Charge Sensitive Amplifiers (CSAs) used in radiation measurement systems require low noise, high gain, and fast rise-time characteristics.

This is especially important for semiconductor detectors, where the characteristics obtained by the first-stage preamplifier are translated into a radiation spectrum through the amplifier and MCA (Multi-Channel Analyzer). The noise gain introduced by the preamplifier cannot be recovered in the subsequent stages, making it a crucial component.

When radiation such as X-rays or gamma rays enters a semiconductor detector, ionization occurs, generating electron-hole pairs and resulting in the creation of charge. The amount of charge produced is proportional to the energy of the radiation, but the signal is extremely small.

By using a charge sensitive amplifier in the semiconductor detector, this charge can be extracted as a voltage pulse proportional to the energy of the radiation.

Fig.1

The charge pulse, Q_s, is fully integrated into the feedback capacitor, C_f, and converted into a voltage, V_o.

The feedback resistor, R_f, is connected in parallel with the feedback capacitor, C_f, and serves to attenuate the charge accumulated on C_f. This is to prevent the pulse waveform from saturating as successive charge pulses are generated and overlap. The attenuation time is given by τ = R_f C_f.

Assuming the detector generates a constant amount of charge over a time interval from t = 0 to t_q, the input charge can be expressed in the Laplace transform as follows:

Here, Q_s represents the total charge injected between t = 0 and t = t_q.

Similarly, the Laplace transform of the transfer function of the charge sensitive amplifier is given by the following equation:

The equation for the output voltage is as follows:

Furthermore, assuming that t_q << τ, the equation can be simplified as follows:

Fig. 2: Output of the Charge Sensitive Amplifier

An important element in the charge sensitive amplifier is the device used in the first stage, which is typically a JFET.

While low-noise bipolar transistors have a lower noise voltage density than JFETs, they require base current, which increases parallel noise in the configuration of a charge amplifier with high input impedance, leading to worsened overall noise compared to FETs. Therefore, they are excluded from selection.

For operational amplifiers, JFET-input types are available, but their noise performance is inferior to that of a standalone JFET. However, the circuit is very simple, making them suitable for measurements where noise is not a primary concern.

MOSFETs cannot be used due to their high 1/f noise and a noise corner frequency ranging from 10 kHz to 1 MHz.

The JFET does not require gate current, which allows for a larger feedback resistor (R_f). Additionally, the noise corner is low, ranging from 100 Hz to 1 kHz, which is sufficiently low for the operating range of 10 kHz to 10 MHz.
In terms of low noise performance, the first stage JFET is particularly critical, and a device with high transconductance (gm) and low input capacitance (Ciss) is selected. The first stage is received by an emitter-coupled folded cascode circuit. The folded cascode increases the dynamic range and achieves higher impedance.

1) gm (transconductance) and input capacitance (Ciss) of the first-stage FET

gm (transconductance) can be adjusted by the I_D drain current.

The higher the drain current, the greater the gm, but this also leads to an increase in power consumption, which can be a limitation in multi-channel systems or battery-operated devices.

The equivalent noise resistance of the FET is given by R_FET ≒ 1/gm, so generally, a higher gm results in lower noise. Therefore, products that carefully select JFETs exist for this reason.

Ciss is the input capacitance of the FET, which significantly impacts the input capacitance (C_i) of the charge sensitive amplifier.

The generated charge, Q_S, is distributed and flows into Q_x and Q_y. To improve the signal-to-noise ratio (S/N), the open-loop gain A should be made as large as possible to direct the charge into A·C_f. Since C_f is also the voltage conversion gain, it cannot be made arbitrarily large. By minimizing C_i, the distribution of charge to Q_x can be maximized.

The charge flowing into Q_y is directed into the detector capacitance (C_d) and the input capacitance (C_i) of the charge sensitive amplifier, which degrades the signal-to-noise ratio (S/N).

When the detector capacitance is small, it is important to minimize C_i as much as possible. When the detector capacitance is large, it is necessary to increase gm to reduce noise. Additionally, FETs with small Ciss have faster rise-time characteristics.

2) Feedback Capacitor (Cf) and Feedback Resistor (Rf)

Let the energy be E, the generated charge be Q, the detector's capacitance be C_d, the input capacitance of the charge sensitive amplifier be C_i, and the feedback resistor be R_f.

