# Plate follower and applications

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#### 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.

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#### J Epstein

"a || b" is probably read "a in parallel with b" would be my guess.

#### tiroth

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.

#### hagtech

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

#### tiroth

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.

#### PassFan

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.

#### hagtech

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

#### PassFan

Hagtech:
Cool site. Lots of nice looking stuff. I like your chassis design on the trumpet. Thanks for the peek.

#### tiroth

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

tiroth said:
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.

#### tiroth

Dice45,

I think you and hagtech are on the money as to the functionality of the original circuit; I tried to simulate it with poor results until I raised B+ and the quiescent current. (and yet it was printed in a textbook?!) I also found that replacing Rk by CCS made an enormous difference in CMRR.

I'd appreciate it if you could comment on using a pair of cathode followers to do differential to single-ended conversion; is this possible? Even a rough sketch of this circuit would really help me as I muddle through this.

Building on the original "common cathode" amp I put together the following circuit. I think the way I did feedback is wrong; it works, but it reduces my CMRR from a simulated 100dB (no feedback) to about 30dB. (I know the inputs should be AC-coupled in the real world)

Distortion is higher than in the differential circuit; -72dB 2nd, -90dB 3rd versus -90dB 2nd, -110dB 3rd. Is this due to a poor design on my part?

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#### dice45

tiroth,

somehow forgot to stick to this thread ..
Drawing some diff.cathode follower variants: Be patient please. I am not yet equiipped to post pixes; will be soon.

In the meantime, imagine two cathode followers drawn side by side, both having either a load resistor or a CCS (to your taste) as cathode load. Now feed the two cathode follower's inputs with your diffential signal. Or u feed your signal into one grid and keep the other at a contant voltage (e.g. resistive voltage divider). Then u connect both ends of your output (either two coupling caps or two ends of an output transformer primary) to both cathodes. Ready. This is a diffentially working cathode follower pair.

Your diff.amp simulation: if it claims 100db CMRR, it simply hmmmmh... makes glorious but unkeepable promises. . I have never seen CMRR of more than 60, maybe 65 dB for diffential tube circuits and if the tubes are poorly matched and/or driven at the wrong operating point, yes, then it drops to 30dB or less.

Referring to your two posted pixes now:
I am no feedback expert, but to me your application of FB looks weird, never seen anything like that. U apply the same AC output-derived signal to both inputs.
I always thought, negative feedback is meant to correct errors, but this only will work if both sides of the circuit are fed with inverted output signal portions, so your NFB2 should be derived from T1, not from T2.
And then, the original circuit had same load resistor for both plates. Methinks this should be maintained, even if u use only one side for the output.
Methinks NFB should be avoided at all. Biased me . A differntial pair has outstanding bench performance, no need for correcting via NFB as your figures prove, so why do it? Sounds beautifully, too.
Moreover, you need coupling caps for NFB, messing up sonics. Another reason ....

U could linearize your long-tailed pair by putting smallish resistors (say, below 1k) between cathode and virtual ground, is u do not need the amplification. Those resistors act as current feedback as they would do in a common cathode amplifier. Transconductance is decreased, transconductance change caused by aging, too. So the influence of (now) poorly matched tubes is decreased too which is mainly a thing of tube aging.

Pixes coming soon

#### tiroth

Bernhard,

Thanks for the help. I'm afraid I probably won't have time for a couple of days to respond properly, but here are some thoughts.

Feedback loop of my posted circuit: ok, this is all wrong. I'll try to work on this. The primary reason for NFB was too much gain in the circuit, which a cathode follower variant would solve. I will probably use low-mu 5687 tubes, but still anything much over unity will likely be not desireable. I also had a problem with distortion in the single-ended variant that was not completely addressed by NFB. As you pointed out, a reasonable balanced topology looks beautiful distortion-wise without feedback, but the gain is too high.

Plate resistor of T1: Neither my text nor Glass audio's circuit (linked above) uses a plate resistor for the input tube. I don't think I fully understand the reasons for this, but since it is basically being operated as a cathode follower there is not strictly a reason for a plate resistor.

I think your cathode follower differential amp sounds good...I'll be happy to see your pix though. Because one can never have too much, I'm still hoping that it is possible to derive a single-ended output from such a circuit as well. I haven't decided whether I want a differential stage or a differential->single ended stage, but it would be nice to have the flexibility.

Tyler

#### hagtech

low gain diffamp

Do what Dice45 suggests. Add degeneration resistors between cathodes. If you use low mu tubes (even the 12AU7) and these resistors, the gain can be brought way down. Try aim for 6dB or so.

Regarding the missing plate resistor, sometimes this is done to lower input capacitance. It removes the Miller feedback. On the other hand, I far prefer to keep it. Without identical plate loads, the tubes will be biased at completely different operating points and you will lose the ac balance.

jh

#### dice45

Tyler,

no problem, take your time .
BTW, abandoning the ultra-expensive
12AX7 (one always ends up with strong desire for a gold-pin diamond-bottom Telefunken ) and using the comparatively dirt-cheap 5687 always is a good idea, particularly if the high gain, and the sweet coloration are not asked for and the high input capacitance and plate resistance hurt.
Yes, there is also a diamond-bottom \$\$\$ 5687, its the 6900.

