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In a wide variety of applications, including free-space communications, target illumination, and radar (laser, microwave, millimeter wave, etc.), an electromagnetic pulse is collected by a receiver and converted to an electronic signal. This electronic pulse is then amplified before it is processed into digital data, tracking information, or range and velocity values. In this paper it is shown that an optimum amplification half-power bandwidth—in terms of maximum signal-to-noise ratio (SNR)—can be determined, based almost exclusively on the full width at half maximum (FWHM) of the pulse and the roll-off rate of the amplifier at frequencies above the high-frequency cutoff. The shape of the pulse and the specific amplification filter (e.g. Butterworth, Chebyshev, Elliptic, etc.) has little effect on the optimum bandwidth. For example, if the amplifier includes a low-pass first-order Butterworth filter whose half-power frequency is Δν, a pulse whose FWHM is Δ<i>t</i> will be amplified at the maximum possible SNR if Δν = 0.146/Δ<i>t</i>. This assumes that any noise in the system is essentially white, in that the total noise is proportional to the square root of the amplification bandwidth. It should be noted, and is discussed in this paper, that the maximum SNR may not lead to the ideal bandwidth, since it with distort the shape of the input pulse. This distortion alters the shape of the pulse and may affect the calculation of the pulse centroid, which is particularly important in range and velocity calculations. This may lead to an increase in the optimum bandwidth.
DOI: 10.1117/12.2558339