440
V. Radeka
pulse shaping (a few tens of nanoseconds) and it can tolerate a noise level of several
hundred electrons rms. Consequently, a leakage (dark) current contributing shot
noise may be 1 nA/cm 2 or more. A silicon detector for x-ray spectroscopy in photon
science must be read out with a total noise of less than ten electrons rms with a
shaping time of the order of 1 μs. This allows a leakage current of only ~10 pA/cm 2
or less. This chapter should enable the reader to evaluate the relations among such
detector and readout parameters.
Signal processing for particle detectors rests on understanding of signal formation and of the sources of noise and their effects on measurement accuracy.
Signal formation in detectors is based on electrostatics and it is calculated relatively
easily starting from the Shockley-Ramo theorem [11, 12]. It gets more involved
in multi-electrode detectors [13] and in crosstalk analysis. Signal processing with
time-invariant systems has been extensively covered in the literature and is well
understood.
Most innovations in signal processing in recent years have been in circuit
implementations using monolithic CMOS technology. This technology has brought
about a significant shift in the circuit concepts to time variant circuits due to the use
of switched capacitance circuits for which CMOS transistors are well suited.
The noise analysis of time variant circuits brings up the question of whether to
perform the analysis in frequency domain or in time domain. Analysis in frequency
domain provides sufficient insight into time invariant circuits and it has been used in
most of the literature. Frequency domain is less well suited for time variant circuit
analysis as it does not provide much insight into the system transfer function. This is
where the concept of the weighting function and Campbell’s theorem [14] provide
the tools which are simpler to use and provide more insight. While both analytical
methods provide the same results in noise calculations, we note that particle detector
signals are best described and are observed in the time domain, and so is the system
response and the weighting function. In contrast, the noise analysis of narrow band
circuits is best done in the frequency domain. The time domain analysis is based
on the representation of noise as a random sequence of elementary impulses. In
spite of our thinking and observing in the time domain, the device and circuit noise
sources are customarily characterized in the frequency domain, e.g., we talk about
the “white noise”, “1/f noise”, etc. Thus we switch our thinking between the two
(Fourier transform related) domains depending on which one provides better insight
and is easier to analyze in a particular case.
This chapter is intended to provide some insight into detector signal processing.
Detailed circuit design, particularly of the monolithic circuits, has been rapidly
developing and there has been a proliferation of publications. Advanced simulation
tools are being used for noise analysis. Sometimes such an analysis provides
numerical results without providing much insight into the role of various noise
sources and into the overall weighting function of the signal processing chain. We
concentrate here on the interpretation of the weighting function and on those aspects
of signal processing and noise that have been less covered in the literature such as
the induced signals in multi-electrode (strip and pixel) detectors, the “kTC” noise,
correlated sampling and basic properties of low noise charge amplifiers. Induced
V. Radeka
pulse shaping (a few tens of nanoseconds) and it can tolerate a noise level of several
hundred electrons rms. Consequently, a leakage (dark) current contributing shot
noise may be 1 nA/cm 2 or more. A silicon detector for x-ray spectroscopy in photon
science must be read out with a total noise of less than ten electrons rms with a
shaping time of the order of 1 μs. This allows a leakage current of only ~10 pA/cm 2
or less. This chapter should enable the reader to evaluate the relations among such
detector and readout parameters.
Signal processing for particle detectors rests on understanding of signal formation and of the sources of noise and their effects on measurement accuracy.
Signal formation in detectors is based on electrostatics and it is calculated relatively
easily starting from the Shockley-Ramo theorem [11, 12]. It gets more involved
in multi-electrode detectors [13] and in crosstalk analysis. Signal processing with
time-invariant systems has been extensively covered in the literature and is well
understood.
Most innovations in signal processing in recent years have been in circuit
implementations using monolithic CMOS technology. This technology has brought
about a significant shift in the circuit concepts to time variant circuits due to the use
of switched capacitance circuits for which CMOS transistors are well suited.
The noise analysis of time variant circuits brings up the question of whether to
perform the analysis in frequency domain or in time domain. Analysis in frequency
domain provides sufficient insight into time invariant circuits and it has been used in
most of the literature. Frequency domain is less well suited for time variant circuit
analysis as it does not provide much insight into the system transfer function. This is
where the concept of the weighting function and Campbell’s theorem [14] provide
the tools which are simpler to use and provide more insight. While both analytical
methods provide the same results in noise calculations, we note that particle detector
signals are best described and are observed in the time domain, and so is the system
response and the weighting function. In contrast, the noise analysis of narrow band
circuits is best done in the frequency domain. The time domain analysis is based
on the representation of noise as a random sequence of elementary impulses. In
spite of our thinking and observing in the time domain, the device and circuit noise
sources are customarily characterized in the frequency domain, e.g., we talk about
the “white noise”, “1/f noise”, etc. Thus we switch our thinking between the two
(Fourier transform related) domains depending on which one provides better insight
and is easier to analyze in a particular case.
This chapter is intended to provide some insight into detector signal processing.
Detailed circuit design, particularly of the monolithic circuits, has been rapidly
developing and there has been a proliferation of publications. Advanced simulation
tools are being used for noise analysis. Sometimes such an analysis provides
numerical results without providing much insight into the role of various noise
sources and into the overall weighting function of the signal processing chain. We
concentrate here on the interpretation of the weighting function and on those aspects
of signal processing and noise that have been less covered in the literature such as
the induced signals in multi-electrode (strip and pixel) detectors, the “kTC” noise,
correlated sampling and basic properties of low noise charge amplifiers. Induced