How do I mimic a cathode bypass cap/resistor's frequency response in a non-tube circuit?

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15
I've been using this calculator to figure out the frequency response of the gain stages in my amps:


I'd love to be able to approximate this on a breadboard, but I don't understand the math behind why a 2.7k resistor and 0.68uF cap creates such a dropoff in lows from 1kHz on down. When I put those numbers in an RC hi pass calculator it gives a corner frequency of 86Hz, so I don't understand the other factors at play in a tube gain stage that causes those values to roll off at a higher corner frequency.

Could you help me understand how to approximate the low end rolloff of a cathode bypass cap/resistor with a simple CR non-tube circuit on a breadboard?

Thanks!
 
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pdf64

Member
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8,917
I don't understand the math behind why a 2.7k resistor and 0.68uF cap creates such a dropoff in lows from 1kHz on down. When I put those nubmers in an RC hi pass calculator it gives a corner frequency of 86Hz
When you see such frequency response charts, the key frequency to note is that at which the output has dropped by 3dB.

You may need to consider the valve’s internal cathode resistance.
That’s why the output impedance of a cathode follower is much lower than the typical 100k or 56k cathode resistor.
Hence 2k7, whilst it play a part, is not the relevant R term.
See Aiken http://aikenamps.com/index.php/designing-common-cathode-triode-amplifiers

I prefer this calculator, the display seems better, it cites its source, and its results have been peer reviewed http://bmamps.com/CapCal.html

Could you help me understand how to approximate the low end rolloff of a cathode bypass cap/resistor with a simple CR non-tube circuit on a breadboard?
So a passive circuit, or what?
If passive, the source and load impedances will be key design constraints.
 
Messages
15
When you see such frequency response charts, the key frequency to note is that at which the output has dropped by 3dB.

You may need to consider the valve’s internal cathode resistance.
That’s why the output impedance of a cathode follower is much lower than the typical 100k or 56k cathode resistor.
Hence 2k7, whilst it play a part, is not the relevant R term.
See Aiken http://aikenamps.com/index.php/designing-common-cathode-triode-amplifiers

I prefer this calculator, the display seems better, it cites its source, and its results have been peer reviewed http://bmamps.com/CapCal.html


So a passive circuit, or what?
If passive, the source and load impedances will be key design constraints.
Thanks! When I nudge the sliders to 2.7k for the resistor and adjust the "desired half boost frequency" until the capacitor value is 0.68 at the bottom of the page, I end up with a half boost frequency of 109.6Hz. I'm not sure what "half boost" means in this case, but when I mouse over the graph it looks like the 3dB down point is at 200Hz. The cathode bypass frequency response looks like a low shelf, but for 80Hz and up it looks like it behaves close to a high pass, and when I mess around with an RC calculator it looks like I could get a high pass filter with corner frequency of 194 by using a 0.1uF capacitor and an 8.2kOhm resistor.

I'm new to this and don't fully understand impedance, so I've been building little passive EQ circuits on breadboards in between a pair of Boss pedals so the circuit is isolated between the 1k-10k output impedance of the first Boss pedal and the 1M input impedance of the 2nd Boss pedal. Do you think a 0.1uF/8.2kOhm passive high pass would be fine, or would it be more ideal if the cap and resistor were some other combination that also results in a ~200Hz corner frequency? (like 8.2MOhm and 0.1nF as an example)
 

Trem-o-lux

Member
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1,188
I think you want to duplicate the shelving behaviour of the bypass cap, and so you do not want a simple RC filter. The bypassed cathode gives you a gain at low frequencies that is constant, and a gain at high frequencies that is constant, and a crossover region in between. You can duplicate that with a RC high-pass filter (i.e. signal passes through a cap and the output of the cap is loaded by a resistor to ground) to which you add a resistor in parallel with the cap. At low frequencies the parallel resistor limits the attenuation, so you get a shelf instead of a roll-off that just keeps rolling off...

