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## 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.

## 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.