Calculating gain of Amplifiers

Question

I have read an interesting formula that says that

\$\mbox{Gain of an amplifier} = \dfrac{\mbox{resistance connected at the output}}{\mbox{total resistance between source and gate of the amplifier}}\$

well, this has simplified the gain calculation and helped me avoid the small signal analysis which proves to be cumbersome in quite many cases.

But i was wondering how to manage the sign in the expression i.e lets say for common source amplifier the gain has a negative sign before it but the common gate amplifier has a positive sign before its gain formula.

Any help as to explain me the significance of the sign?

edit: i am here referring tot he common source amplifiers and the common gate amplifiers, basically types of mosfets

Answer 1

I see you are talking of the resistor from source to ground, and the total resistance on output for the gain of a common source/emitter 1 transistor amplifier.

As regards the sign, I don't think the equation takes it into account as the common source/emitter amplifier is an inverting amplifier. It is just the absolute gain.

Of course you could specify the equation as $$ -\begin{equation} \ Rdrain \over\ Rsource \end{equation} $$ to make sure you always get the right polarity.

In fact (just noticed) if you check the Wiki page on Common source the (more exact) equation is as follows: