These preamplifiers are preferred for most energy spectroscopy applications. The signal from a semiconductor detector or ion chamber is a quantity of charge delivered as a current pulse lasting from 10^–9 to 10^–5 s, depending on the type of detector and its size. For most applications the parameters of interest are the quantity of charge and/or the time of occurrence of an event. A charge-sensitive preamplifier (Fig. 3) can deliver either or both. Because it integrates the charge on the feedback capacitor, its gain is not sensitive to a change in detector capacitance, and in the ideal case, the rise time of the output pulse is equal to the detector current pulse width.

The output voltage from the preamplifier has an amplitude V_o, and a decay time constant t_f, given respectively by

where Q_D is the charge released by the detector, C_f is the feedback capacitor (0.1 to 5 pF), and R_f is the feedback resistor. R_f is a noise source and in direct-coupled system, is made as large as possible consistent with the signal energy-rate product and the detector leakage current. The preamplifier package is kept small to permit mounting it as close as practical to the detector, thus reducing input capacitance caused by cabling and decreasing microphonic noise, ground loops, and radio frequency pickup, all of which are sources of noise for the charge-sensitive preamplifier.

In the selection chart, sensitivity is generally expressed in mV per MeV of energy deposited in a given detector material. The charge released by the detector is a function of the photon or particle energy and the detector material, and is given by

where E is the energy in MeV of the incident radiation, e is the charge of an electron (1.6 X 10^–19 coulomb), 10⁶ converts MeV to eV, and ε is the amount of energy required to produce an electron-hole pair in the detector. Approximate values for ε for various detectors are given in Table 1. For the special case of a proportional counter, the right hand side of Equation (3) must be multiplied by the gas gain of the proportional counter.

From Eqs. (2) and (3) the output voltage produced by a charge-sensitive preamplifier is

Therefore, the preamplifier gain can be expressed as

The sensitivity of a preamplifier with C_f = 1 X 10^–12 F connected to a room-temperature silicon detector is

The input of the preamplifier appears as a large capacitor to the detector because the effect of the feedback capacitor at the input is magnified by the open loop gain of the charge loop. This input capacitance must be much greater than the other sources of capacitance connected to the preamplifier input (such as the detector or input cabling) in order for the preamplifier sensitivity to be unaffected by external capacitance changes. Since C_f is generally ~1 X 10^–12 F, the preamplifier open loop gain must be very large, usually greater than 10,000. The stability of the preamplifier sensitivity is dependent on the stability of C_f (the feedback capacitor), and the preamplifier open loop gain. C_f is selected for good temperature stability, and the open loop gain is made very large so that small changes in it can be neglected. Preamplifier sensitivity variations can contribute to the error in measuring the energy of the detected radiation.

Noise in charge-sensitive preamplifiers is generally controlled by four components: the input field effect transistor (FET), the total capacitance at the input (C_f, the detector capacitance, etc.), the resistance connected to the input, and input leakage currents from the detector and FET. The FET is selected for low-noise performance, and in some applications it is cooled to near liquid-nitrogen temperature to improve its performance. In cooled-FET applications the detector and preamplifier are generally built as an integral assembly. with room-temperature preamplifiers, the user controls the major sources of input capacitance in most applications, because the preamplifier is designed with minimum internal circuit capacitance. These sources are from the detector selected for an experiment and from the cabling between the preamplifier and the detector. Figure 4 is a graph showing the noise versus external capacitance for a typical preamplifier.

The noise of a charge-sensitive preamplifier can be measured by the system shown in Fig. 5. Charge Q, equivalent to the known energy, E, must be injected into the preamplifier, and the amplitude of the pulse V_p resulting from this charge must be measured at the output of the filter amplifier to determine the system gain V_p/E. The charge can be injected by a detector and radiation source or a step pulse generator connected to the preamplifier input through a capacitor, sometimes referred to as a charge terminator. The preamplifier noise can be determined by measuring the root-mean-square (rms) noise voltage V_rms at the output of the filter amplifier in the absence of any pulses, and using the following equation:

Charge-sensitive-preamplifier noise performance is generally specified as the full width at half maximum (FWHM) of the energy line generated in the spectrum by a test pulser injecting charge into the preamplifier input. This value is normally given in keV. The parameter V_rms must be multiplied by 2.35 to convert it to a FWHM specification.

The rise time of the voltage pulse V_o at the output of the charge-sensitive preamplifier, in the ideal case, is equal to the charge collection time of the detector. When detectors with very fast collection times or large capacitances are used, the preamplifier itself may limit the rise time of V_o. If a time reference mark is being determined from V_o, it is desirable that the rise time t_r of V_o be as short as possible. For silicon detectors, the time resolution of the timing system following charge-sensitive preamplifiers is generally limited by the ratio of the FWHM preamplifier output noise e_no to the slope dV_o/dt of V_o at the timing threshold:

timing resolution (FWHM) = e_noV_o/dt).           (8)

A plot of a charge-sensitive-preamplifier output rise time versus detector capacitance is shown in Fig. 6. It is desirable to keep the external capacitance at a minimum to obtain the best timing resolution, as well as the best energy resolution.

To estimate the maximum counting rate r_max that can be accommodated by a charge-sensitive preamplifier at a particular energy, it is necessary to identify the type of preamplifier being considered (see IEEE Standard 301-1988). With charged-particle detectors, the signal is normally extracted from the same detector electrode that accepts the bias voltage, and the preamplifier input is ac-coupled to the detector. The maximum counting rate tolerated by ac-coupled preamplifiers (r_max,ac) is controlled by the signal fluctuations and the maximum voltage V_m allowed at the charge loop output:

The units are: r_max,ac in s^–1, V_m in volts, ε in eV, E in MeV, C_f in farads, and R_f in ohms. If the "energy-squared count-rate product" (i.e., E²CRP = E²r_max,ac) is listed for the ac-coupled preamplifier, the maximum counting rate tolerated at the energy E can be calculated by dividing the E²CRP value by E².

The charge-sensitive preamplifiers used with germanium gamma-ray detectors and Si(Li) x-ray detectors are normally dc-coupled to the detector. For dc-coupled preamplifiers, the maximum counting rate accommodated at the energy E is controlled by R_f and V_m.

If the "energy count-rate product" (i.e., ECRP = Er_max,dc) is specified for the dc-coupled preamplifier, the maximum counting rate tolerated at the energy E can be calculated by dividing the ECRP value by E.

With pulsed-reset preamplifiers, the maximum counting rate limit for the preamplifier is the counting rate at which the percent dead time caused by the resetting becomes intolerable. The percent dead time resulting from preamplifier resetting is computed from

Percent Reset Dead Time = 100 E r T_reset/E_reset           (11)

where r is the counting rate of the events of energy E, E_reset is the total energy accepted between resets, and T_reset is the dead time caused by each reset. A rough approximation for T_reset can be obtained by adding the preamplifier reset time to the amplifier overload recovery time. Typically, amplifier overload recovery from the large reset pulse is the major contribution to the reset dead time.