Referring to Figure 1 (Nanometrics 1990), the equations to be solved to find the relationship

between input and output signals ( and ) of the fourth order low-pass filter are:

After some algebra, equations 2-6 give:

where:

Inserting numbers for the components of the 4th order filter (see Appendix A) gives:

Similarly, for the second order bandpass filter, the frequency response is:

The frequency response of the two filters is then given by:

where:

and the *k*'s are given by equation 12 and the *b*'s by
equation 13. Inserting numbers, the frequency response of
the RD3 system is:

The function obviously has one zero at zero frequency.
The poles where found
using standard numerical routines (programmes `zroots` and `laguer`,
(Press et al. 1988))
and are:

The frequency independent gain of the system is the multiple of the pre-amplifier (0.908), the post-amplifier ( ) and the filter gains ( V/bit), i.e.:

See Figure 4 in Nanometrics (1990) and Appendix B for explanations of the numbers given above. The frequency response of the RD3/OSD3 digitizer can then be written:

Wed Mar 19 12:54:50 GMT 1997