Rise Time

Introduction link

The Rise Time block computes the elapsed time a unipolar pulse needs to rise from a lower percentage of its maximum amplitude to a higher one.
Operation sequence:

1. Trigger – a rising edge on TRIGGER arms the state machine.
2. Peak search – within WINDOW samples the maximum value PEAK is detected while the incoming stream is delayed by WINDOW + PRE_TRIGGER samples.
3. Threshold generation – absolute thresholds
   $$V_{thr1} = \frac{THRS_1}{2^{16}};PEAK ,\qquad V_{thr2} = \frac{THRS_2}{2^{16}};PEAK$$ are computed.
4. Timestamp extraction – the delayed waveform is scanned until it crosses the two thresholds, providing TIME_1 and TIME_2.
5. Result – RISETIME = TIME_2 - TIME_1 together with TIME_PEAK, PEAK and a one-cycle strobe DV.

Pin Description link

Properties link

Functional overview link

Let $x[n]$ be the input sample stream and $B$ the baseline.
The block first produces the baseline-corrected waveform

$$ y[n] = \max\bigl(0,;x[n] - B\bigr) $$

which is written into a circular buffer of depth MAX_RISE_LEN. A delayed copy

$$ y_d[n] = y\bigl[n-(WINDOW+PRE_TRIGGER)\bigr] $$

is used for threshold comparison so that the timestamps refer to the original trigger instant.

After a trigger, the peak value is searched for WINDOW clock cycles:

$$ PEAK = \max_{0 \le k < WINDOW};y[n_0+k] $$

Absolute thresholds are then generated from the user-defined 16-bit fixed point coefficients THRS_1 and THRS_2 (0 → 0 %, 65535 → 100 %). The delayed waveform is scanned further until

$$ y_d[n_1] \ge V_{thr1},\qquad y_d[n_2] \ge V_{thr2},\qquad n_1 < n_2 $$

yielding

$$ TIME_1 = n_1,\quad TIME_2 = n_2,\quad RISETIME = n_2 - n_1 $$

Optional interpolation link

When EN_INTERPOLATION is true, a 4-bit linear interpolation refines the crossing times giving a resolution of one sixteenth of a sample:

$$ \Delta n = \frac{V_{thr}-y_{prev}}{y_{curr}-y_{prev}};;,\qquad TIME_{INTP}= (n \ll 4) + \left\lfloor 16 ;\Delta n \right\rfloor $$

link

Timing link

Clock to clock latency of the data path DATA_IN → DATA_OUT is 1 cycle (pipeline register).
Latency from the trigger edge to a valid result (DV = '1') is

$$ L \approx PRE_TRIGGER + 2\cdot WINDOW + 6;\text{cycles} $$

The formula covers the peak search, threshold calculation and final scanning phases. Worst-case latency is obtained when WINDOW equals its maximum value.

For a 125 MS/s digitizer (4 ns/sample) and settings
THRS_1 = 0.1·2^16, THRS_2 = 0.9·2^16, WINDOW = 128, PRE_TRIGGER = 32:

$$ RISETIME = 7;\text{samples} ; \Rightarrow ; 56;\text{ns} $$

Example – n/γ discrimination with a ³He proportional counter (125 MS/s) link

Theory in brief
In a ³He proportional tube, neutron capture (n + ³He → p + ³H + 764 keV) releases two heavy charged particles that deposit energy along a several-cm track. The resulting current pulse has a fast electron component (tens of ns) and a slow ion component (hundreds of ns–µs). After the charge-sensitive preamplifier (≈ RC integration), the output can be modeled as the sum of two exponentials:

[ v(t)=A_f\left(1-e^{-t/\tau_f}\right)+A_s\left(1-e^{-t/\tau_s}\right),\quad \tau_f \ll \tau_s ]

For γ interactions (mainly Compton electrons), (A_s) is small and the pulse is dominated by the fast term → shorter 10–90 % rise time. For neutrons, the slow ion term contributes significantly, stretching the leading edge → longer rise time. Measuring

[ RISETIME = t_{90%}-t_{10%} ]

therefore discriminates n/γ. (If only one exponential is present, (t_{p%}=-\tau \ln(1-p)) and (RISETIME\approx 2.2,\tau); the presence of a second slow component effectively increases the measured rise time.)