Cathode bypass calculator help

[tonescout]

Hi,

I have the following circuit and am trying to work out if I can get away with a smaller Cathode bypass capacitor on the 6c45 driver valve by calculation.


I managed to find someone quoting the plate resistance of the 6C45 at 2.5K and was using this calculator

But I got stuck on what the effective plate load is with the transformer, any help greatly received 🙂

Merry Christmas

Rich

 

[Merlinb]

You don't need to know the plate load, you can use the formula:
f = 1/ (2 pi Rk Ck)
That gives you the frequency of the 'zero'. The pole won't be much higher.

 

[tonescout]

Thanks for this, I saw that in another thread, but also the discussion about the fact that this was incorrect (or incomplete) here

I guess looking at both of these calculations (and guessing plate load through the transformer) I think I can get away with 200uF or even 100uF, and not need 1000uF.

 

[rongon]

Question about this...
I've found that a shortcut for finding the value of Ck for f = 1Hz is 156,000/Rk.

If Rk = 330 ohms
156,000/330 = 472.73uF (470uF is closest standard value)

If Rk = 1.5k ohms
156,000/1500 = 104uF (100uF is closest standard value)

Is that useful, or is that just completely wrong?

 

[tonescout]

Thanks, but Rk is 108R so that would make it 1,447 uF which does not add up to other equations, where did this come from?

 

[rongon]

I think I remember reading that in an old electronics textbook, long ago. I've been using it because it has appeared to work for me. Let's test it.

If Rk = 108R and we want to get F3 = 1Hz

Example A, by the book:

f = 1/ (2 pi Rk Ck) (where Ck is given in Farads, not uF, so Ck = 0.0015, and 2pi = 6.283)
1/(6.283*108*0.0015) = 0.9825 Hz (1500uF is a standard value)

Example B, the shortcut:

156,000/108 = 1444uF (1500uF is closest standard value)
- That works well enough, I think.


1000uF instead of 1500uF:
1/(6.283*108*0.001) = 1.473 Hz

470uF instead of 1500uF:
1/(6.283*108*0.00047) = 3.1355 Hz

______________________

I guess all I can say is 156,000/Rk will put you in the ballpark for a value of Ck if the target is to bypass down to F3 = 1Hz.
That's a starting point. You can reduce the value of Ck as you see fit, to create the Rk//Ck high pass filter with a higher target F3 (-3dB zero frequency).

It appears that F3 rises in proportion to the reduction in value of Ck. If you decrease the value of Ck by 2, the F3 will be higher in frequency by 2. Let's test that:

For 100R, Ck = 1500uF gives you F3 of about 1Hz.

• Decrease the value of Ck to 1000uF -- reduced by one-third or 33% -- the F3 goes up by 33%, to 1.5Hz (actually 1.59Hz, but close enough).
• Decrease the value of Ck to 750uF -- reduced by 50% -- the F3 goes up by 2 to 2Hz (actually 2.122Hz, but again close enough).
• Decrease the value of Ck to 150uF -- reduced by 10x -- the F3 goes up by 10 to 15Hz (actually 15.9Hz, but again close enough).

For me, using a 150uF Ck in parallel with Rk=100R would put the F3 zero (= 15.9Hz) too close to the low end of the audio band (20Hz). But of course, YMMV.

Hopefully that's not just completely wrong. I'm hoping someone who has a better understanding can confirm or debunk, with an explanation why. Thanks.
--

 

[euro21]

The basic question is that what's the goal?
Most "linear" first stage LF bandwidth of IT loaded stage (where no secondary load)?
Most "linear" LF bandwidth of whole amplifier, where power tube OPT LF transfer hiding most of the previous stage LF behaviour?

 

[rongon]

That's a very good question!

If the input stage has a lot of gain, and the power supply impedance is high at infrasonic frequencies, reducing the value of Ck can cause positive feedback between the psu and gain stage at very low frequencies. That could even artificially boost audible bass frequencies.

So, your question begs the question, what does the power supply look like? Is it regulated (low impedance at all audio frequencies and lower)? Is it a very well filtered passive PSU with large values of L and/or C? Or is it a lightly filtered 'fast' passive type psu, using lower value film caps and relatively low values of series R and/or L?

 

[20to20]

I guess looking at both of these calculations (and guessing plate load through the transformer) I think I can get away with 200uF or even 100uF, and not need 1000uF.

You should choose the bypass cap size so that the frequencies below 20hz stay unbypassed for low freq. stability.

