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Hoffman Amps Forum image Author Topic: Need help with 2nd gain stage calculation  (Read 3210 times)

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Offline RobBozic

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Need help with 2nd gain stage calculation
« on: January 28, 2015, 06:25:33 pm »
Hi,
 
I've done a cascaded 2nd gain stage (see attachment) in a 5F6A style amp.
I've used the JCM800 style 2nd gain stage consisting of a 100K anode / 10K cathode / 2.7n coupling cap into a 1M pot (DRIVE) with a 120K resistor hanging of the tail to ground. I inserted this 2nd gain stage on a switch and I noticed with the 2nd gain stage engaged and at '0' DRIVE volume the 2nd gain engaged it didn't add any additional gain, which was my aim. Therefore, I can then just dial in how much extra gain I require. However, I noticed some top end loss.
 
If I scale down the DRIVE pot to say 250K and scale up the 2.7n cap to 10n, this will increase the top end? However, I have no idea on how to calculate this? and how to calculate how much top end loss I was losing etc...
 
Also, what do I do with the 120K resistor hanging of the tail, I'm assuming this has to reduce in value as well (say 120K to 33K).
 
My aim is to have the DRIVE control at '0' and have it effectively not contributing any gain or causing any top end loss. Can someone help with the math?
 
Thanks for your help
Rob

Offline HotBluePlates

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Re: Need help with 2nd gain stage calculation
« Reply #1 on: January 28, 2015, 07:03:43 pm »
... a 1M pot (DRIVE) with a 120K resistor hanging of the tail to ground. ... at '0' DRIVE ... I noticed some top end loss.

The top end loss happens as you dial down to 0; when that happens, you have 1MΩ in series with the tube grid. This resistance interacts with the input capacitance of the next stage.

Input capacitance is given on a 12AX7 data sheet as at least 1.6pF, but that is probably just grid-to-cathode. Also given is grid-to-plate capacitance (1.7pF) which is then amplified by the tube's stage gain. Without doing the math to verify your 3rd stage gain, I'll guess a bit high at 60. So input capacitance = 1.6pF + 1.7pF * 60 = ~104pF. Add to that stray capacitance to ground for wiring (you might guess this as high as an additional 100pF, but we'll ignore it for now).

F-3dB = 1/(2*pi*R*C) = ~1.1kHz

You can't directly reduce tube or stray capacitance. The coupling cap doesn't really factor in, because at/above 1kHz where the roll-off is happening the cap appears substantially as a short-circuit. So you'd do just as you thought: scale down the pot and tail resistance, and scale up the coupling cap to keep the same bass roll-off.

With 250kΩ pot and ~30kΩ to ground, F-3dB = 1/(2*pi*R*C) = 1/(2*pi*250kΩ*104 * 10-12) = ~6.1kHz

That roll-off may not be substantially worse than the normal treble roll-off of the speaker. Now that the load after the 2nd stage is reduced, you may want to go back to the 2nd gain stage calculations to see if you need such a high cathode resistor to choke back gain. Or maybe you'll consider a different plate load resistor, or both.

Or maybe you'd reduce gain at stage 2 & 3 a different way, if you needed to extend treble response even higher. Maybe a feedback loop from 3rd stage plate to 2nd stage cathode, with normal-gain-stage cathode resistance in the 2nd stage. The amount of feedback would be the ratio of the resistor from the 3rd-stage plate to the 2nd-stage cathode, working against the 2nd-stage cathode resistance. Add a largish blocking cap and a pot as part of the interstage resistance, and you've got controllable feedback & gain.

Offline HotBluePlates

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Re: Need help with 2nd gain stage calculation
« Reply #2 on: January 28, 2015, 07:13:02 pm »
Oh yeah... Instead of passing the 1st gain stage output through a volume control and then a voltage divider which cuts output by half, why not just remove the cathode bypass cap? That will also cut stage gain by about half with the cathode resistor you have shown.

Offline jjasilli

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Re: Need help with 2nd gain stage calculation
« Reply #3 on: January 28, 2015, 07:40:06 pm »

I'm thinking that with the drive pot @ -0-, the next stage grid leak resistance is only 120K, the resistor under the drive pot.  Anything under 220K into a 12a_7 tube is really low and will probably darken tone. 


Oh yeah... Instead of passing the 1st gain stage output through a volume control and then a voltage divider which cuts output by half, why not just remove the cathode bypass cap? That will also cut stage gain by about half with the cathode resistor you have shown.


