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## Q. 7.6

A transistor of width W is laid out with one gate finger and exhibits a total gate resistance of $R_G$ [Fig. 7.23(a)]. Now, we reconfigure the device into four equal gate fingers [Fig. 7.23(b)]. Determine the total gate resistance thermal noise spectrum of the new structure.

## Verified Solution

With a width of W/4, each gate finger now has a distributed resistance of $R_G/4$ and hence a lumped-model resistance of $R_G/12$. Since the four fingers are in parallel, the net resistance is given by $R_G/48$, yielding a noise spectrum of

$\overline{V_{n R G}^2}=4 k T \frac{R_G}{48}$                    (7.31)

(In general, if the gate is decomposed into N parallel fingers, the distributed resistance falls by a factor of N².)