[B._Beckhoff,_et_al.]_Handbook_of_Practical_X-Ray_(b-ok.org).pdf

The enc of the detection system in the following

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The ENC of the Detection System In the following section the way to calculate the ENC will be outlined. The main results are here presented and discussed. See Appendices 1 and 2 (pp. 256–259) for more details. It turns out that the squared value of the ENC can be expressed as the sum of three independent contributions: ENC 2 = ( C D + C G ) 2 a 1 τ A 1 + ( C D + C G ) 2 cA 2 + bτA 3 . (4.22) The first contribution is due to the channel thermal noise of the input FET. The second one is due to the 1/f noise associated with its drain current. The third contribution is due to the shot noise of the leakage current of the detector and of the FET and to the thermal noise of any resistor connected to the gate of the input FET. The noise power spectra a , c , and b (introduced in Section “The Noise Sources” see (4.21)) correspond, respectively, to the three equivalent noise generators at the input of the signal processor: the white series noise generator, the 1/f series noise generator and the white parallel noise generator. For this reason, the three contributions to the ENC are usually called respectively white series noise contribution, 1/f series noise contribution and parallel noise contribution. The capacitances C D and C G are the detector and the gate to source capacitance of the transistor, respectivly. It must be noted that any parasitic capacitance in parallel to the detector must be included in C D (for instance the parasitic capacitance due to the connection between the detector and gate of the input transistor). In the case of the charge-preamplifier configuration, the feedback capacitance has also to be included in C D . The characteristic time τ represents the width of the output pulse (for instance τ can be the peaking time, or the time width at half height, or a time constant of the filter). The characteristic time τ is also called “shaping time” of the filter. The coefficients A 1 , A 2 , and A 3 are constants which depend only on the “shape” of the output pulse of the filter and not on its “width”. If a different choice of the characteristic time τ is performed (for instance if the peaking time instead of the time width at half height is chosen) the value of the
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240 A. Longoni and C. Fiorini coefficients A 1 , A 2 , and A 3 changes. In section 4.2.10 (Appendix 2) it will be shown that, if τ = , the new set of coefficients is given by A 1 ( τ ) = kA 1 ( τ ) A 2 ( τ ) = A 2 ( τ ) A 3 ( τ ) = 1 k A 3 ( τ ) . (4.23) By using the explicit expressions for the noise power spectra given in (4.21), (4.22) can be written in the following useful way ENC 2 = A 1 C D C D C G + C G C D 2 α 2 kT ω T 1 τ + A 2 C D C D C G + C G C D 2 α 2 kT ω T ω 1 + A 3 qI L τ. (4.24) Figure 4.32 shows the ENC 2 versus the shaping time τ and the contributions of the series, parallel and 1/f noise sources.
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