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Parallel Triodes, this comes up repeatedly so lets give it some analysis.
Two identically biased triodes in parallel give you an effective "composite" tube of:
- Double the gm
- half thr rp
- identical mu.
Since gain of a common cathode stage is mu x [RL /(RL + rp)] then
Assume 12AX7 with mu = 100, rp = 65K and an anode load of 100K AND next stage load of 1M so RL is 100K||1M = 90.9K
For the single triode you get a gain of 58.
For the parallel triode with same RL you get a gain of 74.
Normally you would halve the anode load resistor to say 47K giving RL of 47K||1M = 44.9K
In which case the gain will be 58 ( That is, the same as for a single triode).
What is different:
You need to understand where distortion in a triode stage comes from.
To get a signal voltage swing at the anode you need a signal current swing through the tube which means through the load resistor AND through the internal tube impedance rp.
As current through the tube changes so does gm and rp but mu stays almost constant.
From an AC signal point of view you have a SIGNAL voltage generator of mu x delta Vgk with a series resistance of rp into the RL load resistance. The output at the anode is a voltage division of the voltage generator output between RL and rp. As rp changes with current you get a different voltage division and that is the source of the distortion. Positve going signal at anode is from reduced tube current which means higher rp, neagtive going signal at anode is from increased tube current which means lower rp. That is you get asymmetrical distortion which is primarily 2nd harmonic.
With parallel triodes with the same RL (100K) you get about half the distortion, if you reduce the anode load to 47K you will end up with about the same distortion.
Noise is Statistical in nature so with parallel triodes you get 1/root 2 = 0.707 (NOT HALF) the noise.
Summary:
If you parallel two triodes and halve the anode resistor you really only get a 1/root 2 reducton in noise. gain and Distortion remain the same.
If you leave the anode resistor as is then you get a gain of 74 instead of 58 with reduced distortion.
You can get some distortion reduction and some gain increase by choosing a new anode load resistor of say 68K or 75K.
Why change the anode load resistor at all? Because if you leave it at the 100K value you get double the DC voltage drop at idle and anode voltage may become too low.
With a 12AX7 this can cause grid current problems, I try to keep the anode voltage at around +180V or more to avoid excess grid current (which also adds noise).
That change of rp is why cold biased stages have more distortion (you are operating in the part of the rp vs anode current curve where rp varies the most and the ratio of RL to rp is lowest. That is, the variable rp term is more significant in the voltage divider and so more distortion results. In addition the rp curve changes slope more rapidly which will mean that you get some higher order harmonics in the distortion.
Most series tube connections (Cascode'ish) really just use the second triode as an active load for the bottom triode. That is you are maximising the value of RL which gives increased gain and reduced distortion.
The other (main) reason for using parallel triodes is that you can bias one triode normally for good gain and low, mostly 2nd harmonic distortion distortion and the parallel triode colder, to add in some higher order harmonic emphasis.
The other reason you might parallel triodes is reduce teh output impedance to better drive a tone stack or similar.
If you look at Rivera era Fenders with a parallel 12AX7 front end you see he usually opted for 75K as the anode load.
Hope there is something of value in this.
For gm , rp and Mu vs Anode Current graphs see here:
http://tdsl.duncanamps.com/dcigna/tu...rex/ax7-8h.gif
This graph is probably the least used of the published specifications but I find it very useful. If you operate the tube at the low end of the anode current range you can see that you have a high slope on the rp curve inferring higher distortion. This delta rp as the source of the distortion is a way of looking at the circuit which I haven't seen emphasized. It gives you the same info as doing the analysis off the load line would, I just find it easier to get an overview by thinking about it in this fashion.
When you see circuits with low values of stage load (the Rg1 of the next stage or an interstage attenuator with low values) you can see that this reduces the effective RL and hence the gain, in fact some people even call these low loads "gain dumping". Since the level of distortion is the ratio of rp to effective RL (which is the anode load in parallel with the driven impedance) you can see that "gain dumping" is also a way to increase the distortion.
Running a cold biased stage with high voltage and hence a high RL will not necessarily give more distortion because you don't need to swing as much current in the higher RL so that reduces the delta rp even though you are on the high rp slope part of the curve.. Swings and Roundabouts.
