Help check my tube math?

[OneRoomStudio]

I'm still not 100% confidant in my tube theory, so please help me with some math to confirm my assumptions:

-If I'm running a 6922/E88CC triode as a fixed-bias cathode follower, with a Vcc of 135V and Rk of 4K7, I should have around 68V on the cathode, so I'd have a cathode current of around 14.5mA.
-14.5mA can swing 29mA peak-to-peak, or around 20.5mA RMS.
-20.5mA RMS into 600 ohms is 12.3V RMS.
-Even though it would never fully do 12.3V RMS, if it did 70% of that (8.6V RMS) that would still be plenty for line level.

In other words, a 6922 in this configuration would have no trouble driving a 600:600 OT, right? Am I missing something? Did I make a mistake in my math anywhere? Thanks!

 

[CJ]

this is not a power amp,

power amps are most efficient when the the source matches the load,

but for line level audio you generally want about ten times the load as the source,

so for you that means 10 x 600 = 6K load for the transformer primary

just take the square root for your turns ratio so 10:1 Z = 3:1 turns ratio

so your rms voltage output will get divided by about 3

UTC A-24 is about a 5:1 ratio or 15 K primary

Jensen uses 4:1 or about 10K to 600 but with a ton of primary inductance for bass

not much audio gear has 600 input anymore unless its vintage,

more like 10K, so you can use a 1:1 XFMR but make it 10K:10K (more turns, 80% Ni core)


as far as the tube math, maybe somebody else can chime in but it seems logical

this circuit will breadboard in about 1 day then you can do real life experiments with resistors, caps, transformers, chokes and pwr supply voltage and it is a lot of fun vs slide rule.

 

[JohnRoberts]

this is not a power amp,

thats OK I'm not a tube guy...

power amps are most efficient when the the source matches the load,

actually I think they mean that power transfer is maximum when source Z= load Z.

but for line level audio you generally want about ten times the load as the source,

AKA a "bridging" termination to maximize voltage transfer not power transfer.

so for you that means 10 x 600 = 6K load for the transformer primary

just take the square root for your turns ratio so 10:1 Z = 3:1 turns ratio

so your rms voltage output will get divided by about 3

UTC A-24 is about a 5:1 ratio or 15 K primary

Jensen uses 4:1 or about 10K to 600 but with a ton of primary inductance for bass

not much audio gear has 600 input anymore unless its vintage,

more like 10K, so you can use a 1:1 XFMR but make it 10K:10K (more turns, 80% Ni core)


as far as the tube math, maybe somebody else can chime in but it seems logical

this circuit will breadboard in about 1 day then you can do real life experiments with resistors, caps, transformers, chokes and pwr supply voltage and it is a lot of fun vs slide rule.

tubes and transformers... I'll tap out now.

JR

 

[ruffrecords]

I'm still not 100% confidant in my tube theory, so please help me with some math to confirm my assumptions:

-If I'm running a 6922/E88CC triode as a fixed-bias cathode follower, with a Vcc of 135V and Rk of 4K7, I should have around 68V on the cathode, so I'd have a cathode current of around 14.5mA.
-14.5mA can swing 29mA peak-to-peak, or around 20.5mA RMS.
-20.5mA RMS into 600 ohms is 12.3V RMS.
-Even though it would never fully do 12.3V RMS, if it did 70% of that (8.6V RMS) that would still be plenty for line level.

In other words, a 6922 in this configuration would have no trouble driving a 600:600 OT, right? Am I missing something? Did I make a mistake in my math anywhere? Thanks!

29mA peak to peak is not 20.5mA rms it is 29/2.828 = 10.25mA rms

Cheers

Ian

 

[OneRoomStudio]

29mA peak to peak is not 20.5mA rms it is 29/2.828 = 10.25mA rms

Cheers

Ian

Aha! I figured I screwed something basic up. Thank you for catching that!
Ok, so 10.25mA rms into 600 ohms is 6.15V rms. Taking around 70% of that, I'd get 4.3V rms.
Dividing that by 3 (per @CJ's note), and I'd be at 1.4V rms, which is still a hair over the 1.228V rms +4 level.
So assuming that math is right, is my conclusion that a 6922 cathode follower with Vcc=135V and Rk=4k7 could drive a 600:600 OT at line level correct?

