Radiation detection systems often consist of a detector, a charge sensitive pre-amplifier, a pulse shaping amplifier and a multi-channel analyser. The detector converts interaction of photon energy from an X-ray source into an electrical signal. The electrical signal voltage is proportional to the energy of the incident photon. When a semiconductor detector is used for soft x-ray measurement or gamma-rays, the output signal is a current pulse with a pulse width of few nanoseconds. The signal is usually weak and requires amplification. Operational amplifiers conigured as integrators with feedback capacitance are commonly used. When a weak charge pulse signal is presented at the high impedance input of an integrator, the signal is integrated to produce a voltage pulse. This type of integrator amplifiers are known as Charge Sensitive Amplifier (CSA).  
The characteristics of a good charge sensitive amplifier are:
- Low noise.
- High Gain.
- Integration linearity.
- Stable with a big range of detector capacitance.
- High speed; Fast Rise time.
Figure 1: Charge Sensitive Preamplifier
When X-rays strike a semiconductor detector, current pulses are generated and the amplitude of those pulses are dependant on the particle energy. When a current pulse is generated, the input of the CSA rises but at the same time a potential with reverse polarity will appear at the output. Amplifiers tend to have a large open loop gain and so the output work through the feedback loop to make the input potential zero instantaneously. As a result, the current is integrated across the feedback capacitor Cf. A voltage appears at the output Vout and this output voltage is proportional to the charge contained in the input current pulse.
The Feedback Resistor
Charge Sensitive amplifiers are usually not stable and requires a mechanism to reset the charge stored in the feedback capacitor Cf. The simplest way involves putting a resistor Rf in the feedback loop as shown in Figure 1. The feedback resistor Rf will cause the output voltage Vout to look like a voltage pulse that discharges slowly with a time constant given by tau=Cf.Rf. The resistor Rf also establishes a well defined DC operating point to the amplifier. The feedback resistor provides a path for the leakage current of the detector. However, the resistor Rf is known to introduce additional noise to the output signal. In semiconductor X-ray spectrometers, the noise produced by the charge sensitive amplifiers can contribute a considerable noise to the output signal and thus limiting the energy resolution. 
Although a higher feedback resistance will introduce higher thermal noise, it is still desirable to have a large resistance as when a shunt capacitance is placed with the feedback resistor; it will limit the resistor thermal noise.
Figure 2: Shunt Resistor and Capacitor circuit
If vn is considered as an input, Vout can be written as:
As Rf increases, vn also increases. However the signal vn starts attenuating with a -3dB point at f = 1/(jwRfCf). As Rfincreases, vn increases but the bandwidth of the noise signal decreases. Figure 3 below shows the spectral density of different Rf shunt with a Cf of 1pF.
Figure 3: Spectral density of Resistor and Capacitor shunt circuit
A higher resistor will produce a higher noise but because of the RC network arrangement, the noise spectral density will show a lower cut off frequency. For circuit operating at high frequency, the resistor noise will have significantly less effect on the circuit noise performance. 
Other systems reported in literature consist of replacing the feedback resistor with an optical reset method where a pulsed light source is shone onto an unpackaged FET which is sensitive to light. Optical reset method can considerably reduce the noise of the system but it is known to introduce dead time and the effect of the reset pulse need to be remove at the acquisition stage. It also required sensing the output voltage and comparing it to a preset voltage and when the preset voltage is exceeded, the feedback capacitor Cf is reset. This method can be troublesome. It is more desirable to implement a system with continuous feedback rather than one that relies on pulse gating circuits.[5-8]
[9-11] proposes a novel circuit where the feedback resistor Rf is removed and where the circuit remain stable. In the novel circuit, Bertuccio uses the gate to channel junction of the input JFET as a path for the feedback capacitor Cf to discharge and for the detector leakage current to flow.
Figure 4: Charge Sensitive Preamplifier without feedback resistor Rf 
In a n-channel JFET, the gate-to-channel junction looks like a p-n junction. In reverse bias mode, the gate leakage current is very low, resulting into a high input impedance. Forward bias mode is not often used because this then results into a low input impedance. Bertuccio also investigate the use of JFETs in the so called `forward bias mode” and concludes that it is possible to forward bias them.
His novel idea consists of forcing a forward bias on the gate with respect to the source and in principle, the detector leakage current current will flow towards the source. Bertuccio’s measurements shows a rise time just under 30ns which is slow when compared to the Amptek commercial amplifier for instance.
If you are looking to make an ultra low noise CSA, Bertuccio novel idea is a good start. His findings has lead to a lot of newer and sometimes better version of the circuit.
If you need any further answers with regards to charge sensitive amplifiers and Spectrometers, do get in touch 🙂