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## Q. 7.5

Find the maximum noise voltage that a single MOSFET can generate.

## Verified Solution

As shown in Fig. 7.20, the maximum output noise occurs if the transistor sees only its own output impedance as the load, i.e., if the external load is an ideal current source. The output noise voltage spectrum is then given by $S_{\text {out }}(f)=S_{\text {in }}(f)|H(f)|^2$ , i.e.,

\begin{aligned} \overline{V_n^2} &=\overline{I_n^2} r_O^2 (7.29)\\ &=\left(4 k T \gamma g_m\right) r_O^2 (7.30) \end{aligned}

Let us make three observations. First, (7.30) suggests that the noise current of a MOS transistor decreases if the transconductance drops. For example, if the transistor operates as a constant current source, it is desirable to minimize its transconductance.

Second, the noise measured at the output of the circuit does not depend on where the input terminal is because for output noise calculation, the input is set to zero.$^9$ For example, the circuit of Fig. 7.20 may be a common-source or a common-gate stage, exhibiting the same output noise. Third, the output resistance, $r_O$ , does not produce noise because it is not a physical resistor.

$^9$Of course, if the input voltage or current source has an output impedance that generates noise, this statement must be interpreted carefully. 