SNR and MDP for Two Gaussian Signals

For quantum-noise limited detectors such as photoemitters and reverse-biased photodiodes operating in the infrared and optical [7.4—7,10,14,15], assuming that the incident radiation and the coherent LO are polarized in the same plane, the input SNR to the nonlinear device is [see (7.1) and (7.42b)] 

Here is the detector quantum efficiency. P, is the total received signal radiation power, and kT is the thermal excitation energy (k is Boltzmann s constant and T is the detector temperature). For photovoltaic and photo-conductive detectors, the input SNR is generally one-half that given in (7.186) [7.5, 14]. 

Heterodyne detectors in the microwave and millimeter regions (hv kT) include square-law mixers such as the crystal diode detector [7.93], the InSb photoconductive detector [7.94-96], the Golay cell [7.95], the pyroelectric detector [7.95], the metal-oxide-metal diode, and the bolometer [7.87]. The latter three types of detectors have also been used successfully in the middle infrared (at 10.6 pm) [7.97-100]. For this type of detector Johnson noise generally predominates, and the input SNR is given by [7.100] 

For simplicity, we have lumped a number of detector parameters and operating conditions into the receiver effective temperature 7 cff Of particular interest in 

Inserting (7.186) or (7.187) into (7.185), and letting (SNR)q = 1, we obtain a minimum detectable total power (MDP) at the output of the three-frequency system given by 

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