Physics and Engineering of Radiation Detection

8.9. Electronics Noise 509

adders,

delay function, and

multipliers.

Since typical digital filters consist of very large number of such building blocks
or functions, therefore they are prone to errors introduced by the associated mathe-
matical operations. The errors introduced by additions and multiplications can pile
up and become significant at the output. Therefore designing a digital filter not
only warrants care in designing the algorithms but also in its implementation.
Most of the modern digital filters are based on floating point mathematics with
feedback. That is, the functions are recursively calculated until some predefined
condition is met. The technical name of such filters isinfinite impulse response
filters, since here the transfer functions are actually represented by infinite recursive
series. The foremost advantage of this technique is that it can be used to design and
implement filters that are not realizable in conventional analog signal processors.
That is why most modern multi channel analyzers have built in digital filters and
can therefore be called digital signal processors.

8.9 ElectronicsNoise

In the real world, there are no electronic components that behave ideally. Their
deviation from the expected ideal behavior can be random or systematic, both of
which are collectively calledelectronics noise. Depending on the particular applica-
tion, this noise may or may not be a significant source of degradation of the signal
to noise ratio in radiation measurement systems. It is therefore important to first
estimate the contribution of the electronics noise to the overall noise and make a
judgment on whether to invest in electronics noise reduction or not. Low resolution
systems working at high rates, generally do not require low noise electronics. On
the other hand for high resolution systems, reduction in electronics noise is a major
challenge.
One of the highly desired traits of a good system is that its electronics noise
should not depend on the signal itself. That is, the output fluctuations with no input
(often called pedestal fluctuations) should not change when an actual signal enters
the electronics chain. Fortunately, with modern electronics components, deviation
from this behavior is only seldom observed. Therefore, in most situations, we are
left with quantifying the pedestal noise. Comparing this noise with the expected
signal would then tell us whether it is worthwhile to put efforts to decrease the noise
further or not. Let us elaborate this with an example.
Suppose we want to measure the energy of 90keV photons using a silicon de-
tector. The mean number of electron hole pairs generated by photons depositing
energyEdepcan be calculated from

N=

Eγ

W

whereW is the energy needed to create a charge pair. For silicon we haveW =
3. 6 eV. We suppose that the incident photon is completely stopped in the active