 

[soulmerchant]

Thanks, but Rk is 108R so that would make it 1,447 uF which does not add up to other equations, where did this come from?

For 100 ohms, the bias is not going to be very much so yes, your bypass cap could very well be un-necessary. The formula that has been noted is from the Radiotron Designer's Handbook, 4th edition, (Harrison: RCA, 1953), page 484. - F. Langford-Smith, editor.

I think rongon's math is not far off. "For 100R, Ck = 1500uF gives you F3 of about 1Hz." I calculated 1600uF for 1Hz. - do you listen to vinyl records? maybe you won't want such a low cut-off to hear the rumble of the record player...

For 20Hz, go for around 100uF. The precise value was 76.8uF

Also - I see '4x 25 ohm' allen bradley for the cathode resistor on your schematic. Just get a decent 100 ohm metal film. Btw - there is usually no problem finding 120 ohm metal film resistors if you want... Also, If you want, user higher valued resistors in parallel to trim to a precise value. I always find this to be much easier than resistors in series...

Ok.. here is the tough part: I hate to say this, but your schematic looks faulty to me. Maybe I am wrong. I hope so. Prove me wrong please. 🙂

The LL1660 has a source impedance of only 14k ohm. If you are trying to drop 860 volts across it's primary while drawing 13-16mA then Ohm's law tells me that won't work. I am assuming here you were wanting to do SE to SE Interstage 4 : 4.5 with this LL1660 right? I am pulling this 14k ohm primary impedance value straight off the Lundahl specs sheet.

Ohm's law tells me that your 6C45pi plate is going to be at 1000v-200v = 800V if this is the case... Is this what you wanted? or is your B+ on the 6C45pi something different than 1000v? Sorry for asking these painful questions. The other posters probably think the same thing but are hesitant to stick their fingers in the socket. Tell me that the value for the 6C45pi is a different B++ value than the B+ for the 211 and it is significantly lower than 1000v... 😉

Also those russian valves (tubes) are cheap for a reason (sorry to say). The 6C45pi sounds really good but you need to carefully measure and select them using a (digitally) calibrated valve (tube) tester to find ones that match the specs sheet (or for whatever purpose you want them for). They are supposed to have an amplification factor of 52, but I found most of them to be +/- 10% (sometimes more). Maybe 1/10 fit the specs sheet numbers. Of course you could buy a LOT of them and test them... Just warning you. I got a whole box of them years ago for less than $5 apiece. Now they want something rediculous like $40 apiece for them. The world is insane today....

That said, they are super nice sounding and rugged tubes. But clearly they were hard to build to a narrow standard. I ONLY use them with SS regulation. Then they sound FANTASTIC If (and only If) you can dial in the correct operating point and bias easily. That is hard to do with a plate choke vs. SS regulation.

You can consider looking for some other plate choke with much higher primary inductance... I think you will find that its hard to find an ideal one. Maybe you can wind your own (some DIY'ers do this). Eventually you might land on the idea to use a separate plate choke and inter-stage choke. Been there, done that. It gets HEAVY and needs additional space plus it costs a lot more than originally budgeted for...

Anyway, please advise us on this schematic - it seems to be missing some information for me at least.

 

[kgrlee]

The CATHODE bypass capacitor has little to do with the plate resistance. It needs to bypass the effective CATHODE resistance in parallel with the cathode resistor (your 124R).

The CATHODE resistance is 1/transconductance which for 6c45pi is 1/(45mA/V) = 22R2. That's why they need to be so big. The cathode resistor (and for a triode, Rk too) is in parallel with this but you can see these are trivial in comparison.

In many datasheets, Rk is the triode ANODE or plate resistance NOT the cathode

 

[Miles Prower]

The biggest problem with this design is that capacitor in the 6C45pi cathode. That means capacitive currents in the plate, and that can cause resonance that lead to massive distortion. I did a similar design when I was in high school, that being an IST phase splitter to drive PP 6V6s. The xfmr loaded stage was half a 5963 with a bypassed 560R for cathode bias. This led to unlistenable distortion that went away when the cathode bypass was removed. The unbypassed 560R cathode resistor led to loss of bass due to the increased r_p. That meant redesigning the first gain stage (the other 5963 triode) to incorporate a low frequency compensation circuit to get back the low frequency gain. If I were to do a design that included an IST, I'd go with fixed bias and directly ground the cathode of the xfmr loaded stage. That way, no capacitive currents and no resonance distortion.

