Plate follower and applications
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tiroth
diyAudio Member

Join Date: Dec 2001
Location: Pittsburgh, PA, USA
Plate follower and applications

Can someone please supply me with equations for gain and Zout for this basic circuit? There is an article[http://www.tubecad.com/october99/page9.html] on TubeCAD which gives equations, but their usage of the || notation is unknown to me, and I don't understand their gain equation.

I'm actually shooting for a unity gain buffer, so feedback usage would be extensive. Probably a 12au7/e88cc tube. I'm also interested in a balanced circuit such as the one below. It appears that the cathodes are simply tied together to form a difference amplifier from a plate follower.
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 11th April 2002, 05:59 PM #2 J Epstein   diyAudio Member   Join Date: Feb 2002 "a || b" is probably read "a in parallel with b" would be my guess.
 11th April 2002, 06:25 PM #3 tiroth   diyAudio Member   Join Date: Dec 2001 Location: Pittsburgh, PA, USA Thanks--that makes sense. I'd only ever seen || as a vector operator before. I still don't understand their gain equation, though; how can Gain=aRatio/(a + Ratio + 1) ever be greater than 1? Even with no feedback (r2=infinity) this equation only approaches unity, as 'a' is always less than 1.
 11th April 2002, 07:31 PM #4 hagtech diyAudio Member     Join Date: Mar 2002 Location: Hawaii Diffamp The gain of that circuit is around 50. But it's hard to tell, with the values given, the tubes are barely turned on. They are operated in a very non-linear portion of their characteristics. The plate currents are an anemic 0.225mA. First thing you need to do is increase the plate supply to 300V or 400V. Then change the standing current to 1mA or more. Try to get about 200V on the plate. The difference in sound is night and day. You could add feedback to drop gain down to unity, but why not just use a cathode follower? jh
 11th April 2002, 09:09 PM #5 tiroth   diyAudio Member   Join Date: Dec 2001 Location: Pittsburgh, PA, USA hagtech: The schematic is right out of a textbook; I didn't intend to use the circuit values as-is. Is there a similar circuit that can be built using cathode followers? What about balanced to single-ended conversion? There are a ton of tube schematics out there, but I'm having a surprisingly hard time finding "building block" schematics that list basics like input/output impedance, gain equations, etc.
 11th April 2002, 09:26 PM #6 PassFan   diyAudio Member   Join Date: Aug 2001 Location: Central FL Tiroth: The tubecad software has nothing but basic circuit building blocks. You can even adjust values and it will recalculate it out. AES sells the program for about 40.00 It's pretty cool.
 11th April 2002, 10:57 PM #7 hagtech diyAudio Member     Join Date: Mar 2002 Location: Hawaii tiroth I haven't tried it, but maybe you should try the tubecad as PassFan has suggested. Don't get me wrong, the circuit topology you show is an excellent one - I use it in my "Trumpet" phono stage. The easy way to go from balanced to single-ended is to just ignore one of the signals. Of course, to maintain CMRR a differential pair is a great way to go. You can take one of the plate signals to drive a cathode follower. From this buffered output, you can then apply feedback to the input. But be careful, ac-coupled feedback will just lead to a huge rise in gain at low frequencies (usually infrasonic). You'll need to balance it will a low pass filter in the forward path (inside the loop). jh www.hagtech.com
 11th April 2002, 11:10 PM #8 PassFan   diyAudio Member   Join Date: Aug 2001 Location: Central FL Hagtech: Cool site. Lots of nice looking stuff. I like your chassis design on the trumpet. Thanks for the peek.
 12th April 2002, 03:40 AM #9 tiroth   diyAudio Member   Join Date: Dec 2001 Location: Pittsburgh, PA, USA Thanks for the input hagtech. I'll try to implement your suggestion for the feedback loop...hopefully you won't mind me bugging you about it again as I work this out. ^_^ For anyone who is interested, there is a whole writeup on this circuit, the "Common Cathode Amplifier", found here. Perhaps the most salient page is this one.
dice45
diyAudio Member

Join Date: Jan 2002
Location: Munich, Bavaria
Re: Plate follower and applications

Quote:
 Originally posted by tiroth Can someone please supply me with equations for gain and Zout for this basic circuit? There is an article[http://www.tubecad.com/october99/page9.html] on TubeCAD which gives equations, but their usage of the || notation is unknown to me, and I don't understand their gain equation. I'm actually shooting for a unity gain buffer, so feedback usage would be extensive. Probably a 12au7/e88cc tube. I'm also interested in a balanced circuit such as the one below. It appears that the cathodes are simply tied together to form a difference amplifier from a plate follower.
tiroth,
looking very puzzled here, and wondering noone else refused to swallow the term "plate follower" or "anode follower".
Where i have been brought up, a "follower" is a non-inverting unity gain device, no matter if made from tubes (cathode F), FETs (source F) BJTs (emitter F) or opamps (voltage F).
The correct term for "plate follower" is "common cathode" or "grounded cathode" amplifier stage which is an inverting gain >1 device (see below).

I am speaking up as i do want to shoot at misleading terms which hide misleading concepts. I know that such foggy terms are fervently used in other forums ... and consider them to be mentally infective ...
I presume this term to be picked up elsewhere, so, no personal offense meant

As to your question, the circuitry you posted is a differntial pair with the R_c (200k) acting as a modest constant current device. The node connecting R_c and both cathodes is acting as a virtual ground. So the equation for the stage's amplification is the one applying for a common cathode stage:
G=µ*(R/R+r_p). In your case R is 100k, µ is 100, r_p is 62k5, so G is theoretically 61.5 as a fixed-bias EC83 with B+ 350V= and R=100k would have (presuming the values i took below and not those from the posted circuit).
After a rough calculation methinks the posted circuit will not work well with those values. I agree with hagtech, not enough quiescent current. 100k for the plate resistors would be ok provided B+ is raised to 350 V=, B- is kept at -90V= and R_c is reduced to 40k5. Quiescent current is then 1.11mA for each tube.
I took the recommended values for the ECC83/12AX7 from my Ratheiser tube manual and took care that the virtual ground of the differential stage is close to real ground. R_c has to drop 90V @ 2.22mA.

For a collection of formulae, i recommend the Radiotron Designer's Handbook 4th ed., it covers all. Available as reprint from Old Colony Sound Lab or as original from ebay auctions.

If one should want to increase this circuit's gain to the tube's open loop gain (µ=100), please replace each plate resistor by a constant current source (CCS). In this case do not replace R_c by a CCS.

But for your unity gain device, please use a cathode follower, it does exactly what you want. And if you need it differntial, use two cathode followers with the differential signal applied earth-free to both grids. Replacing a cathode follower's load resistor by a CCS is strongly recommended, on the bench as well as sonically.

You will need an output coupling device, either coupling cap(s) or another amp stage (possibly DC-coupled) or an output transformer. A pair of differntially used cathode followers having each CF output connected with one end of an output transformer is a truly differential output stage with very low output Z.
Use of CCS as CF "load resistor" is particularly recommended here.
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Regards,
Bernhard

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