Effective cathode resistance

skajam66 · 21st November 2011, 09:13 AM

Reading through Morgan Jones' 'Valve Amplifiers', in the section on selecting a cathode by-pass capacitor, MJ states that the effective resistance looking in at the cathode is: (ra + RL)/(u + 1) in parallel with the cathode bias resistor (p79, Third Edition).

Can anyone point me to the derivation of the (ra + RL)/(u + 1) part?

Many thanks.

ac

DF96 · 21st November 2011, 10:05 AM

Any good book on valve circuit theory should include it. It may be presented as the input impedance of the grounded grid amplifier.

A rough-and-ready way to understand it goes something like this:
The valve acts like a resistance ra, which is in series with the anode load RL, so you get ra+RL. However, when looking from the cathode (with a fixed grid potential) the amplification of the valve greatly increases the current flow for a small change in voltage so instead of ra+RL you get (ra+RL)/u. An exact calculation gives u+1 instead of u.

21st November 2011, 09:13 AM	#1
skajam66 diyAudio Member Join Date: Dec 2010	Effective cathode resistance Reading through Morgan Jones' 'Valve Amplifiers', in the section on selecting a cathode by-pass capacitor, MJ states that the effective resistance looking in at the cathode is: (ra + RL)/(u + 1) in parallel with the cathode bias resistor (p79, Third Edition). Can anyone point me to the derivation of the (ra + RL)/(u + 1) part? Many thanks. ac

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21st November 2011, 10:05 AM	#2
DF96 diyAudio Member Join Date: May 2007	Any good book on valve circuit theory should include it. It may be presented as the input impedance of the grounded grid amplifier. A rough-and-ready way to understand it goes something like this: The valve acts like a resistance ra, which is in series with the anode load RL, so you get ra+RL. However, when looking from the cathode (with a fixed grid potential) the amplification of the valve greatly increases the current flow for a small change in voltage so instead of ra+RL you get (ra+RL)/u. An exact calculation gives u+1 instead of u.

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