Lab 12 - Leading Edge with Hysteresis, Derivative, and Trapezoidal Trigger Comparison

In modern signal processing for nuclear or high‐speed detectors, triggers are crucial for identifying when a relevant event occurs in an analog signal. Depending on the signal type, noise level, and pulse shape, different trigger algorithms yield better timing accuracy, noise immunity, or high‐rate performance. In this lab, we compare Leading Edge (LE) triggers with hysteresis, Derivative triggers, and Trapezoidal triggers.

Below is a block diagram illustrating how these trigger methods fit into a typical front‐end readout chain (amplification, shaping, thresholding):

Leading Edge Trigger with Hysteresis

1. Leading Edge Concept

   • A leading edge trigger simply looks for the instant the input signal crosses a defined threshold. This provides a straightforward way of detecting pulse arrivals, but it can be sensitive to noise near the threshold.

2. Hysteresis

   • Hysteresis adds a second threshold that must be crossed on the way back down, preventing rapid switching when the signal hovers near the main threshold. This is useful for noisy signals, as it requires the pulse to fall well below a lower threshold (or a slightly different level) before re-arming.

   • The images below show how hysteresis avoids spurious triggers caused by small fluctuations around the threshold:

     • Trigger LE Config: The basic setup for the Leading Edge with Hysteresis block.
       

       

     • Trigger LE Waveforms: Demonstrates the crossing event.
       

       

     • Hysteresis Effect: Shows how the second threshold prevents the trigger from flapping on minor noise. In this example the hysteresis is set to 1 LSB to show the effect of disabling hysteresis.
       

       

Derivative Trigger

1. Derivative Logic

   • A derivative trigger applies a digital derivative (or slope detection) to the input signal. It triggers when the slope exceeds a set threshold. This approach can be more robust at high rates because it focuses on the rate of change of the signal rather than the absolute level.

2. High‐Rate & Pileup Handling

   • If pulses overlap (pileup), a derivative trigger can often discern new leading edges even when the signal baseline has not fully returned. The following figures illustrate derivative setup, waveforms, and how it handles pileup events:

     • Trigger DE Config: Configuration panel for the derivative trigger.
       

       

     • Trgger DE Waveforms: Shows how the slope crossing triggers.
       

       

     • Trgger DE Pileup: Demonstrates how derivative logic discriminates pulses even with overlapping signals.
       

       

Trapezoidal Trigger

1. Trapezoidal Filter Concept

   • A trapezoidal filter is effectively a digital filter that approximates a moving average minus a delayed version of itself, creating a fast rise and plateau. For exponential signals with relatively long decay constants (e.g., 50 µs), it “deconvolves” the exponential, yielding a flatter, shorter pulse suitable for precise and noise‐resistant triggering.

2. Operation & Formula

   • The trapezoidal filter can be tuned by parameters like Rise Time and Flat Top. The “derivative of the trapezoid” can also be used as a fast trigger signal.
   • The DECONV_M parameter helps scale the filter to the input signal’s decay constant and sample rate. A typical formula is: \[ \text{DECONV_M} = \mathrm{int}\Big(\frac{256}{\exp(\tfrac{\text{clock_sampling_time}}{\tau}) - 1}\Big) \] where \(\tau\) is the decay constant of the input exponential, and \(\text{clock_sampling_time}\) is the ADC sampling period.

3. Noise Rejection & High‐Rate Performance

   • Because the trapezoidal filter transforms a long exponential into a shorter plateau, it can handle high count rates without pulses smearing into one another. The filter’s output also tends to be more robust to baseline noise than a simple derivative approach.
   • The figures below show:

     • The input exponential (50 µs signal),

     • The fast trapezoidal output and its derivative,

     • How these signals appear in a high‐rate regime:

       • Input exponential 50us signal
         

         

       • Fast trapezoidal output
         

         

       • All signals together
         

         

       • Trapezoidal filter trigger in high‐rate scenario
         

         

By flattening the long tail of the exponential pulses, the trapezoidal filter reduces pileup and offers improved noise immunity. This ensures reliable triggering even when dealing with elevated noise levels where a simple derivative trigger might fail.

Conclusion:

• Leading Edge with hysteresis is a straightforward approach with improved stability near threshold.
• Derivative triggers excel at high rate but can suffer under high noise.
• Trapezoidal filtering transforms long decays into stable, short pulses, making it ideal in noisy or high‐rate conditions.

Each method has trade‐offs in complexity, noise sensitivity, and rate performance. Understanding the signal properties (pulse shape, decay constant, baseline noise) is key to selecting the optimal trigger strategy.