Optimizing the Amplifier Bandwidth for Pulse Reception

Detecting and recognizing pulses is a critical task, in fields as widely separated as telecommunications, lidar, and target illumination. In all cases, the signal-to-noise ratio (SNR) is a key parameter that can be used to determine both the potential rate of errors and the probability of correct detection. In this paper the relationship among pulse width, amplifier bandwidth, and SNR is determined through modeling four approximations to pulse shapes and four amplifier lowpass filter configurations. The analysis determined that, given a specific filter and pulse shape, the bandwidth that maximizes SNR is a constant divided by the pulse width. For example, if the pulse has a Gaussian shape and the amplifier incorporates a second-order Chebyshev lowpass filter, this constant is 0.3389. Applying this, if the pulse width is 20 ns the maximum SNR comes for a filter bandwidth of 16.95 MHz, while if the pulse width is 50 µs the SNR is maximized at a 6.778-kHz bandwidth. Passing the signal through a filter also distorts the signal shape; the temporal shift and pulse lengthening are also determined. The calculated values are offered as inputs to a potential trade space that includes SNR, pulse distortion by the filter, and cost.