Good clear information on valve partition noise is surprisingly hard to find on the Internet. It is caused by the random 'choice' made by each electron at it lands on g2 or anode. The noise current In in either g2 or anode is given by In^2 = 2 e Ig2 Ia / (Ig2 + Ia) (I think, that was from memory. 'e' is the charge on an electron=1.6 x10^-19 coulombs). It is antiphase at the two electrodes, so triode connection recombines the currents and cancels the partition noise.
Partition noise is basically white, but there is a small 1/f contribution at low frequencies. I don't know what a typical corner frequency is, but I suspect that for most purposes partition 1/f noise is swamped by cathode 1/f noise so can be ignored.
Partition noise is basically white, but there is a small 1/f contribution at low frequencies. I don't know what a typical corner frequency is, but I suspect that for most purposes partition 1/f noise is swamped by cathode 1/f noise so can be ignored.
As I understand it, bypassing the Cathode resistor in a commen cathode amplifier, increases gain a bit, and lowers the output impedance.
But how about the distortion spectrum? Is the harmonic structure of that changed?
I think I read somewhere that going from cathode bias to fixed bias in a power amp changes the spectrum from almost only 2. harmonic to more 3. harmonic?
This might be a parameter to "tune" the circuit for performance, perhaps with the cathode resistor partly decoupled (470 Ohm changed to e.g. 150 Ohm+330Ohm decoupled)?
But how about the distortion spectrum? Is the harmonic structure of that changed?
I think I read somewhere that going from cathode bias to fixed bias in a power amp changes the spectrum from almost only 2. harmonic to more 3. harmonic?
This might be a parameter to "tune" the circuit for performance, perhaps with the cathode resistor partly decoupled (470 Ohm changed to e.g. 150 Ohm+330Ohm decoupled)?
As I understand it, any time you have negative feedback you reduce distortion.
An unbypassed cathode resistor privides negative feedback and reduces both gain and distortion.
Bypassing the cathode resistor will reduce the reduction (in relative terms increase) in distoriton, ie it will go back to the same level and spectrem as if the cathode were grounded and you applied teh equivalent voltage developed across the cathode resistor as negative bias the grid.
In a triode distortion is predominatly 2nd order but other haromoics exist at lower levels.
The distortion spectrem will vary with tube type, anode current, and probably other parameters as well.
An unbypassed cathode resistor privides negative feedback and reduces both gain and distortion.
Bypassing the cathode resistor will reduce the reduction (in relative terms increase) in distoriton, ie it will go back to the same level and spectrem as if the cathode were grounded and you applied teh equivalent voltage developed across the cathode resistor as negative bias the grid.
In a triode distortion is predominatly 2nd order but other haromoics exist at lower levels.
The distortion spectrem will vary with tube type, anode current, and probably other parameters as well.
My understanding is that you multiply the harmonics, and reduce the distortion a bit. I'm not therefore convinced of degeneration unless you start off with a pretty linear triode in the first place.
Also of course degeneration kills your output impedance (drive) which will probably have more effect than the actual feedback itself
If you start with a pure square-law device (i.e. linear plus second-order) and then add degeneration you will create all higher order distortions too. A triode is not a pure square-law device, so it already has all higher order components anyway. Degeneration reduces distortion and noise, but raises output impedance which may be unhelpful - depends on what comes next.
When I say 'reduces noise' what I mean is that if you want, say 2mA/V gain, you will get a quieter stage by using a 4mA/V valve and adding 250ohm degeneration. A straight 4mA/V stage would be quieter still, but with more gain than you want.
When I say 'reduces noise' what I mean is that if you want, say 2mA/V gain, you will get a quieter stage by using a 4mA/V valve and adding 250ohm degeneration. A straight 4mA/V stage would be quieter still, but with more gain than you want.
Hello
Considering the cathode resistor and the resistor bypass capacitor what is the goal or considerations? My version of this is improving the performance of the amplifier.
Including a cathode resistor provides bias. Adding a bypass capacitor changes the performance of the tube.
John Broskie posted a very interesting classic article by George Fletcher Cooper regarding the cathode resistor and various degrees of bypassing with a capacitor. By adjusting the value of the cathode resistor the transfer function can be straightened out and 3rd harmonic distortion can be reduced. Also by adding a resistor in series with the bypass capacitor the transfer function can be straightened out. See http://tubecad.com/2005/March/02/Which Tube Shall I Use.pdf
I would also like to add thoughts of my own (I know that it is all vanity and has been done before).
First and always minimize the noise. Plan some extra gain (not too much) for dynamic peaks and some extra. Distortion is usually reported at full output. As output increases so does THD, 3rd and higher order distortion becomes more prominent. If output is a fraction of maximum so is THD, 3rd and higher order distortion tends to be nonexistent. I call this truncating the output distortion.
DT
All just for fun!
Considering the cathode resistor and the resistor bypass capacitor what is the goal or considerations? My version of this is improving the performance of the amplifier.
Including a cathode resistor provides bias. Adding a bypass capacitor changes the performance of the tube.
