Question 8.19: Suppose an amplifier has an output noise PSD, Vonoise(f), of......
Suppose an amplifier has an output noise PSD, V_{o n o i s e}(f), of 1\ \mu V/{\sqrt{H z}} (we get this PSD if \textstyle{\mathit{R}}_{s} is a short or an open), a gain of 100, and an input capacitance of 1 pF (infinite input resistance). Determine the input-referred noise sources for the amplifier.
With the input shorted, Fig. 8.43a, we get an input-referred noise voltage spectral density of
A\cdot V_{i n o i s e}(f)=V_{o n o i s e}(f)=1\ \mu V/\sqrt{H z}or since A = 100
V_{i n o i s e}(f)=10\:\mathit{n}V/\sqrt{\mathit{H z}}With the input opened, Fig. 8.43b, we get
I_{i n o i s e}(f)\cdot|Z_{i n}|\cdot A=\frac{I_{i n o i s e}(f)}{2\pi f\cdot\,1p F}\cdot\,100=1\ \mu V/\sqrt{H z}or
I_{i n o i s e}(f)=62.8\times10^{-21}\cdot f\ A/\sqrt{H z}Note that the spectral density increases with f (Fig. 8.44). The noise current contributions to the output noise is insignificant until the frequency gets comparable to 1/(2\pi R_{s}C_{i n}) (noting that squaring I_{i n o i s e}(f) and integrating to find the RMS value results in an f³ term). Unless the source resistance, frequencies of interest, or input capacitance are relatively large, the single input-referred noise voltage source is all that is needed to model the amplifier’s output noise.
