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Screen current through cathode resistors

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In amplifiers with pentodes as the output devices, we all know there is often a small cathode resistor so that the bias current can be sampled. If it's small enough, say 10 ohms, you can forego a bypass capacitor.

The problem with this is, the screen current also goes through this resistor, which is highly distorted compared to the input or output waveforms. Even with a 10 ohm resistor there ought to be at least a little bit of degeneration so surely this can cause a bit of added distortion...

Is this actually a problem in practise? Should we in fact tie the cathode directly to earth and measure bias from a small ANODE resistor?
 
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Actually degeneration from an un-bypassed cathode resistor, which is negative feedback, reduces distortion.

In some cases it has been quite clearly documented that this form of local feedback may increase distortion rather than reduce it.. (I think SY might have some insight on this issue, I don't remember the references, I do remember encountering this to some degree in some of my designs. It certainly raises rp which is generally not desirable..) Where the plate and screen currents sum in that resistor I suspect if the screen current is highly distorted it might degrade the linearity to some degree, as DF96 points out if this sampling resistor is small compared to 1/GM it shouldn't be an issue. A 1 ohm current sampling resistor would certainly eliminate this as a concern and of course then no minor feat of math would be required for the conversion.. :D (I've used 1 - 33 ohm resistors in the past so you can see what I am getting at - now use 1 or 10 ohms only.. :D)
 
The problem with this is, the screen current also goes through this resistor, which is highly distorted compared to the input or output waveforms. Even with a 10 ohm resistor there ought to be at least a little bit of degeneration so surely this can cause a bit of added distortion...

Is this actually a problem in practise?

No. A 10R current sampling resistor is tiny in comparison to the actual rk (~1/Gm) so it makes no difference. (Different story with SS, where 10R could be excessive by an order of magnitude at least.)

Should we in fact tie the cathode directly to earth and measure bias from a small ANODE resistor?

No. That presents a possible safety issue. Even if you have a plate current meter permanently installed, a metal case could possibly become "hot". Better to keep the current sampling resistors on the cathode. Besides, cathode current sampling resistors can do double duty as a last ditch "fuse" to possibly prevent OPT burn-outs.
 
Even with a 10 ohm resistor there ought to be at least a little bit of degeneration so surely this can cause a bit of added distortion...

10 ohms seems high. I typically use a 1 ohm resistor. I think the amount of added distortion is so low that it does not matter. The only way to know for sure is a Spice simulation as I'm sure the effect to to small to measure on the bench.
 
In some cases it has been quite clearly documented that this form of local feedback may increase distortion rather than reduce it..
Ah, so degeneration (negative feedback) now increases distortion instead if reducing it. I think Reich, Tremaine and several others just rolled over in their graves hearing that bit of modern day wisdom. :rolleyes: I'd be interested in knowing the exact and precise account of that.
 
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Ah, so degeneration (negative feedback) now increases distortion instead if reducing it. I think Reich, Tremaine and several others just rolled over in their graves hearing that bit of modern day wisdom. :rolleyes: I'd be interested in knowing the exact and precise account of that.

I know it sounds odd, and I will need to dig for references - did not make sense to me either, and I used lots of local feedback in my early designs, so this caught me somewhat off guard as well. I think SY may have done some actual measurements illustrating the effect or I might be completely off base here.. :D

Edit:

Referring to Pullen here: http://www.pmillett.com/tubebooks/Books/Pullen_Conductance.pdf p.32 which I quote below, your original understanding and mine were correct. I'm not sure who told me it wasn't true:

TRIODE DEGENERATIVE AMPLIFIERS
The equation for the gain of this amplifier was derived in Chapter 2,
and is:
K = -gm RL / [ 1 + ( gm + gp ) Rk1 + gp RL ] (8)
where Rk, is the portion of the cathode bias resistor which is not bypassed.
The equation for the load line for this amplifier is slightly
modified from that of the ordinary triode amplifier:
eb = Ebb - ib ( Rk1 + RL ) (23)
In other respects, the design technique is unchanged.
Example 13. To illustrate the effect of degeneration clearly, the design
of Example 4, Case 1, may be modified by assuming Rk1 = 400 ohms.
Find the change of amplification and distortion.
As Rk1, is negligible compared to RL, the same data may be used, giving:
.
ec 0 -2 -4 -6 -8 volts
K -14.1 -13.0 -11.8 -10.7 -9.4 .
DISTORTION
The distortion generated by the degenerative amplifier may be calculated
using either Equation 15 or the Fourier technique. Using Equation
15 with a peak-to-peak signal voltage es of 8 volts, the amplifier
of Example 13 will have a distortion of 5%. In a similar manner, a
peak signal of 4 volts yields a distortion of 2.4% ( Ec1 = -4 volts ). As
can be seen from page 13, the distortions without degeneration are 6.0
and 3.0%, respectively.

