Sources for stripline-mode excitation

[Lauren Barr]

Hi there,

Thanks so much for this fantastic piece of piece of software!

I am using gprMax to study pulses propagating along transmission lines, and trying to recreate some experimental results. I am struggling a bit to understand one thing - in my experiment I apply a time-varying potential difference between two or three parallel wires, or the wires and a ground plane. How could this be replicated in the modelling with a 'point' voltage source (or any alternatives)?

I thought about having two voltage sources with pi phase difference between the waveforms, but I'm not sure this is correct, or how the sources should be oriented.

Any advice would be really appreciated!

Lauren

[Andres Altieri]

Hi,

there are several feed models that you can use to feed this  type of circuit. I am attaching a few papers discussing such models.

The Luebbers-Langdon model uses a voltage source with internal resistor. To connect two horizontal parallel metal plates, for example of a microstrip or stripline it makes a vertical staircase and then applies the voltage source. The staircase acts as a taper to minimize reflections and reduce the size to place a single voltage source with a resistor. In my experience, this works reasonably well if the circuit is well matched but if there are reflections, the source is not very well matched and generates multiple reflections.

The other model uses a vertical electric field between both the metallizations and introduces some compensations. I haven't tried this because it involves going under the hood in the software and I don't know or want to do this.

A simple solution I have found (I believe it is similar to the second model but the analysis is beyond me) is to use a planar current (Hertzian dipole) to inject a current between the metals. You can use a current of a width of a single cell or multiple cells, the results are similar.

After the current pulse is injected the source becomes an open circuit (disappears). If you embed the structure on one side on the PML any rebounds are completely absorbed by the PML so this source is very well matched (I have discussed this approach with Craig and Antonis in a previous post).  For example to simulate a perfectly matched microstrip you could do this:

When you feed the current vertical (vertical edge feed current), there is a forward wave (going to the right) and a backwards wave (going to the left). The backwave is absorbed by the PML and the forward wave you can study. For example, you can measure the voltage a few cells away. There will be no reflected wave because of the PML on the right. The voltage wave generated is follows very closely the current pulse, with some minimal distorsion and the wave achieves a steady state solution within a few cells.

Then you can do the same with a loading circuit and measure the total voltage for example. This will have the forward and reflected wave of the load (the backwave additionally is canceled by the PML). By substracting the wave from the first simulation from this one you can separate the incident and reflected wave from the load.

Some detail on this  can be found in this paper (Section II-A beginning and Section II-B).

https://arxiv.org/abs/2106.13737

This may suit your needs depending on what you want to do with the stripline.

Kind regards,

Andres

[Lauren Barr]

Hi Andres,

Thank you very much for your detailed reply, I will look into the method you suggest with the current source applied between the two conductors. I have a practical question about how to do this.

When writing my script I can only define a source in one unit cell, so if I want to have a current applied along a line, do I just define multiple sources each spaced by one unit cell's length from the other? Eg.

#dx_dy_dz: 0.1 0.1 0.1

#waveform: gaussian 1 1e6 my_pulse

#hertzian_dipole: 1.0 1.0 1.0 my_pulse
#hertzian_dipole: 1.1 1.0 1.0 my_pulse
#hertzian_dipole: 1.2 1.0 1.0 my_pulse
#hertzian_dipole: 1.3 1.0 1.0 my_pulse

Or is there an easier way to do this?

I am also finding some peculiarities in the Hertzian dipole when I define a gaussian pulse. In a plot of the electric field with time, after the pulse has switched off I was left with a residual electric field that didn't decay away. However when I used the first time derivative of a gaussian as the pulse profile I didn't have this problem, nor when I used a voltage source instead of current. This was in a model with just a source surrounded by air, nothing more complicated than that. Is this what you describe as "the source becomes an open circuit (disappears)", or something else I may have misunderstood?

Many thanks again,

Lauren

[Lauren Barr]

Quick correction to my code snippet! The sources should have the orientation specified as x

[Andres Altieri]

Hello,

Sorry for the late reply.

In order to simplify the code you should use the Python scripting option (Link), where you can use for loops and other python routines and data types.

In your script you write:

#python:

----> write python code here

#end_python:

I am attaching a basic script which generates a parallel plate waveguide with a current source excitation using Python:

 To make the stripline you should add the embedded conductor in the middle and modify the feed lines. In general it is better to work in mm in my opinion. Since dimensions are critical I convert from mm to m and define the domain carefully in number of cells instead of specifying the dimension in meters which may result in imprecisions. If the top and bottom sheets are PEC you could disable the PML an use this as a boundary condition above and below. Keep in mind the symmetry: for example is the plate is 10 cells wide one should place two current source in cells 5 and 6.

What you observe of the electric field is reasonable. When you use a current pulse you are basically moving charges between the plates. Total shifted charge is the integral of the current over time. The gaussian pulse has a positive integral, hence when the electric pulse goes back to zero there will be a charge difference between the plates and the plates behave as a capacitor. There will be a residual electric field between the plates which generates a DC voltage between them.

The derivative of the gaussian pulse has a zero integral, hence the charges are moved from one plate to the other and then sent back to the original plate. The net displaced charge is zero, so the DC voltage difference at the end is zero. When you use a voltage source the voltage goes to zero, meaning that in the end there is not charge difference. It depends on what you want to do if this affects you or not.

Kind regards,

Andrés