When the open-loop gain A is sufficiently large, the value will become constant, determined by the feedback capacitor C_f.

The output charge Q corresponding to the actual radiation energy is given by the following equation:

ε: The energy required to create one electron-hole pair.

The output voltage per 1 MeV, when the feedback capacitor Cf is 0.5 pF in a Si semiconductor detector, is as follows:

When the feedback capacitor C_f is 1 pF, the output is 44 mV, and when C_f is 2 pF, the output decreases to 22 mV. To improve the signal-to-noise ratio (S/N), it is important to select the smallest possible C_f.

The larger the feedback resistor R_f, the lower the noise. Here, we will consider the noise of the CR parallel resistor.

The admittance of the CR parallel resistor is:

Rearranging equation (11) to express the impedance, we get:

Rearranging equation (12) with the imaginary unit j, we get:

The real part of equation (13) represents the resistive component. Therefore, the equivalent resistance RX of the CR parallel circuit is:

The thermal noise voltage of the resistor, Vn, is:

B: Bandwidth 　T: Tempature 300[k]　(27℃)

From equations (14) and (15), let's compare the case where the feedback resistor R_f is 100 MΩ and the feedback capacitor C_f is 0.5 pF, with the case where the feedback resistor R_f is 1 GΩ and the feedback capacitor C_f is 0.5 pF.

In the low-frequency region up to around 1 kHz, the 100 MΩ feedback resistor results in less noise. However, in the high-frequency region, the 1 GΩ feedback resistor results in lower noise.

The noise accumulation in the 10 kHz to 1 MHz range, which is important for charge-sensitive amplifiers, is 20.3 μVrms for the 100 MΩ resistor and 12.8 μVrms for the 1 GΩ resistor. Since the noise is approximately 1.58 times lower, using the 1 GΩ resistor is beneficial.

3) Open Loop Gain (A)

By using a high-bandwidth operational amplifier (OP-AMP) instead of discrete components such as transistors for the middle and output stages, it is possible to miniaturize the design.

The circuit configuration consists of an emitter-grounded folded cascode combined with an OP-AMP, targeting open loop gains in the range of several thousand to tens of thousands.

When selecting an OP-AMP, an important performance factor to consider is the open loop gain. With a single FET, the open loop gain is only around 10 to 50 times, so ideally, we want a gain of over 300 times at 1 MHz. While noise characteristics are determined primarily by the first-stage FET, there is no particular need to focus on them, but personally, I tend to select low-noise OP-AMPS. High-bandwidth OP-AMPS naturally offer fast rise time characteristics.

The productAPG1603 is designed with optimized parameters for gm, C_i, Cf, R_f, and A.

Now, let’s compare the noise characteristics of APG1603 with those of other products (with excellent noise characteristics of 1 keV) to see how much the difference in noise performance affects actual measurements.

First, below are the specifications.

First, we will test whether the catalog data is correct by using a pulser. The pulser will generate pulse heights equivalent to 1 MeV.

The Shaping amp time constant is 2μs

APG1603 has a pulser resolution of 0.7 keV.

Product A from another company has a pulser resolution of 0.945 keV.

Now, we will measure the spectrum using a CdTe semiconductor detector.
The peak to be measured is the 59.5 keV peak of Am-241.

The Shaping amp time constant is 2μs

APG1603 has a resolution of 2.49 keV (4.19%) at 59.5 keV.

Product A from another company has a resolution of 3.01 keV (5.07%) at 59.5 keV.

The measurement results show that APG1603 has a resolution of 2.49 keV (4.19%), while Product A from another company has a resolution of 3.01 keV (5.07%).

The difference of 0.75 keV and 1 keV in the catalog data is also reflected in the actual measurements. This can be attributed to the fact that it is a semiconductor detector and the energy of 59.5 keV is relatively low, but we highly recommend trying APG1603.

With that, all of us at the company will continue to work hard to create better products.

We appreciate your support and encouragement.

References
[1] Okamura Michio, Interface, CQ Publishing, February 1976.
[2] Matsui Kunihiko, 100 Practical Techniques for Using OP Amps, CQ Publishing, 1999.
[3] Kowalski, Nuclear Electronics, Asakura Publishing, 1971.