DISTORTION
The second-harmonic distortion of an input signal as generated in the
amplifier may be determined by using the small-signal amplifications
in the following equation:
D = 25 ( Kp - Kn ) / ( Kp + Kn ) (15)

Should put that contention to rest.. I think the real crux of the matter is that it just raises rp significantly and that may affect the AC load line adversely depending on what it is driving..
 
Cathode degeneration, like all feedback, can shift the relative magnitudes of distortion orders while reducing the total. For most valves, a little degeneration will increase the relative amount of third vs second. An exception is those, like remote cutoff, whose gain graph curves the other way. In this case the right amount of degeneration can cancel third. For a perfect exponential response, I think this corresponds to Rk=1/(3gm) - from memory, so don't quote me!
 
How easy do you guys think it would be to measure in the real world?

I have an 807ish test rig set up at the moment using four output valves. I have 10R cathode resistors at the moment and could easily swap them to 1R.

I only have a HP334A to measure with but I have built an extremely low distortion oscillator and a half decent notch filter allowing me to get down to around -85dB or so(also modified the HP a bit)

Its past messing with valve time now. Something I learnt from Tubelab, dont mess about past ten.

So can it be measured in the real world?

Cheers Matt.
 
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For a perfect exponential response, I think this corresponds to Rk=1/(3gm) - from memory, so don't quote me!

Which could just be an unbypassed portion of the total cathode bias resistance equivalent to that value. :D

The Pullen conductance paper I referenced is well worth a read if you are interested in graphical design techniques and includes the required graphs for many common triodes and pentodes. It looks quite useful actually. :D
 
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How easy do you guys think it would be to measure in the real world?

I have an 807ish test rig set up at the moment using four output valves. I have 10R cathode resistors at the moment and could easily swap them to 1R.

I only have a HP334A to measure with but I have built an extremely low distortion oscillator and a half decent notch filter allowing me to get down to around -85dB or so(also modified the HP a bit)

Its past messing with valve time now. Something I learnt from Tubelab, dont mess about past ten.

So can it be measured in the real world?

Cheers Matt.

I suspect the difference between 10 ohms and 1 ohms would be difficult to measure, but a more gross change for 100 ohms to 1 ohms probably would be easily measured. (You'd need to make sure the dc operating point was unchanged by the change in cathode resistor value, not to mention the interaction with your transformer and load - probably best done in a small signal stage to illustrate.) I think looking at both the spectrum and distortion amplitude would be useful if you can do FFTs using a computer sound card based set up. Your set up though would probably do it with some careful attention to detail, and you would want to measure the individual harmonics if there is anyway of doing that with something at hand..
 
If it's a problem, you can just bootstrap it so the ac screen current doesn't flow through the cathode resistor. Am I missing something here? :confused:
 

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I think the real crux of the matter is that it just raises rp significantly and that may affect the AC load line adversely depending on what it is driving..
Are you sure about this? Like you, I never use greater then 10 ohms in the cathode of an output tube to monitor current. When added to the total internal anode resistance, I believe 10 ohms is extremely low even with it's tiny amount of degeneration. Many times I have added them to amplifiers I've repaired for others so I could adjust things to my liking without anyone knowing.
 
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Are you sure about this? Like you, I never use greater then 10 ohms in the cathode of an output tube to monitor current. When added to the total internal anode resistance, I believe 10 ohms is extremely low even with it's tiny amount of degeneration. Many times I have added them to amplifiers I've repaired for others so I could adjust things to my liking without anyone knowing.

I don't think the values being discussed would cause any issues at all in power stages as they should be smaller than the 1/gm value DF96 cited, and should be relatively insignificant compared to say several hundred ohms. At least this is what I have assumed.. :D

It has just occurred to me that a 10 ohm resistor in the cathode circuit of a 300B could raise rp by ~ 40 - 50 ohms (rk*mu+1 approximately) and this would represent an increase in rp of more than 5% - probably still not enough to matter.. Assumption here of course is that 1/gm is not much greater than 10 ohms which is unlikely given the transconductance of the tube. (I'd need to calculate it)

Edit: I got off my duff and calculated 1/gm for the 300B and it turns out to be 181 ohms, so the effect of adding that 10 ohm resistor I believe based on a simplistic calculation might raise rp from 700 ohms to 726 ohms as best I can figure. IMHO not a big deal.

In pentode mode I would assume this would be much less significant a concern as long as 1/gm was not violated?

In terms of small signal stages where the value of the unbypassed cathode resistor is probably > = 1/gm the rp increases substantially - that was mostly what I was thinking about. again rk*mu+1

Not sure.. I'm rambling.. :D
 
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I ultimately would trust what DF96 comes up with, I'm not entirely certain that I've got it completely right, but I'm relatively sure I'm within a reasonable error band.. Note that you should look at the calculated result as opposed to the earlier swag. :D I tend not to think about this stuff as much as I should... :p
 
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