## Chapter 7

## Q. 7.10

What is the total output noise voltage of the common-source stage shown in Fig. 7.29(a)? Assume that λ = 0.

## Step-by-Step

## Verified Solution

We must identify the sources of noise, find their transfer functions to the output, multiply their spectra by the squared magnitude of the transfer functions and add the results. We model the thermal and flicker noise of M_1 by two current sources: \overline{I_{n, t h}^2}=4 k T \gamma g_m and \overline{I_{n, 1 / f}^2}=K g_m^2 /\left(C_{o x} W L f\right) We also represent the thermal noise of R_D by a current source \overline{I_{n, R D}^2}=4 k T / R_D Since these currents flow through R_D, the output noise voltage per unit bandwidth is equal to

\overline{V_{n, \text { out }}^2}=\left(4 k T \gamma g_m+\frac{K}{C_{o x} W L} \cdot \frac{1}{f} \cdot g_m^2+\frac{4 k T}{R_D}\right) R_D^2 (7.44)

Note that the noise mechanisms are added as “power” quantities because they are uncorrelated. The value given by (7.44) represents the noise power in 1 Hz at a frequency f . The total output noise is obtained by integration.