That will leave gain roughly the same.  But that nice little 2.2uF bypass cap is "boosting" highs at the 1st stage; so it's removal might darken the amp. 


Other options might be:  reduce the value of the bypass cap on the vol pot.  And/or at the voltage divider after the vol pot, bypass the series resistor with a 470pF or smaller cap.  Perhaps these things will boost hi's enough to compensate for the small grid leak resistor under the drive pot.  Or increase the value of that resistor to at least 220K.  (Then maybe reduce the value of the pot.)   
« Last Edit: January 28, 2015, 07:43:02 pm by jjasilli »

Offline HotBluePlates

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Re: Need help with 2nd gain stage calculation
« Reply #4 on: January 28, 2015, 09:46:05 pm »
I'm thinking that with the drive pot @ -0-, the next stage grid leak resistance is only 120K, the resistor under the drive pot.  Anything under 220K into a 12a_7 tube is really low and will probably darken tone.

Remember that resistance by itself has no frequency-dependent effect. A purely-resistive circuit creates the same voltage drops at any given point for all applied frequencies.

It's when you add C or L that the circuit becomes frequency-dependent. In this case, it's C added which ultimately has the effect of a small capacitance to ground. That forms a low-pass (or hi-cut) filter. Making any series-R large moves the -3dB point of the filter lower and lower, cutting more highs.

Compare to the 68kΩ input resistors at a 1st gain stage. 0Ω causes no high-frequency roll-off, 34kΩ causes some roll-off, 68kΩ moves the -3dB point lower (which is equivalent to more roll-off at the 34kΩ -3dB frequency), 1MΩ moves the -3dB point very much lower.

I think you're thinking of a series-C and shunt-R, which forms a high-pass (low-cut) filter, where smaller R moves the -3dB point higher thereby cutting more lows.


I'm thinking that with the drive pot @ -0-, the next stage grid leak resistance is only 120K, the resistor under the drive pot.  Anything under 220K into a 12a_7 tube is really low and will probably darken tone. 


Oh yeah... Instead of passing the 1st gain stage output through a volume control and then a voltage divider which cuts output by half, why not just remove the cathode bypass cap? That will also cut stage gain by about half with the cathode resistor you have shown.

That will leave gain roughly the same.

Right. I wanted to leave roughly the same net-effect as the circuit he's using, but with fewer parts. Arguably, it might result in marginally-less noise, because there's fewer resistances in the circuit. Really, I just thought it more effective if he wants a net-gain of half (and max volume) of what is at the V1's plate to simply amplify only half as much at V1.

But that nice little 2.2uF bypass cap is "boosting" highs at the 1st stage; so it's removal might darken the amp.

It's best to see the cathode bypass cap as reducing local negative feedback to increase gain. At some frequency, the cap becomes a less-effective bypass and gain begins to revert to the with-feedback level. The cap value by itself can't tell you what that frequency will be; you have to plug it into the formula along with R. Where R and XC are equal, there is -3dB in response.

"R" for the equation is really Rk in parallel with the resistance seen looking into the cathode [which is rp/(mu+1)], but it's usually close enough to use  Rk, and know the frequency will be a little higher than calculated. It's even better to check by ear after you have a guess of a suitable bypass cap value.

F-3dB = 1/(2*pi*R*C) = 1/(2*pi*1.5kΩ*2.2uF) = ~48Hz

You can estimate there will be roughly no roll-off an octave higher than the -3dB point, which means almost no cut at a guitar's low E. So removing the cap should cut gain by about half while leaving tonal balance substantially the same.

In any event, it's a quick test to remove 3 components and see if the result is judged worthwhile. If no-good, it's easy to put them back.

Offline RobBozic

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Re: Need help with 2nd gain stage calculation
« Reply #5 on: January 29, 2015, 08:25:41 pm »
Thanks for the help gents.
 
I'll remove the 2.2 cathode cap, the 470K voltage divider, and scale down the DRIVE control and then tweak from there.
 
Rob

Offline 2deaf

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Re: Need help with 2nd gain stage calculation
« Reply #6 on: January 29, 2015, 10:07:06 pm »
I'll remove the 2.2 cathode cap, the 470K voltage divider, and scale down the DRIVE control and then tweak from there.

jjasilli was talking about a 470pf bypass cap. across the first 470K resistor in the 470K/470K voltage divider.  This arrangement gives a frequency response that is often associated with a "Marshall Sound".  If you are seeking such a sound, it would be better to follow jjasilli's advice than to remove the divider altogether. 

 


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