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Old 11th June 2013, 11:59 PM   #1
JFace is offline JFace  Canada
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Default 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.
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Old 12th June 2013, 12:18 AM   #2
tomchr is offline tomchr  United States
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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
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Old 12th June 2013, 02:06 AM   #3
JFace is offline JFace  Canada
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Quote:
Originally Posted by tomchr View Post
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
Plate Load: 100K
Cathode Resistance: 1.5K + 10K
A ~= 8
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Old 12th June 2013, 10:12 AM   #4
DF96 is offline DF96  England
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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).
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Old 12th June 2013, 11:18 AM   #5
JFace is offline JFace  Canada
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Quote:
Originally Posted by DF96 View Post
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.
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File Type: gif Amp-K_Degen_S.gif (3.1 KB, 143 views)
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Old 12th June 2013, 11:25 AM   #6
DF96 is offline DF96  England
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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.
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Old 12th June 2013, 12:10 PM   #7
JFace is offline JFace  Canada
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Is this also called cathode degeneration? How does the resistor in series with the bypass capacitor affect frequency response?
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Old 12th June 2013, 12:15 PM   #8
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Degeneration = Feedback, so cathode degeneration typically means un-bypassed cathode resistor. What you showed is a partially bypassed grounded cathode amplifier.
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Old 12th June 2013, 12:32 PM   #9
DF96 is offline DF96  England
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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.
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Old 12th June 2013, 09:26 PM   #10
JFace is offline JFace  Canada
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Quote:
Originally Posted by JFace View Post
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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