with a tweeter is a great idea, and with a conventional, passive filter, it is the norm anyway.
George,
The caps are both 6,800uF and the linking resistors are 0.15R, with time constant around 14Hz. The idea is to reduce rectifier charge pulses into the cap closest to the amplifier output stage. This in turn removes some of the switching noise in that cap and reduces intermodulation with the voice coil return currents from the speaker.
Anthony,
No problem, you're in, thank you for your interest. I need to do some sums on this, it will increase cost, but it won't be too much. I will likely solder in the VAS as well.
Cheers,
Hugh
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