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## Q. 7.8

For an NMOS current source, calculate the total thermal and 1/ f noise in the drain current for a band from 1 kHz to 1 MHz.

## Verified Solution

The thermal noise current per unit bandwidth is given by $\overline{I_{n, t h}^2}=4 k T \gamma g_m$. Thus, the total thermal noise integrated across the band of interest is

\begin{aligned} \overline{I_{n, t h, t o t}^2} &=4 k T \gamma g_m\left(10^6-10^3\right) (7.35)\\ & \approx 4 k T \gamma g_m \times 10^6 A ^2 (7.36)\end{aligned}

For 1/ f noise, the drain noise current per unit bandwidth is obtained by multiplying the noise voltage at the gate by the device transconductance:

$\overline{I_{n, 1 / f}^2}=\frac{K}{C_{o x} W L} \cdot \frac{1}{f} \cdot g_m^2$                                                (7.37)

The total 1/ f noise is then equal to

\begin{aligned} \overline{I_{n, 1 / f, t o t}^2} &=\frac{K g_m^2}{C_{o x} W L} \int_{1 kHz }^{1 MHz } \frac{d f}{f} (7.38)\\ &=\frac{K g_m^2}{C_{o x} W L} \ln 10^3 &(7.39) \\ &=\frac{6.91 K g_m^2}{C_{o x} W I} &(7.40)\end{aligned}