Cheers,
Ian
Two identically biased triodes in parallel give you an effective "composite" tube of:
- Double the gm
- half thr rp
- identical mu.
Since gain of a common cathode stage is mu x [RL /(RL + rp)] then
Assume 12AX7 with mu = 100, rp = 65K and an anode load of 100K AND next stage load of 1M so RL is 100K||1M = 90.9K
For the single triode you get a gain of 58.
For the parallel triode with same RL you get a gain of 74.
Normally you would halve the anode load resistor to say 47K giving RL of 47K||1M = 44.9K
In which case the gain will be 58 ( That is, the same as for a single triode).
What is different:
You need to understand where distortion in a triode stage comes from.
To get a signal voltage swing at the anode you need a signal current swing through the tube which means through the load resistor AND through the internal tube impedance rp.
As current through the tube changes so does gm and rp but mu stays almost constant.
From an AC signal point of view you have a SIGNAL voltage generator of mu x delta Vgk with a series resistance of rp into the RL load resistance. The output at the anode is a voltage division of the voltage generator output between RL and rp. As rp changes with current you get a different voltage division and that is the source of the distortion. Positve going signal at anode is from reduced tube current which means higher rp, neagtive going signal at anode is from increased tube current which means lower rp. That is you get asymmetrical distortion which is primarily 2nd harmonic.
With parallel triodes with the same RL (100K) you get about half the distortion, if you reduce the anode load to 47K you will end up with about the same distortion.
Noise is Statistical in nature so with parallel triodes you get 1/root 2 = 0.707 (NOT HALF) the noise.
Summary:
If you parallel two triodes and halve the anode resistor you really only get a 1/root 2 reducton in noise. gain and Distortion remain the same.
If you leave the anode resistor as is then you get a gain of 74 instead of 58 with reduced distortion.
You can get some distortion reduction and some gain increase by choosing a new anode load resistor of say 68K or 75K.
Why change the anode load resistor at all? Because if you leave it at the 100K value you get double the DC voltage drop at idle and anode voltage may become too low.
With a 12AX7 this can cause grid current problems, I try to keep the anode voltage at around +180V or more to avoid excess grid current (which also adds noise).
That change of rp is why cold biased stages have more distortion (you are operating in the part of the rp vs anode current curve where rp varies the most and the ratio of RL to rp is lowest. That is, the variable rp term is more significant in the voltage divider and so more distortion results. In addition the rp curve changes slope more rapidly which will mean that you get some higher order harmonics in the distortion.
Most series tube connections (Cascode'ish) really just use the second triode as an active load for the bottom triode. That is you are maximising the value of RL which gives increased gain and reduced distortion.
The other (main) reason for using parallel triodes is that you can bias one triode normally for good gain and low, mostly 2nd harmonic distortion distortion and the parallel triode colder, to add in some higher order harmonic emphasis.
The other reason you might parallel triodes is reduce teh output impedance to better drive a tone stack or similar.
If you look at Rivera era Fenders with a parallel 12AX7 front end you see he usually opted for 75K as the anode load.
Hope there is something of value in this.
For gm , rp and Mu vs Anode Current graphs see here:
http://tdsl.duncanamps.com/dcigna/tu...rex/ax7-8h.gif
This graph is probably the least used of the published specifications but I find it very useful. If you operate the tube at the low end of the anode current range you can see that you have a high slope on the rp curve inferring higher distortion. This delta rp as the source of the distortion is a way of looking at the circuit which I haven't seen emphasized. It gives you the same info as doing the analysis off the load line would, I just find it easier to get an overview by thinking about it in this fashion.
When you see circuits with low values of stage load (the Rg1 of the next stage or an interstage attenuator with low values) you can see that this reduces the effective RL and hence the gain, in fact some people even call these low loads "gain dumping". Since the level of distortion is the ratio of rp to effective RL (which is the anode load in parallel with the driven impedance) you can see that "gain dumping" is also a way to increase the distortion.
Running a cold biased stage with high voltage and hence a high RL will not necessarily give more distortion because you don't need to swing as much current in the higher RL so that reduces the delta rp even though you are on the high rp slope part of the curve.. Swings and Roundabouts.
Cheers,
Ian
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