# Numerical comparisons¶

This section presents comparisons of models using different numerical modelling techniques.

## FDTD/MoM¶

The Finite-Difference Time-Domain (FDTD) method from gprMax is compared with the Method of Moments (MoM) from the MATLAB antenna toolbox.

### Bowtie antenna in free space¶

This example considers the input impedance of a planar bowtie antenna in free space. The length and height of the bowtie are 100mm, giving a flare angle of $$90^\circ$$.

#### FDTD model¶

antenna_bowtie_fs.in

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 #python: from gprMax.input_cmd_funcs import * title = 'antenna_bowtie_fs' print('#title: {}'.format(title)) domain = domain(0.200, 0.200, 0.100) dxdydz = dx_dy_dz(0.001, 0.001, 0.001) time_window = time_window(30e-9) bowtie_dims = (0.050, 0.100) # Length, height tx_pos = (domain[0]/2, domain[1]/2, domain[2]/2) # Source excitation and type print('#waveform: gaussian 1 1.5e9 mypulse') print('#transmission_line: x {:g} {:g} {:g} 50 mypulse'.format(tx_pos[0], tx_pos[1], tx_pos[2])) # Bowtie - upper x half triangle(tx_pos[0], tx_pos[1], tx_pos[2], tx_pos[0] + bowtie_dims[0] + 2 * dxdydz[0], tx_pos[1] - bowtie_dims[1]/2, tx_pos[2], tx_pos[0] + bowtie_dims[0] + 2 * dxdydz[0], tx_pos[1] + bowtie_dims[1]/2, tx_pos[2], 0, 'pec') # Bowtie - lower x half triangle(tx_pos[0] + dxdydz[0], tx_pos[1], tx_pos[2], tx_pos[0] - bowtie_dims[0], tx_pos[1] - bowtie_dims[1]/2, tx_pos[2], tx_pos[0] - bowtie_dims[0], tx_pos[1] + bowtie_dims[1]/2, tx_pos[2], 0, 'pec') # Detailed geometry view around bowtie and feed position geometry_view(tx_pos[0] - bowtie_dims[0] - 2*dxdydz[0], tx_pos[1] - bowtie_dims[1]/2 - 2*dxdydz[1], tx_pos[2] - 2*dxdydz[2], tx_pos[0] + bowtie_dims[0] + 2*dxdydz[0], tx_pos[1] + bowtie_dims[1]/2 + 2*dxdydz[1], tx_pos[2] + 2*dxdydz[2], dxdydz[0], dxdydz[1], dxdydz[2], title + '_pcb', type='f') #end_python: 

A Gaussian waveform with a centre frequency of 1.5GHz was used to excite the antenna, which was fed by a transmission line with a characteristic impedance of 50 Ohms.

The module plot_antenna_params from the tools subpackage was used to calculate and plot the input impedance from the FDTD model.

#### MoM model¶

The bowtie antenna was created using the antenna toolbox in MATLAB, and the bowtieTriangular class.

bowtie = bowtieTriangular('Length', 0.1)
zin = impedance(bowtie, 33.33e6:33.33e6:6e9)


### Results¶

Fig. 48 shows the input impedance (resistive and reactive) for the FDTD (gprMax) and MoM (MATLAB) models. The frequency resolution for the FFT used in both models was $$\Delta f = 33.33~MHz$$.

The results from the FDTD and MoM modelling techniques are in very good agreement. The biggest mismatch occurs in the resistive part of the input impedance at frequencies above 3GHz.