We know that transconductance is defined as:
$$g_m=\frac{\Delta i_{\text{output}}}{\Delta V_{\text{input}}}$$
My question is: why is such a quantity as transconductance defined in the way it is? How is it helpful to electrical engineers?
I ask this because I am having difficulty memorizing this formula. I always mess it up as \$g_m=\frac{\Delta i_{\text{input}}}{\Delta V_{\text{output}}}\$ instead of the correct one. I know conductance is inverse of resistance, so the current will always be in the numerator and voltage in denominator. But, I am not sure which one is output and which one is input. Perhaps, if I know the logic of this definition, I'll be able to recall better.
Sorry if this reason is apparent to you, but I am a beginner, and it is not at all apparent to me, so kindly explain in simple language. Thank you!
Note: Please restrict your answer to a Bipolar Junction Transistor only.
Best Answer
The ‘trans’ bit is short for ‘transfer’, and the transfer referred to is from input to output.
So think of transconductance as a transfer function, which is always in the form \$\frac{output}{input}\$, and ‘conductance’ is \$\frac{current}{voltage}\$, hence \$g_m=\frac{output\:current}{input\:voltage}\$