How to Calculate the Time Response for a Given Input Signal

This How-To describes how to calculate the time response for a given input signal in POSTFEKO.

Consider a dipole antenna with a near field sampled from 1 to 30 metres away from the centre of the dipole on its electric symmetry plane.
Figure 1. Dipole antenna.

The excitation pulse is taken as:

u(t)=exp( −t 70e−9 )−exp( −t 5e−9 )
Note: The frequency range should match with the signal bandwidth, see Guidelines for Defining a Time Signal for more details.

Option 1 - Using Time Analysis

  1. Define a time signal in POSTFEKO for input signal given in Equation 1.
    Figure 2. The Create time signal dialog in POSTFEKO.
  2. On the Time Analysis tab, from the Near field drop-down list, select the near field result.
    Figure 3. The time response of the near field for the given input time signal on the x-axis at 10 m.

Option 2 - Using Math Traces

  1. Define the input time signal using math traces in POSTFEKO:
    1. Define a ramp function t with duration 1e-6 s and the number of sample points as 201.
      t = ramp ( 0,1 e − 6,201 )
      Figure 4. The defined ramp time signal, t.
    2. Define the input time signal u in terms of t:
      u = exp ( − t / 70 e − 9 ) − exp ( − t / 5 e − 9 )
      Figure 5. The input time signal, u.
  2. Calculate the complex spectrum of the input time signal u, using an FFT and get the real and imaginary parts using math traces:
    U _ r e a l = r e a l ( f f t ( u ,200 e 6 ) )
    U _ i m a g = i m a g ( f f t ( u ,200 e 6 ) )
    where the bandwidth was calculated as 200 MHz.
    Figure 6. The real and imaginary parts of the complex spectrum of the time signal.
  3. Determine the real and imaginary parts of the z-component of the electric field at 10m distance.
    Tip:
    1. Create two near field traces using the near field result.
    2. In the result palette, select the Z-component check box and Real or Imaginary.
  4. Calculate the Fourier transform of the electric field at 10 m:
    E z ( t ) = 100 ∗ i f f t ( ( U _ r e a l ∗ E z _ r e a l − U _ i m a g ∗ E z _ i m a g ) + i ∗ ( U _ i m a g ∗ E z _ r e a l + U _ r e a l ∗ E z _ i m a g ) ,1 e − 6 )
    Figure 7. The time response of the near field for the given input time signal on the x-axis at 10 m.