2.1 Time measurement

Analog signals are converted into digital signals with timing discriminator for time measurement. To reduce design complexity, the leading edge timing discriminator is employed [7-9]. The time measurement part is shown schematically in Fig. 2. An input start signal passes through two discriminators of different thresholds to a coincidence gate, which is linked by a delay line to the discriminator with low threshold. Then, the start and stop signals pass through the TDC-GP2 chip to the FPGA. TDC-GP2 is a general-purpose TDC chip suitable for cost sensitive applications. Its measurement ranges can be from 3.5 ns to 1.8 μs or from 500 ns to 4 ms [10, 11]. We use the 3.5–1800 ns range with the typical resolution of 50 ps [12].

Fig. 2Full-screen View

Block diagram of time measurement

2.2 Charge measurement

Charge measurement of preamplifier output signal is equivalent to amplitude or area measurement of the signal [13]. The charge measurement circuit is shown in Fig. 3. The pole-zero cancellation network acted as a differentiator attenuates low frequencies and the two-stage RC filter acted as an integrator attenuates high frequencies. The adjustable resistor in the pole-zero cancellation circuit should be adjusted to an optimal value to minimize undershoot [14]. The time constant is 0.1 μs to generate a semi-Gaussian signal of 1μs pulse width at 0.1% of the pulse amplitude. The shaped signal is then passed through a full differential amplifier to ADC for digitization. Digital data are sent to FPGA for numerical integration, each time about 40 points are accumulated [15].

Fig. 3Full-screen View

Schematic diagram of charge measurement

3.1 Time measurement test

The resolution and integral nonlinearity (INL) of time measurement were tested. For time resolution test, multiple measurements were conducted for a specific delay, and the standard deviation of the multiple results was the time measurement resolution. From Fig. 4(a) showing the typical counts histogram at a specific delay, the corresponding resolution was 67.7 ps at 502.8 ns delay; while from Fig. 4(b), resolutions of all 32 channels of two MQT boards are less than 100 ps. As a calibration was conducted following the time measurement each time in TDC-GP2, the tested resolution is relatively stable with variation of temperature and supply voltage.

Fig. 4Full-screen View

(a) Typical counts histogram at a specific delay; (b) Time resolutions of all 32 channels of two MQT boards

The time measured at different delays from 0 ns to 500 ns are shown in Fig. 5(a). The INL was calculated at 0.095%, and the linear fitting equation of T=0.9975D+3.6479 was obtained, where D is the delay and T is measured time. As slope and intercept of each fitting line for every channel is different, a linearity correction was implemented with this equation [16]. Fig.5(b) shows that all 32 channels of the two MQT boards have excellent linearity for time measurement.

Fig. 5Full-screen View

Linearity between delay and measured time (a) and the time measurement INLs of all 32 channels of the two MQT boards (b).

3.2 Charge measurement test

As the detector and preamplifier were not completed, an equivalent INL test was conducted. A customized signal in similar shape to the preamplifier output was used as the input, and the signal amplitude was proportional to the charge. The measured pulse areas at different input signal amplitudes from 50 mV to 500 mV are shown in Fig. 6(a) and from a linear fitting of the data, the INL was calculated at 0.08%, indicating excellent linearity of the charge measurement. In fact, the INLs of all 32 channels are less than 0.15%, as shown in Fig. 6(b). As resolution and range of charge measurement were designed to be 15 fc and 1800 fc, respectively, a 12 bit ADC AD9228 was employed, and the effective number of bits (ENOB) of each channel was greater than 9, which meets the requirement. In fact, the charge information is also useful for correction of leading edge timing discrimination.

Fig. 6Full-screen View

Linearity of the charge measurement data (a) and the charge measurement INLs of all 32 channels of the two MQT boards (b).