tracking::digitization::FourPoleShape Class Reference

Fourth-order shaper with two time constants. More...

#include <PulseShape.h>

Public Member Functions
	FourPoleShape (double tp, double tp2)
double	eval (double t) const override
	Evaluate the peak-normalised pulse amplitude at time t [ns] after charge arrival.
Public Member Functions inherited from tracking::digitization::PulseShape

Private Attributes
double	tp_
double	tp2_
double	A_
double	B_
double	peak_amp_
	g(t_peak), used for normalisation.

Additional Inherited Members
Static Public Member Functions inherited from tracking::digitization::PulseShape
static std::unique_ptr< PulseShape >	make (const std::string &name, double tp, double tp2=0.0)
	Factory: construct a pulse shape by name.

Detailed Description

Fourth-order shaper with two time constants.

The un-normalised amplitude is: g(t) = A · [exp(−t/tp) − exp(−t/tp2) · (1 + t·B + ½·(t·B)²)] where A = tp² / (tp − tp2)³ B = (tp − tp2) / (tp · tp2)

The peak position is approximated by t_peak ≈ 3 · (tp · tp2³)^(1/4)

eval(t) returns g(t) / g(t_peak), i.e. peak-normalised.

Parameters

tp	First (slower) time constant [ns].
tp2	Second (faster) time constant [ns]. Must be < tp.

Definition at line 98 of file PulseShape.h.

Constructor & Destructor Documentation

FourPoleShape()

tracking::digitization::FourPoleShape::FourPoleShape	(	double	tp,
		double	tp2 )

Definition at line 11 of file PulseShape.cxx.

                                                  : tp_(tp), tp2_(tp2) {
  if (tp2_ <= 0.0 || tp_ <= tp2_) {
    EXCEPTION_RAISE("InvalidArgument", "FourPoleShape: requires tp > tp2 > 0");
  }
 
  A_ = (tp_ * tp_) / std::pow(tp_ - tp2_, 3.0);
  B_ = (tp_ - tp2_) / (tp_ * tp2_);
 
  // Approximate peak time: 3·(tp·tp2³)^(1/4)
  const double t_peak = 3.0 * std::pow(tp_ * std::pow(tp2_, 3.0), 0.25);
 
  // Evaluate un-normalised amplitude at the peak for normalisation.
  peak_amp_ = A_ * (std::exp(-t_peak / tp_) -
                    std::exp(-t_peak / tp2_) *
                        (1.0 + t_peak * B_ + 0.5 * t_peak * t_peak * B_ * B_));
}

Member Function Documentation

eval()

double tracking::digitization::FourPoleShape::eval ( double t ) const

overridevirtual

Evaluate the peak-normalised pulse amplitude at time t [ns] after charge arrival.

Returns 0 for t < 0.

Implements tracking::digitization::PulseShape.

Definition at line 28 of file PulseShape.cxx.

                                         {
  if (t <= 0.0) return 0.0;
  const double g =
      A_ * (std::exp(-t / tp_) -
            std::exp(-t / tp2_) * (1.0 + t * B_ + 0.5 * t * t * B_ * B_));
  return g / peak_amp_;
}

Member Data Documentation

A_

double tracking::digitization::FourPoleShape::A_

private

Definition at line 106 of file PulseShape.h.

B_

double tracking::digitization::FourPoleShape::B_

private

Definition at line 106 of file PulseShape.h.

peak_amp_

double tracking::digitization::FourPoleShape::peak_amp_

private

g(t_peak), used for normalisation.

Definition at line 107 of file PulseShape.h.

tp2_

double tracking::digitization::FourPoleShape::tp2_

private

Definition at line 105 of file PulseShape.h.

tp_

double tracking::digitization::FourPoleShape::tp_

private

Definition at line 105 of file PulseShape.h.

---

The documentation for this class was generated from the following files:

• Tracking/include/Tracking/Digitization/PulseShape.h
• Tracking/src/Tracking/Digitization/PulseShape.cxx