 

[rongon]

You should choose the bypass cap size so that the frequencies below 20hz stay unbypassed for low freq. stability.

Why? My experience is that inadequate bypassing of Rk can cause instability, not prevent it.

Choosing a value for Ck to get F3 of 20Hz or higher will cause the triode's internal plate resistance (rp or ra) to go up as frequency goes down.

If the psu output impedance is also going up as frequency goes down, the resulting frequency dependent decrease in PSRR at low frequencies can cause positive feedback down low.

This seems to me to be particularly problematic using a transformer in the plate circuit, since the transformer will have its own F3 zero and possible resonances down low (as well as up high).

I once inadvertently made a 'relaxation oscillator' in a 12AX7 based RIAA preamp.

• The first stage 12AX7 had an unbypassed Rk.
• The first stage 12AX7 Rp (plate load resistor) was something like 220k ohms.
• The decoupling RC to the first stage plate supply had a series resistor of only about 2.2k ohms, and a fairly small value capacitor (47uF, I think).
• The result was an artificial bass boost and low rumbles exploding here and there in the audio output, seemingly at random.

The cure was to recalculate the values of the RC decoupling series resistor and triode's Rp to keep DC voltages the same, but get the decoupling to bypass down to 2Hz or so.

I don't know if that was exactly the same mechanism as is being discussed here, but it's made me look at the gain stages and power supply as a system, working together, interdependently --- and to watch out for accidental positive feedback.

The most sure-fire way to avoid these kinds of problems is to regulate the B+.

Once again, it would be useful to get a look at the power supply too. Thanks.

 

[ejp]

you can use the formula:
f = 1/ (2 pi Rk Ck)

That’s not correct. The cathode also sees (mu+1) times the internal anode and load resistances, taken in parallel with the cathode resistor. If you neglect that you will end up with too small a value for C.

The 156,000 thing must be for a specific example.

 

[MarcelvdG]

You don't need to know the plate load, you can use the formula:
f = 1/ (2 pi Rk Ck)
That gives you the frequency of the 'zero'. The pole won't be much higher.

Only if 1/g_m >> R_k, in which case you don't need the decoupling cap anyway. (I assume R_k is the resistance of the resistor from cathode to ground, 124 ohm in this case.)

 

[rongon]

Hmmm...
I have a headphone amplifier I made from a single triode-wired 12GN7A per channel.
The gm of 12GN7A with Ia = 40mA is about 30mA/V.

1/gm = 1/0.03 = 33.33

I'm using Rk = 62 ohms in circuit, with Ck = 2200uF

Because of the very limited Lpri of the OPT, I need the 12GN7A-triode's rp to be as low as I can possibly get it.
If I leave the 12GN7A Rk unbypassed, I notice a lack of bass response from the amplifier, into several different headphones with their own impedances ranging from 50 ohms to 300 ohms.

Is that because the 12GN7A-triode's 1/gm is 0.5X (half) the value of Rk?

 

[rongon]

The 156,000 thing must be for a specific example.

Can you give some more detail on why you say that?

I gave examples of why it might be useful as a starting point 'rule of thumb' (to easily get to a value that gets you close; then adjust on test).

 

[MarcelvdG]

Reply to post #16: without cathode resistor, you have local series feedback that roughly triples the output resistance, as 1 + g_mR_k is about three. If R_k were much smaller than 1/g_m, the local series feedback would have almost no loop gain and have almost no effect.

 

[20to20]

Why? My experience is that inadequate bypassing of Rk can cause instability, not prevent it.

Because you want to let the degenerative FB to kll those LF's that are unwanted. So the cap only bypasses the audio band for max audio freq. gain. No amp needs to have those infrasonic freqs. passing through it if they get in from who knows where.... transients that trigger LF oscillation, if the amp is prone.

 

[rongon]

Reply to post #16: without cathode resistor, you have local series feedback that roughly triples the output resistance.

Thanks. That's what I thought I'd found in testing, but I was beginning to doubt my thinking.

Can you think of an example of a triode with 1/gm >> Rk?

If I take type 5687 and really roast it with Ea = 120V, Ia = 36mA, Ec = -2V, I get
1/gm = 1/11.5 mA/V = 87
Rk = 55.55 ohms

Does that qualify as 1/gm >> Rk?

If I understand it correctly, you'd only be likely to see that if running relatively high gm triodes at low voltages and high plate currents (for lowest impedance).