John Broskie posted a very interesting classic article by George Fletcher Cooper regarding the cathode resistor and various degrees of bypassing with a capacitor. By adjusting the value of the cathode resistor the transfer function can be straightened out and 3rd harmonic distortion can be reduced. Also by adding a resistor in series with the bypass capacitor the transfer function can be straightened out. See http://tubecad.com/2005/March/02/Which Tube Shall I Use.pdf
I would also like to add thoughts of my own (I know that it is all vanity and has been done before).
First and always minimize the noise. Plan some extra gain (not too much) for dynamic peaks and some extra. Distortion is usually reported at full output. As output increases so does THD, 3rd and higher order distortion becomes more prominent. If output is a fraction of maximum so is THD, 3rd and higher order distortion tends to be nonexistent. I call this truncating the output distortion.
DT
All just for fun!
Does anyone know what year that was originally published? I don't think Broskie references it properly (as is usual for him).
Whether cathode degeneration can reduce 3rd order distortion depends on the sign of the cubic term in the original transfer function. For a typical valve, following something like the theoretical 3/2 power rule, the 3rd produced by degeneration will be the same sign as the intrinsic 3rd so it cannot cancel it. To guarantee cancellation you either need to use a remote cutoff valve, as this will have the right sign, or by trial and error find a suitable valve.
To put it another way, you want a valve which expands signal peaks; most valves compress them. The 3rd arising from degeneration will always compress, due to the sign of the 2nd order term. I think John Broskie was being too hopeful, or just happened to find a lucky combination which worked and assumed it was normal.
To put it another way, you want a valve which expands signal peaks; most valves compress them. The 3rd arising from degeneration will always compress, due to the sign of the 2nd order term. I think John Broskie was being too hopeful, or just happened to find a lucky combination which worked and assumed it was normal.
11/57, page 58 14th line down
Audio Anthology volume 4 - book contents list
according to my google skilz.
Audio Anthology volume 4 - book contents list
according to my google skilz.
Thanks!
Interestingly, the first part of Coopers article appears to have been cribbed from
Roddam, T. (June 1951) How to Choose a Valve. Wireless World. pp221-3
Hello
I think something is confused here.
A grounded cathode triode with no cathode resistor and fixed grid bias sort of follows Childs law (to the 3/2 power). The resulting plate curves are text book triode data sheets with positive increasing slope. Since we are speaking math both the first and second derivatives are positive. (Concave up)
Add an unbiased cathode resistor and the new curve starts with a decreasing positive slope with a positive 1st derivative and a negative 2nd derivative. (Convex down).
To help with the visual, think triode plate curves, pentode plate curves and much closer to ultra-linier plate curves in between.
Add just the right pinch of cathode degeneration and we see an ultra-linear straightening of the triode curves. Add a lot of cathode degeneration and it is surprising how pentode like the curves begin to look.
After reading the Cooper article I simulated and then built a breadboard circuit and dialed the cathode degeneration using a 6BQ6GTB. The 3rd harmonic was reduced more than the 2nd. My current headphone amplifier has 15 ohm resistors in series with the triode conected 6BQ6GTB bypass capacitors .
DT
All Just for fun!
Interesting post DT, I did not realise there was an optimal bypass point for this. I guess for a 1k cathode resistor a 1k pot with the centre tap to a bypass capacitor would be able to explore this further - now I just need to get hold of a distortion meter.
15ohms is amazingly small - and I suppose also tells us that cheap capacitors may sometimes work better than low esr ones in a bypass position..
15ohms is amazingly small - and I suppose also tells us that cheap capacitors may sometimes work better than low esr ones in a bypass position..
and the third derivative is negative. It may be that feedback from the anode modifies this, but the basic 3/2 law gives 3rd order compression.
Current goes like V^(3/2), gm like 3/2 V^(1/2), 2nd order like 3/4 V^(-1/2), 3rd order like -3/8 V^(-3/2) - so 3rd order term is negative. However, at low currents many valves have more like a 5/2 rule due to the island effect, so in this case 3rd order will be positive - but it seems a bit perverse to deliberately bias a valve into a non-linear region in order to straighten it out with feedback.
Hello DF96 and All,
The curve or graph Cooper is discussing is grid voltage on the X axis and transductance on the Y. The near straight line portion is where there is minimum 3rd harmonic distortion. The difference between the curve and a straight line is the 3rd harmonic. For a sample of the type graph look at page 3 of this data sheet http://www.mif.pg.gda.pl/homepages/frank/sheets/093/5/5670.pdf . For Cooper’s discussion of the origin of the 3rd harmonic open his article and search for mixer.
The way that I have applied this approach is to bias the tube in the center of the straight line portion of the graph. This is fairly high current for reduced noise and lowest possible 3rd. Then bypass the cathode resistor with just a pinch of degenerative feedback.
The next thing to try is getting rid of the cathode resistor or perhaps a very small value and bias the grid with a regulated power supply.
Using a PC based FFT makes measuring all this stuff possible and fun. Otherwise it is all just math and theory based on assumed mu, rp and gm.
DT
All just for fun!
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