 

[ccaudle]

1.4V rms, which is still a hair over the 1.228V rms +4 level

What kind of standard are you shooting for? By your calculations you can get to +4dBu peak level, right? So you have 0dB headroom over nominal?
Most line level pro audio devices were designed for +18dB to +20dB headroom over nominal. Traditionally +24dBu max output, although modern semi-pro aka "prosumer" devices often top out at +18dBu or +20dBu.
Maximum output of +4dBu would traditionally be called a -16dBu nominal output, which would be somewhere between mic and instrument level.

 

[OneRoomStudio]

What kind of standard are you shooting for? By your calculations you can get to +4dBu peak level, right? So you have 0dB headroom over nominal?
Most line level pro audio devices were designed for +18dB to +20dB headroom over nominal. Traditionally +24dBu max output, although modern semi-pro aka "prosumer" devices often top out at +18dBu or +20dBu.
Maximum output of +4dBu would traditionally be called a -16dBu nominal output, which would be somewhere between mic and instrument level.

Very good point. Technically, the “peak RMS” value would be the 10.24mA rms into 600 ohms, or 6.15V divided by 3 per CJ = 2.05V, which is about +8.5dBu, but that is still a little on the low side.

Using a 2:1 output transformer would get me 10.24mA into 2400 ohms, or 24.6V rms, divided by 3 is 8.2V, or +20.5dBu. Much better.

 

[ruffrecords]

Aha! I figured I screwed something basic up. Thank you for catching that!
Ok, so 10.25mA rms into 600 ohms is 6.15V rms. Taking around 70% of that, I'd get 4.3V rms.
Dividing that by 3 (per @CJ's note), and I'd be at 1.4V rms, which is still a hair over the 1.228V rms +4 level.
So assuming that math is right, is my conclusion that a 6922 cathode follower with Vcc=135V and Rk=4k7 could drive a 600:600 OT at line level correct?

The math is OK but the conclusions are not because there are some built in assumptions which are likely not correct.

The main problem is the cathode follower is single ended. This means it can source current on the positive cycles but not on the negative cycles. For small signals this does not matter but for large swings it does. This is because on the negative swings the current has to discharge though the 4K7 resistor which becomes the effective output impedance for this half cycle.

Cheers

Ian

 

[OneRoomStudio]

The math is OK but the conclusions are not because there are some built in assumptions which are likely not correct.

The main problem is the cathode follower is single ended. This means it can source current on the positive cycles but not on the negative cycles. For small signals this does not matter but for large swings it does. This is because on the negative swings the current has to discharge though the 4K7 resistor which becomes the effective output impedance for this half cycle.

Cheers

Ian

Wow, this comes as a revelation. Thank you. I never thought of it that way, but it makes perfect sense. Ok, I have some more math ahead of me.

Thank you all for your help!

 

[ruffrecords]

Wow, this comes as a revelation. Thank you. I never thought of it that way, but it makes perfect sense. Ok, I have some more math ahead of me.

Thank you all for your help!

The math for working out high level drive capability is not at all simple. A better approach is to get a simulator to do it all for you. Most people here use LTspice for simulating analogue circuits. It is free and quite easy to use. Use the transient analysis to see exactly what happens when you ac couple a 600 ohm load to a cathode follower.

Cheers

Ian

 

[OneRoomStudio]

The math for working out high level drive capability is not at all simple. A better approach is to get a simulator to do it all for you. Most people here use LTspice for simulating analogue circuits. It is free and quite easy to use. Use the transient analysis to see exactly what happens when you ac couple a 600 ohm load to a cathode follower.

Cheers

Ian

That's a fair point. I'm still learning how to do this though, plus it's hard to find data on a lot of transformers (including the Edcor's I was hoping to use).

