Operation at Low Frequencies and in Various Configurations

Thus far, we have been especially concerned with absorption detectors operating in the optical and infrared regions of the electromagnetic spectrum (hv kT, where k is the Boltzmann constant and T is the detector temperature). In this case, the intensity of the incoming wave is obtained from the analytic signal and excludes double- and sum-frequency components [7.10, 12-14]. Nevertheless, (7.77) is a general result for intensity detection which applies also to the microwave and radio wave regions (hv kT). 

For low frequencies, the intensity is related to the square of the electric field, IccE. For a diode mixer which is either operating in the square-law regime or in 

Note that /l cos (cof + 0) = (+V2)[l+cos(2mf + 20)]. Now, since the detector generally does not follow the instantaneous intensity at double- and sum-frequencies (2cOi, cui +CO2,. ..), only dc and difference-frequency terms remain. Hence (7.121) will in practice reduce to (7.36). The calculations leading to (7.121) will remain correct, provided of course, that we insert the proper relation for (SNR)i in the classical low frequency detection regime. Generally, this is obtained by replacing hv by kTand rj by 1/Fj, where Fj is the noise figure of the receiver. 

Once the target is ascertained to be present, a wide bandpass filter can be gradually narrowed about 2 f[ — f or 2I/2 —/lI and thereby used to obtain Doppler information. Alternatively one could, of course, switch to a conventional configuration. 

It is of interest to examine the operation of the three-frequency nonlinear heterodyne system in a variety of configurations [7.59] different from those assumed earlier. In this section, we consider the behavior of the system under the following conditions 1) at zero frequency (dc), 2) without a final bandpass filter, 3) with increased Doppler information, 4) as an optimum system with no uncertainty in Doppler shift, and 5) with a vth law nonlinear device other than square-law. We also consider the consequences of four-frequency nonlinear heterodyne detection this will be examined in greater detail in Section 7.4. 

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