Transconductance GM meaning, calculation, and why GM*ROUT gives output voltage

Transconductance (GM) is defined as the ratio of output current change to input voltage change (GM = Iout / Vin), representing how effectively a device converts input voltage variations into output current variations. It is not GM = Vout / Iout, which was a common misconception in the discussion. In transistor amplifiers, particularly with FETs and vacuum tubes, GM quantifies the sensitivity of output current to input voltage changes. The output voltage (Vout) is obtained by multiplying the output current (Iout) by the load resistance (ROUT), thus Vout = ROUT * Iout. Combining these relations yields Vout = ROUT * GM * Vin, and the voltage gain (Gain) is therefore Gain = Vout / Vin = GM * ROUT. GM is device-dependent and varies between different FETs or tubes; it is not a fixed constant. The confusion arose from mixing voltage and current terms and misunderstanding the definition of GM. The discussion clarified that GM is a transconductance (current over voltage), not a transresistance (voltage over current), and that the gain calculation requires consistent input-output variable pairing.
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