B.2.1.1 Finite Integrator Gain

The effect of a non-ideal integrator, i.e., finite gain degrades the noise performance to some extent. The integrator frequency response can be modeled as

$$H(s) = \frac{1 }{s\tau_0 + 1/A} = \left\{ { \begin{array... .../s\tau_0 & 1/A\tau_0 < \vert s\vert \\ \end{array}} \right. ,$$ (B.6)

where A is the integrator gain. This sets a lower limit to the noise power spectral density and to the achievable SNR:

$$S/N = \frac{\left<\left\vert x(t)\right\vert^2\right>}{\left<\left\vert e(t)\right\vert^2\right>} A .$$ (B.7)