Noise

The filter output noise level is calculated from the input-referred noise spectra S_{n, i} of the intrinsic integrators and the transfer functions g_i from the inputs of the intrinsic integrators to the output of the filter. If the noise spectra S_{n, i} are white, the output noise level of the filter is

$$\overline{{V_{\rm n, o}^2}} \sum_{{i = 1}}^{n}$$ (24)

The dynamic range is

$${\frac{{ \overline{V_{\hbox{max,out}}^2} }}{{ \overline{V_{\rm n, o}^2} }}}$$ (25)

where $\overline{{V_{\hbox{max,out}}^2}}$ follows either from (17) or from (21) or (23).

In the same way as | f_i|₂² is dependent on an input weighting function, | g_i|₂² is dependent on an output weighting function  S_o(ω) , which by default is identical to 1. Furthermore, one can prove [1] that

$${\frac{{2kT\xi}}{{C_i}}} \left(\vphantom{ \vert b_i\vert + \sum_{j=1}^{n} \vert a_{ij}\vert }\right. \sum_{{j=1}}^{{n}} \left.\vphantom{ \vert b_i\vert + \sum_{j=1}^{n} \vert a_{ij}\vert }\right)$$ (26)

where C_i is the capacitance used for integrator i , and ξ is the noise factor.

FA will determine the dynamic range from the scaling flags, the total capacitance in the filter (the variable ctot), the maximal integrator output level (the variable umax) and the noise factor (the variable noisefactor) upon the command:

output: dr;

If the variable ctot is not set, it will generate an error message.