Differntial cathode follower: u may have noticed i wrote "This is a diffentially working cathode follower pair." It is infact differntially working, But it is no differntial amp stage. It behaves like such with one exception: both + and - side of the "floating" input signal have to referenced somehow to ground, atleast with a high impedance, as if both sides of this input together float around DC-wise, the cathode followers will follow mercilessly.
i must admit, i haven't tried this out, i also admit, i do not dare to in a DC-coupled amp.
Okok, with output coupling cap, this does not hurt that much AC-wise, provided the stage is not yet into saturation.
But a truly differntial amp stage (or stage input like an input transformer) will not respond at its output to common mode input.

Plate resistor of T1:
differential pairs AKA long-tailed pairs have been often been described/derived as a cathode follower driving a common grid stage. Absolutely true and wonderfully suited to demonstrate a lot of math concerning CMRR and symmetry, it is not illustrating at all.

Imagine both tubes as equivalent and equal. Then use a 1st class CCS, not a resistor, between virtual ground and ground or B- . This CCS forces the current thru it to stay constant. Kirchhoffs law #1 applies: sum of currents going into a node is exactly equal to sum of currents leaving a node. Leaving current is kept constant. So if one tube increases current, the other has to decrease its current by the same amount, otherwise the CCS intervenes by changing the potential of virtual ground in a way total current remains constant. Both inputs having the same common mode signal makes the CCS rigorousy lifting or lowering virtual ground thus cancelling any current change in the plate resistors. Only a potential difference at the inputs causes an exactly inverse current change in both tubes.

Both inputs have high impedance, but not equally high. As hagtech wrote (thanx, hagtech !), one input has no Miller feedback hence lower input capacitance. Both grids used as differntial inputs, fine, and we have one input having an input impedance and capacitance differing to the other. Great

If both tubes have the same load (even if one load produces unused voltage swing, only used to heat up the universe), the both have identical input impedance.

I have not tried out much so far but this i have tried out: if you want a long-tailed pair behave symmetrical, build it as symmetrical as possible. Keep both plate loads.

The beauty of a long-tailed pair is that even if you use it single ended at input or output, it keeps its fancy properties like low THD, fantastic CMRR. You just loose 6dB of gain. As return, u have the freedom to choose inverting or non-inverting mode.

Symmetrical / SE:
going SE is not the only target one should neccesarily aim at. One way among other to get happy. REcently i had a discussion with my buddy Hartmut (AKA hifidaddy) who has tube experience but is probably as deep into SS design as Jocko or Harry and as far as sonic hedonism is concerned, probably way deeper. He compared his practical tube and SS experience concerning cascodes and long-tailed pairs, reported that he was never really happy with cascodes although he preferred tube cascodes to SS ones and that he always was happy with proplerly built long-tailed pairs.

Having the long-term listening experience with two tube preamps in mind, one of them having SE tube/SS cascodes as gain stages and the other having long-tailed pairs of identical cascode circuits, Hartmut's statement made me very alert. Because i was not happy with either amp. I did not know exactly which of them to like -- or should i say loathe -- better and found myself slightly preferring the SE unit. HIFI-wise the differential was balsting the SE one into pieces, never had such a marvelous and detailed low end before.
But way worse, i escaped listening to music with both amps, did not know whether it was the fancy complex CF output or the cascodes, so i abandoned both for my projects, no cascodes at all and no CF except where they are suited for the job and facing an output load atleast ten times their output Z and as real/resistive as possible. But long-tailed pairs i will use. Never found anything wrong with them sonically and in one case a power amp built from long-tailed pairs throughout was as magic as another SE amp, just way better low end.

#### tiroth

Final?

I haven't been entirely slacking off during my hiatus. Here is my current design, balanced in, single ended out, using 5687 tubes. Vp=100V, biased at 10mA. Gain is about 6dB.

I'd like to increase the grid stoppers to 50k to obtain some free HF rolloff, but I don't like the idea of such a large valued resistor in the signal path. Should I really be concerned, though? The simulator says input current is only in the 100nA range.

Bernhard/Hagtech, thanks very much for your suggestion of degeneration. Not only does this avoid some NFB issues, I've found the output also measures much better in terms of THD. Unless anyone has comments, I think I am happy with this design. I appreciate all of the assistance.

For anyone that is following this thread (?) here are some test results (simulations only!!)
=====================

For Vp=100V, bias of 10mA
Zin >1M
Zout ~3.5k
CMRR 55dB @20kHz
CMRR 40dB @100kHz
CMRR 24dB @1MHz

The following tests were done with a 1.5V Vpp differential signal.

30Vp
=====
10mA bias
2nd -23dB
3rd -67dB
4th -42dB
5th -100dB
6th -53dB
7th -84dB
8th -62dB

50Vp
======
10mA bias
2nd -64dB
3rd -68dB
4th -92dB
5th -121dB
6th -92dB

80Vp
=====
10mA bias
2st -76dB
3rd -82dB
4th -93dB
5th <-120dB

100Vp
======
5mA bias
2nd harmonic -73dB
3rd harmonic -69dB
4th harmonic -92dB
5th <-120dB

7mA bias
2nd -73dB
3rd -74dB
4th -91dB
5th <-120

10mA bias
2nd -76dB
3rd -82dB
4th -92dB
5th <-120

120Vp
=====
10mA bias
2nd -77dB
3rd -83dB
4th -92dB
5th <-120

150Vp
======
10mA bias