Noise distribution of a peak track and hold circuit

Noise in linear electronic circuits is well characterised in terms of power spectral density in the frequency domain and the Normal probability density function in the time domain. For instance a charge preamplifier followed by a simple time independent pulse shaping circuit produces an output with a predictable, easily calculated Normal density function. By the Ergodic Principle this is true if the signal is sampled randomly in time or the experiment is run many times and measured at a fixed time after the circuit is released from reset. Apart from well defined cases, the time of the sample after release of reset does not affect the density function.If this signal is then passed through a peak track-and-hold circuit the situation is very different. The probability density function of the sampled signal is no longer Normal and the function changes with the time of the sample after release of reset. This density function can be classified by the Gumbel probability density function which characterises the Extreme Value Distribution of a defined number of Normally distributed values. The number of peaks in the signal is an important factor in the analysis. This issue is analysed theoretically and compared with a time domain noise simulation programme. This is then related to a real electronic circuit used for low-noise X-ray measurements and shows how the low-energy resolution of this system is significantly degraded when using a peak track-and-hold.