Characterization of mono-chip amplifier-shaper and discriminator FGATI for muon spin imaging spectroscopy

Abstract

We report test of a trans-impedance fast amplifier FGATI, using a semiconductor-based photo sensors SiPM and a pulsed laser. The FGATI chip contains 16 channels of amplifier-shaper-discriminator (ASD) circuits which generates low-voltage differentiation signal (LVDS) discriminator digital outputs, readily analyzed its timing by a Time to Digital Converter (TDC). The amplifier gain characteristics are tested using a voltage input pulse supplied through a coupling capacitor to FGATI. The current input from SiPM are characterized with/without the coupling capacitor. The analog signal response as well as the threshold control of the digital pulse output is characterized. The timing resolution achieved by FGATI is less than 50 ps for the saturated laser input.

Appendix A: Characteristics of the V-I conversion circuit

With the complex impedance of the coupling capacitance $C_c$ to be $1/i\omega C_c$, the relation between $V_{in}$ and $I_{in}$ from Kirchhoff’s circuit laws becomes

$$\begin{aligned} V_{in}-\{1/i\omega C_c +(R_{ex}+R_{int})\}I_{in} = V_{bias}=0 \end{aligned}$$

(A1)

This directly leads to the relation

$$\begin{aligned} I_{in} = i\omega \tau _c/(1+i\omega \tau _c) \times V_{in}/(R_{ex}+R_{int}) \end{aligned}$$

(A2)

where $\tau _c=(R_{ex}+R_{int})C_c$. The voltage signal $V_{in}$ is high-pass filtered with the cut-off frequency $f_c=1/2\pi \tau _c$, and the current signal $I_{in}$ supplied to the FGATI input is a derivative from $V_{in}$.