Processing math: 100%

Ramp Pulse

Define a ramp time pulse.



Figure 1. Define a ramp time pulse.
Time axis unit
Specify the unit to be used for the time axis.
Total signal duration ( sd )
The total length of the signal in the specified units.
Amplitude ( u0 )
The amplitude of the time signal.
Pulse delay ( t0 )
The pulse delay is the time until the peak of the time signal envelope.
Pulse width ( pw )
This is the half-amplitude pulse width of the signal. The pulse width is the total length of time that the signal is above 50% of its peak value ( u0 ).
Rise time ( τ1 )
The time required for the pulse to reach its peak value ( u0 ) from rest.
Fall time ( τ2 )
The time required for the pulse to reach the rest value from its peak ( u0 ).
Note: The discharge time will be determined by the pulse width ( pw ).
Number of samples
The number of samples taken from the signal’s analytical equation.
(1) u(t)={0for tt1+t0u0(1|tt2t0|τ1)for t1+t0tt2+t0u0for t2+t0tt3+t0u0(1|tt3t0|τ2)for t3+t0tt4+t00for tt4+t0
(2) t1=pw+τ12t2=pwτ12t3=pwτ22t4=pw+τ22

The Fourier transform is as follows:

(3) U(f)={u0[((pwτ1+τ22)sinc((pwτ1+τ22)f))+1τ1(2πf)2(ej2πfτ1(1+j2πfτ1)1)e+j2πf(pw2+τ1)+1τ2(2πf)2(e+j2πfτ2(1j2πfτ2)1)ej2πf(pw2+τ2)]ej2πft0for f>0u0pwfor f=0