Lab 17 - Implementing a Pulse Shape Discriminator (PSD) Based on Amplitude vs. Area Ratio

In this lab, we demonstrate how to discriminate pulses by computing the ratio of a pulse’s peak amplitude to its integrated area. This approach, known as Pulse Shape Discrimination (PSD), is often used in nuclear or radiation detection to distinguish between pulses of different decay times. For exponential pulses, the ratio of amplitude to area is directly linked to the decay constant, allowing us to classify signals based on their shape.

1. Introduction: Theoretical Basis of PSD (Amplitude vs. Area)

Why Use Amplitude vs. Area?

1. Pulse Shape: Many detector outputs (e.g., from photomultiplier tubes or charge‐sensitive preamplifiers) approximate an exponential decay, often with a very fast rise time.
2. Exponential Model: Suppose the pulse has the form $$V(t) = A e^{-t/\tau} \quad t \ge 0,$$ where $A$ is the peak amplitude (at $t=0$) and $\tau$ is the decay time constant.
3. Integrated Area: The total area (integral) under this exponential from $t=0$ to $\infty$ is $$\text{Area} = \int_{0}^{\infty} A e^{-t/\tau} dt = A \tau.$$
4. Amplitude/Area Ratio:
   $$\frac{\text{Amplitude}}{\text{Area}} = \frac{A}{A \tau}= \frac{1}{\tau}.$$ Hence, measuring the peak amplitude and area of an exponential pulse gives a ratio inversely proportional to the decay time $\tau$. In other words, shorter decay pulses yield a larger amplitude‐to‐area ratio; longer decay pulses yield a smaller ratio.

Practical Usage

In Pulse Shape Discrimination, we might measure the amplitude $A$ and the integrated charge $\int V(t),dt$. By comparing their ratio, we can classify pulses originating from different physical processes (e.g., neutron vs. gamma in scintillators, different nuclear transitions, etc.). Here, we focus on implementing that ratio measurement in Sci‐Compiler.

2. Block Diagram

Below is the main block diagram for our PSD (Pulse Shape Discrimination) approach:

In summary, the Trigger detects a pulse; the peak and area are measured during a time window defined by the charge integration signal (DV) from the QDC block. Then the peak/area ratio is computed to discriminate pulses.

• QDC: Integrates the pulse (area) and provides a “DV” (Data Valid) at the end of integration.
• Peak: Computed by subtracting (and saturating at 0) the delayed pre-integration signal (MONITOR from QDC) from the baseline.
• Charge (output of QDC) is the integrated pulse, scaled by a gain factor (QGAIN), typically $2^{16} \approx 1.0$.
• Finally, we do a peak ÷ area ratio to get the PSD value.

We then plot this PSD ratio (Y‐axis) vs. the QDC charge (X‐axis) in a 2D histogram inside Sci‐Compiler.

Configuring the 2D Histogram

We set the histogram for 64 bins in Y (the PSD ratio) vs. 128 bins in X (the QDC charge). Two additional fixed‐point GAIN blocks scale the PSD ratio and QDC charge to fit into the 64×128 plot range.

Using the Oscilloscope, we set:

• Trigger THRESHOLD = 2500,
• INT_SAMPLES = 200 (integration window),
• PRETRIGGER = 10 (samples before trigger).

Gain Blocks and Empirical Tuning

We empirically tune:

• QGAIN (for the QDC area),
• PSDGAIN (for the ratio’s Y‐axis),
• PSD_X_GAIN (for the area’s X‐axis).

We monitor MON_PEAK, MON_CHARGE, and MON_RATIO to ensure the final PSD_X and PSD_Y values stay within the histogram’s 0–128 (X) and 0–64 (Y) range.

1. QGAIN: Digital scaling of the integrated area. If QGAIN = $2^{16}$, then area is effectively “1.0.”
2. PSDGAIN: Scales the ratio so it remains < 64.
3. PSD_X_GAIN: Scales the area so it remains < 128.

Detector Emulator Settings

We configure the Detector Emulator to generate pulses with variable amplitude or decay time:

• Amplitude: from 3500 (just above threshold) up to 12000.
• Tau (decay time): can range from 0.4 µs to 3 µs.
• Rise Time: set as needed.
• Rate: defines how frequently pulses arrive.

Example 1: Varying Amplitude

All points line up horizontally (i.e., same Y value), indicating a constant peak/area ratio for pulses with the same decay shape. The X‐axis changes with amplitude, but the shape is constant, so the ratio stays the same.

Example 2: Varying Tau

Changing tau affects both the integrated charge (X) and the ratio (Y). Shorter tau → higher peak‐to‐area ratio → the points shift upward. Longer tau → lower ratio → the points move downward. Consequently, the distribution shifts in both X and Y, matching the exponential relationship between amplitude, area, and decay constant.

Conclusion: By measuring peak and area from the QDC and computing their ratio, we achieve a Pulse Shape Discrimination metric. The 2D histogram (Area vs. PSD ratio) clearly separates pulses by amplitude (horizontal shifts) and by decay constant (vertical shifts), enabling robust analysis in a single real‐time display.