Noise Equilibrium Frequency as a Measure of the Low Noise Devices Quality Involves the Lambert Function

Lambert Function in the Determining of the Noise Equilibrium Frequency for Radiation Detectors

“…We start with a simple case, partly discussed in [7]. According to the definition, in the bandwidth [ , ] , the white and 1 ⁄ noise have the same power [7].…”

“…We start with a simple case, partly discussed in [7]. According to the definition, in the bandwidth [ , ] , the white and 1 ⁄ noise have the same power [7]. This is not always possible when is predetermined; thus, the solution is not guaranteed for any , moreover the solution is of little use when the result is a too narrow bandwidth for the application considered.…”

“…The noise equilibrium frequency for an amplifier was defined as a bandwidth where white noise and 1/ noise have the same power [7]. When the lower limit of the bandwidth is specified and the noise generators are known, determining the noise equilibrium frequency condition is equivalent with finding the upper frequency, , of the bandwidth.…”

“…When the lower limit of the bandwidth is specified and the noise generators are known, determining the noise equilibrium frequency condition is equivalent with finding the upper frequency, , of the bandwidth. For amplifier noise, for the case of white and 1/ noise, it was shown in [7] that the problem leads to a solution involving the Lambert function. As far as I know, no previous study has applied Lambert function to the radiation sensor plus amplifier circuits.…”

“…As far as I know, no previous study has applied Lambert function to the radiation sensor plus amplifier circuits. In addition, the use of Lambert functions applied to the noise of amplifiers (to computing the "equilibrium frequency" for amplifiers) was never stated or approached, at my best knowledge, before the paper [7].…”