Cathode follower w/ coupling cap

[Russ]

Happy New year everybody!

In the last stage of my preamp, I've got a 12ax7 cathode follower with a 100k cathode resistor, like on a marshall. But I'm not following it with the usual tone stack, but with just a coupling capacitor coming off the cathode resistor/cathode junction. My question is in regard to what's a reasonable value for the coupling cap - how do you calculate the -3 db point for this arrangement? There's going to be a 500k load resistor after the cap.

I'm thinking that you would use the: Cuttoff frequency = 1 / 2*pi(RC) formula, but I don't know what value to plug in for R

Thanks,
Russ

[chipaudette]

I'm no expert, but I believe that the "R" value that you need is the 100K cathode resistor in paralel with the 500 K load resistor after the coupling cap.

R = 100K || 500K = 1/(1/100K+1/500K)) = 83 K

Good luck!

Chip

[Merlinb]

The R value should be the load, 500k. Strictly speaking you should add the output impedance of the cathode follower to this, but because it's such a low value (less than 1k) there's no point.

[Russ]

Yes, I guess what I need for R is the output impedance of the CF. Does anyone know what this is, or better yet, how is it calculated?

[chipaudette]

I checked it in PSPICE and, yes, MerlinB is correct...the corner frequency due to the coupling cap is set by the 500K resistor. The cathode resistor has no effect.

Cool. I learned something.

Chip

[Chris / CMW amps]

No formula's (typo?) needed imho, just use your ears

Not knowing about the used circuit/voltages/transformers: just start with a 0.002 to 0.02uF couplingcap and it's fine in most circuits.

[mytco]

Hi Russ,

From the formula on Randall Aiken's site (also RDHB), the impedance looking into the cathode of a triode is found by the formula:

Rk' = (Rp+ra)/(mu+1)
where:
Rp=plate resistor
rp=anode impedance
mu=triode mu

(12AX7)Rk'=(0+62500)/(100+1)= 619

R= Rk||Rk'
R= (100K*619)/(100K+619)
R= 615

You will need to incorporate this value with the 500K load after the cap to come up with your -3db point.

R= (500K*615)/(500K+615)
R= 614 ohms

Pick your -3db frequency and calculate your cap value.

C=1/(2*pi*R*f)

Hope this helps.

Michael

[Russ]

Thanks a bunch for spotting that. I looked at the Aiken site but didn't look deep enough because the article was for "Common-Cathode Triode Amplifiers" - it didn't specifically say cathode follower.

Anyway, if you're right about the equation, then using conventional coupling cap values (.05u to .001u) would be too small.

When I use 614R for the output impedance, to get the equivalnet response of a .0022u cap (-3db = 134hz) with a conventional anode follower stage, my cathode follower coupling cap would have to be about 19uf - big difference!:

134hz = 1 / 6.28 * 614R * 19.4uf
= 1 / 6.28 * 614R * .000,001,94

but 19uf "seems" a little too big, does this look right?

Thanks, Russ

[mytco]

Wouldn't that be 1.9uF?

[Russ]

Right, .000,001,9 is 1.9uf
.000,019 would be 19uf

The decimal point can be tricky when converting from uF to F

thanks

[Merlinb]

You will need to incorporate this value with the 500K load after the cap to come up with your -3db point.

R= (500K*615)/(500K+615)
R= 614 ohms

Pick your -3db frequency and calculate your cap value.

C=1/(2*pi*R*f)

There's a mistake here. As far as the cap is concerned, the cathode impedance and the load resistance are in series, not in parallel.
You should have added 615 to 500k.
R = 500615 ohms.

Fortunately the cathode impeance is so small that it makes no difference; there is no need to work out the cathode impadance, you can just use the load resistance.

[Russ]

An output impedance of 500,614 ohms can't be right because the output impedance of a 12ax7 anode follower stage with a 100k Rp and fully bypassed Rk is 38.5k (see www.aikenamps.com - Tech Info - Advanced - "Designing common-cathode triode amplifiers"). I know that cathode followers have a lower output impedance than anode followers, so the cathode follower output impedance must be less than 38.5k

[Bruce / Mission Amps]

For many years, I've used a 100nF to 330nF poly cap in this place (simply to block DC from the grid of the next stage)... with virtually no audible difference in bandwidth.
I suggest you divert from the techno, whiz-bang, woof - woof stuff and trust your ears on this one... you'll learn more about what sounds good rather then what reads good on the NET, impresses neophytes or looks good on a scope.

[Russ]

Well I always trust my ears, but I'd still like to know what the bloody output imp. is.

[Merlinb]

An output impedance of 500,614 ohms can't be right

That's not the output impedance, it's the impedance seen by the capacitor. Imagine standing on the capacitor, look in both directions (down each lead). In one direction you see the output impedance of the cathode follower, which is about 615 ohms or whatever. In the other direction you see the 500k load resistor. The total impedance in series with the capacitor is therefore 500615 ohms, and that's the figure you use to get you cap value/freq' roll-off, etc.

The same is true for a regular gain stage and coupling cap. In one direction you see the output impedance of the previosu stage (38.5k as you said) and in the other you see the load, which is usually a 1M pot. The total resistance in series with the coupling cap is therefore 1038500 ohms.