How preamplifier affects system performance?

The preamplifier noise current can be approximated as

i²_PA = 4kT/R_f + i²_n + e²_n /Z²_d

where: i_n and e_n are the preamplifier input current and voltage noise, T– temperature, k– Boltzman constant (1.3806·10^-23 J/K), Z_d - the detector reactance, R_f – feedback resistance

Z_d = Rd/(1 + (2πf)C²_d R²_d )^1/2

The resulting noise of a detector/preamplifier module is:

i² _N = i²_PA + i²_d

Therefore, the effective detectivity of the detector/preamplifier system is:

D*_S = D*/(1 + i²_PA /i²_d)^1/2

In ideal case, when the preamplifier noise is much less than the detector noise, the resulting detectivity is equal to the detecort detectivity. In practice, the preamplifier noise less or equal to the detector noise (3dB D^* reduction) is considered to be satisfactory. The preamplifier noise may significantly reduce the system performance in some situation, homever. This happens for large capacitance detectors operating at hihg frequencies.