An example of a network like that is the 470k/470pF shelf between stages in a Marshall 2203.
 

pdf64

Member
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8,917
I'm not sure what "half boost" means in this case
I think it means the halfway between the upper and lower shelves. So about -4.5dB in this case.
I've been building little passive EQ circuits on breadboards in between a pair of Boss pedals so the circuit is isolated between the 1k-10k output impedance of the first Boss pedal and the 1M input impedance of the 2nd Boss peda
Consider a potential divider, upper resistor 100k, lower 47k.
Then bypass the 100k with around 15nF.
That should form a treble boosted shelf about 9dB above the low frequency shelf, with the -3dB point roughly in the right area.

Those values should work nicely with your pedal buffers.

Do you think a 0.1uF/8.2kOhm passive high pass would be fine
I suggest to scale those values by 10 to get things in the right ballpark for a reasonable impedance bridge with the boss pedal buffers, ie 82k and 10nF.
 
Messages
15
I think you want to duplicate the shelving behaviour of the bypass cap, and so you do not want a simple RC filter. The bypassed cathode gives you a gain at low frequencies that is constant, and a gain at high frequencies that is constant, and a crossover region in between. You can duplicate that with a RC high-pass filter (i.e. signal passes through a cap and the output of the cap is loaded by a resistor to ground) to which you add a resistor in parallel with the cap. At low frequencies the parallel resistor limits the attenuation, so you get a shelf instead of a roll-off that just keeps rolling off...

An example of a network like that is the 470k/470pF shelf between stages in a Marshall 2203.
Alright, so make the RC high pass with the -3dB corner frequency that I'm looking to achieve, then add a resistor in parallel with the cap to keep the lows from rolling off continuously. Cool. How do I figure out the value of the parallel resistor I'd need? Is this concept similar to a bright cap around a volume pot, except instead of the pot it's 2 fixed resistors?

 
Messages
15
I think it means the halfway between the upper and lower shelves. So about -4.5dB in this case.

Consider a potential divider, upper resistor 100k, lower 47k.
Then bypass the 100k with around 15nF.
That should form a treble boosted shelf about 9dB above the low frequency shelf, with the -3dB point roughly in the right area.

Those values should work nicely with your pedal buffers.


I suggest to scale those values by 10 to get things in the right ballpark for a reasonable impedance bridge with the boss pedal buffers, ie 82k and 10nF.
Thanks for helping me visualize that. Why 100k and 47k for the two resistors in your example?

Scaling by 10x for a reasonable impedance bridge makes sense, thanks for pointing that out.
 

reaiken

Member
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1,971
Here ya go. Green is the typical tube response with a 68k input resistor, Red is a passive implementation with equivalent response.

If you don't want the HF rolloff, eliminate R6 and C3. If you want to simulate the effect of a 33k grid resistor, change C3 to 47pF.

Note that the source impedance of the passive filter, simulated as R4 below, must be very small to get the correct response, so it is best driven from a buffer with no build-out resistor.

However, if your source impedance is relatively small compared to the 100K filter resistance, the error will be minimal. For example, a 10k source will only affect it about one dB or so. You could also scale the filter for a higher resistance, such as 470k, to further minimize the effect of a non-zero source impedance. Use the impedance scaling calculations shown here: https://www.aikenamps.com/index.php/tone-control-scaling

Also note that this circuit does not simulate the effect of the load on the output of the tube stage.


PassiveShelvingEQ_sch.jpg


PassiveShelvingEQ_ac_sweep.jpg
 
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Messages
15
Here ya go. Green is the typical tube response with a 68k input resistor, Red is a passive implementation with equivalent response.

If you don't want the HF rolloff, eliminate R6 and C3. If you want to simulate the effect of a 33k grid resistor, change C3 to 47pF.

Note that the source impedance of the passive filter, simulated as R4 below, must be very small to get the correct response, so it is best driven from a buffer with no build-out resistor.

However, if your source impedance is relatively small compared to the 100K filter resistance, the error will be minimal. For example, a 10k source will only affect it about one dB or so. You could also scale the filter for a higher resistance, such as 470k, to further minimize the effect of a non-zero source impedance.

Also note that this circuit does not simulate the effect of the load on the output of the tube stage.


View attachment 644794

View attachment 644796
Wow, thanks for putting in the work for me, Randall, it's very appreciated. I'll be tinkering with this.
 




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