# Output resistance of a MOS current sink

1. Apr 10, 2010

### DivGradCurl

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

Find the output resistance Rout.

[PLAIN]http://img526.imageshack.us/img526/953/pfimg1.jpg [Broken]

2. Relevant equations

$$R_{\rm out} \equiv \frac{v_x}{i_x}$$

3. The attempt at a solution

1) Draw small signal equivalent circuit and attach a test source

[PLAIN]http://img101.imageshack.us/img101/3742/pfimg2.jpg [Broken]

2) KCL at source node:

$$\frac{0-v_s}{1/g_m} + \frac{v_x - v_s}{r_o} = \frac{v_s}{R_S}$$

$$v_x \left( \frac{1}{r_o} \right) = v_s \left( \frac{1}{R_s} + \frac{1}{1/g_m} + \frac{1}{r_o} \right)$$

$$v_x \left( \frac{1}{r_o} \right) = \left( i_x Rs \right) \left( \frac{1}{R_s} + \frac{1}{1/g_m} + \frac{1}{r_o} \right)$$

$$R_{\rm out} \equiv \frac{v_x}{i_x} = r_o \, Rs \left( \frac{1}{R_s} + \frac{1}{1/g_m} + \frac{1}{r_o} \right) = r_o + \left( r_o \, R_s \, g_m \right) + R_s$$

Is this correct? Thanks.

Last edited by a moderator: May 4, 2017
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