# Negative Gain and Resistance

1. Mar 21, 2015

### Zondrina

1. The problem statement, all variables and given/known data

Calculate $R_S$ given the expression:

$$A_v = - \frac{g_m (R_L || R_D)}{1 + g_m R_S}$$

The parameters $g_m = 1.292 \frac{mA}{V}$, $R_L = 180 k \Omega$, $R_D = 18 k \Omega$, $A_v = 5 \frac{V}{V}$.

2. Relevant equations

3. The attempt at a solution

My question is about the negative sign. When I go to compute $R_S$, do I pretend the negative sign isn't there or something? If I leave the negative sign in the calculation I get:

$R_S = - 4.05 k \Omega$

Resistances must be positive, so the above does not make physical sense.

If I pretend the negative sign isn't there then I get:

$R_S = 2.5 k \Omega$

What is the proper way to compute the resistance?

EDIT: I believe the gain should be $A_v = -5 V/V$ even though it was given as 5, so the resistance $R_S = 2.5 k \Omega$ should be correct.

Last edited: Mar 21, 2015
2. Mar 21, 2015

### milesyoung

This is for a common-source amplifier with source resistance $R_S$? If so, then you're right about $A_v$.

3. Mar 23, 2015

### rude man

Generalizing post 2 a bit, I'd venture that the circuit is an inverting stage of some kind, be it MOSFET, JFET, BJT, vacuum tube, etc. - based.

4. Mar 23, 2015

### milesyoung

I just guessed it was FET-based from the subscripts, i.e. D, S, L for drain, source, load.

5. Mar 23, 2015

Sure.