Hello everyone. I just started reading about tubes from the book "Valve Amplifiers" from Morgan Jones. It introduces the cathod bias resistor and the cathod bypass capacitor by first explaining what happens if we omitt the capacitor. We actually have negative feedback which increases the anode resistance and decreases the gain. It starts by computing the gain before we add the cathode resistor ( A = μ(Rp/(ra+Rp)) ). When we add the resistor, the new gain is calculated by the universal negative feedback formula Afbk = A/(1 + βA). The feedback fraction β is equal to Rk/Rp and A is the gain we calculated previously. So far so good. He then proceeds to showing how to find the new anode resistance ra' and he uses the following formula: ra' = ra + (μ+1)Rk. I tried deriving the formula by setting Afbk = μ(Rp/(ra'+Rp)) = A/(1 + βA) and then solved for ra'. I ended up with ra' = ra + μRk and not ra' = ra + (μ+1)Rk. Why does this 1 exist there? Could you please help me because I always try to fully understand everything I read about and if I don't I give up....😕😕
Thank you for your answer, I now know that mu + 1 is correct, but could you explain why and where my mistake was in my derivation.
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There is an internal cathode resistance rk. The plate resistance is rk * mu. The total tube resistance is rk+(mu*rk), which is (1+mu) * rk.