Bootstrapped Cathode Coupled Amplifier
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 11th June 2013, 10:59 PM #1 JFace   diyAudio Member   Join Date: Sep 2011 Location: Toronto Bootstrapped Cathode Coupled Amplifier How do I calculate the gain of a cathode coupled amplifier of a triode valve that has the grid leak resistor bootstrapped to the cathode resistors? Basically it's a cathode follower circuit except measured not from the cathode but from the plate.
 11th June 2013, 11:18 PM #2 tomchr   diyAudio Member     Join Date: Feb 2009 Location: Calgary The gain should still be [Plate load]/[unbypassed cathode resistance]. Assuming a high enough mu anyway. Basically, it's the same gain equation as a regular grounded cathode. The input impedance is just much higher. ~Tom __________________ Modulus-686: 240W/8Ω @ <0.00025% THD. Modulus-86: 40W/8Ω @ 0.000054% THD. DG300B & Other Tube Circuits. Neurochrome : : Audio - www.neurochrome.com - Engineering : : Done : : Right
JFace
diyAudio Member

Join Date: Sep 2011
Location: Toronto
Quote:
 Originally Posted by tomchr The gain should still be [Plate load]/[unbypassed cathode resistance]. Assuming a high enough mu anyway. Basically, it's the same gain equation as a regular grounded cathode. The input impedance is just much higher. ~Tom
Is that the quick and easy equation? I've always used:

A = (u * Plate load) / (Plate Load + anode resistance + Cathode resistance*(u + 1))

In either case, I get a similar answer for my values:

Tube: 12AX7
Cathode Resistance: 1.5K + 10K
A ~= 8

 12th June 2013, 09:12 AM #4 DF96   diyAudio Member   Join Date: May 2007 A circuit diagram would help ensure that we are all talking about the same circuit. The OP in post 1 seems mention two quite different circuits: cathode coupled (first sentence) or cathode degeneration (second sentence)? Boostrapping the grid resistor raises input impedance but has almost no effect on gain. Assuming we are talking about cathode degeneration, post 3 gives the correct formula for gain. An alternative view of that is to regard valve mu and Ranode/Rcathode as two separate gain calculations, then treat them as though they were resistors in parallel: so gain = mu*(Ra/Rk) / (mu + (Ra/Rk) ). However, Rk should strictly be the external cathode resistor plus 1/gm (i.e. the 'internal' cathode resistor).
JFace
diyAudio Member

Join Date: Sep 2011
Location: Toronto
Quote:
 Originally Posted by DF96 A circuit diagram would help ensure that we are all talking about the same circuit. The OP in post 1 seems mention two quite different circuits: cathode coupled (first sentence) or cathode degeneration (second sentence)?
Cathode degeneration is a new term for me and perhaps why I could never find the proper circuit when searching bootstrapped cathode coupled amp.

Attached is the schematic from Fun With Tubes.
Attached Images
 Amp-K_Degen_S.gif (3.1 KB, 191 views)

 12th June 2013, 10:25 AM #6 DF96   diyAudio Member   Join Date: May 2007 That is a grounded cathode amp, with cathode degeneration and grid resistor partial bootstrapping. With equal cathode and anode resistors it becomes a cathodyne phase splitter. With smaller (or zero) anode resistor and output taken from the cathode it becomes a cathode follower. The cathode coupled amp has two valves with cathodes connected together, rather like the long tail pair. I sometimes call it a short tail pair.
JFace
diyAudio Member

Join Date: Sep 2011
Location: Toronto
Is this also called cathode degeneration? How does the resistor in series with the bypass capacitor affect frequency response?
Attached Images
 Amp-K_Degen_P.gif (3.8 KB, 181 views)

 12th June 2013, 11:15 AM #8 jazbo8 diyAudio Moderator     Join Date: Jan 2011 Location: In Transient Degeneration = Feedback, so cathode degeneration typically means un-bypassed cathode resistor. What you showed is a partially bypassed grounded cathode amplifier.
 12th June 2013, 11:32 AM #9 DF96   diyAudio Member   Join Date: May 2007 Putting a resistor in series with the cathode bypass cap is an alternative way of providing cathode degeneration. To calculate the frequency response you need to use circuit theory to arrive at an expression for the net (frequency dependent) impedance at the cathode, and then use that in the expression for gain. What you get is an LF shelf cut. The corner frequencies are proportional to 1/C, but the exact relationship with the resistor values depends on gm too so the algebra can be a bit messy. To some extent it depends on the anode resistor too, although this is often overlooked.
JFace
diyAudio Member

Join Date: Sep 2011
Location: Toronto
Quote:
 Originally Posted by JFace Is this also called cathode degeneration? How does the resistor in series with the bypass capacitor affect frequency response?
I found an explanation here:

Biasing and Gain

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