Here's the circuit I described, using the test data you shared in another thread of the Edcor XSM 2K4:600:

Here is the result:

What am I looking for, exactly?

 

[ruffrecords]

Try changing R6 to 600 ohms and see what happens.

There is very little data on transformers period. For the purposes of this exercise you can assume it is near perfect.

Cheers

Ian

 

[OneRoomStudio]

Try changing R6 to 600 ohms and see what happens.

There is very little data on transformers period. For the purposes of this exercise you can assume it is near perfect.

Cheers

Ian

Well, of course, you're absolutely right. I can't make it drive any real level cleanly.
I did stumble upon a different idea though. @CJ's comment about this not being a power amp rattled something loose in my head, and I remembered a transformer-coupled cathode follower stage I had seen at some point. I thought I'd give that a go, and unless I've made some terrible error somehow, this seems very promising:


Excuse the random order of the components, I built this in stages (backwards). "K2" is an Edcor 600:15K input transformer, "K1" is an Edcor 2K4:600 output transformer. R10 is a vactrol (off). R17/R14 is a gain pot (turned all the way up right now). As-is, this is cleanly driving +25dBu (39Vpp) into 600 ohms.


Did I (once again) overlook some basic law or detail, or is this circuit actually viable?

 

[ruffrecords]

I think you need to check the CF quiescent current. Do a dc operating point analysis to see what this is. In practice with this circuit it will be set by the dc resistance of the primary winding. Did you set a resistance value for L1? I suspect you will find you are dissipating several watts in the CF tube.

Cheers

Ian

 

[OneRoomStudio]

I think you need to check the CF quiescent current. Do a dc operating point analysis to see what this is. In practice with this circuit it will be set by the dc resistance of the primary winding. Did you set a resistance value for L1? I suspect you will find you are dissipating several watts in the CF tube.

Cheers

Ian

Thank you! I knew there must an issue somewhere.

I did set the DCR for the primary (around 97 ohms for the Edcor WSM 2K4:600). Looks like (as I had it setup), the tube would be dissipating around 2.8W. The data sheet max for plate dissipation is 1.8W, so clearly this wouldn't work.

However, by putting a 220 ohm resistor in series with the primary, I can take the total DCR to 317 ohms, which brings the dissipation down to 1.57W while still able to drive +22.7dBu into 600 ohms without much distortion...not too bad.

 

[ruffrecords]

You are definitely moving in the right direction. The only question now is can the Edcor take the 12mA dc current?

Cheers

Ian

 

[OneRoomStudio]

You are definitely moving in the right direction. The only question now is can the Edcor take the 12mA dc current?

Cheers

Ian

I just contacted Edcor, and sadly, no. They said 10mA max.

But, this transformer from UTM (wired 2:1) looks promising. I'll have to run the numbers and see if the DCRs and inductances work.
https://utmindustry.com/utm3590/
BTW, thank you again Ian, I really appreciate you walking me through all the considerations here.

 

[OneRoomStudio]

That appears to do the trick. With a UTM2581 wired 1:2.5 on the input and a UTM3590 wired 2:1 on the output, I can get slightly over +24dBu into 600 ohms without much distortion. The frequency response looks very flat, and the total B+ current draw is still only ~25mA. I have somewhere around 25dB of gain input-to-output. It feels like I'm getting close to something viable.

 

[ruffrecords]

I notice you also have the first stage running at about 12,5mA. I do not why why there are so mnay designs running WCC88s at such high currents. As this is just a voltage gain stage you can run it at a much lower current, say 5mA, have an increased anode resistor which in turn should give you some more gain and less distortion.

Cheers

Ian

 

[OneRoomStudio]

I notice you also have the first stage running at about 12,5mA. I do not why why there are so mnay designs running WCC88s at such high currents. As this is just a voltage gain stage you can run it at a much lower current, say 5mA, have an increased anode resistor which in turn should give you some more gain and less distortion.

Cheers

Ian

Good point. A 15K plate resistor with a 220R cathode resistor gets me down to around 5mA and does around 28dB of gain.