How to calculate the voltage through the output electromagnetic wave

[C Master]

   Hi

I got the waveform I wanted through A scan. Now I want to calculate the voltage value corresponding to the electromagnetic wave intensity received by the receiver.

I looked at the previous forums and the developer said U= -ed and described d, but I didn't quite understand what he meant.

This is my.in file, and the corresponding output waveform. My receiver is 0.18m above the transmitter, and dx, dy and dz are all 0.002m.

1. So what is the value of d, and how can I get it?

2. Which of the values of E should I choose, the crest or the trough?

And any help would be appreciated!

#title: A-scan from a metal cylinder buried in a dielectric half-space

#domain: 0.240 0.2 0.2

#dx_dy_dz: 0.002 0.002 0.002

#time_window: 5e-9

#material: 6 0 1 0 half_space

#voltage_source: y 0.12 0.1 0.18 50 my_wave

#waveform: gaussian 1 10e8 my_wave

#rx: 0.12 0.1 0.198

#box: 0 0 0 0.240 0.1 0.18 half_space

#box: 0 0 0.004 0.24 0.2  0.006 pec

#geometry_view: 0 0 0 0.240 0.2 0.2 0.002 0.002 0.002 test_01_Ascan n

    

[Andres Altieri]

Hi,

I am sure that Craig and Antonis will provide a better answer, but the voltage difference between to points is the line integral of the electric field along any path that joins this two points.

In this case the volume is discretized in Yee Cells, so, you discretize this integral moving through the Yee cells.  For example, imagine the cell at coordinate (is, js, ks). This coordinates are normalized, that is, they are the points in space normalized by the discretization (is, js, ks are natural numbers). You want to calculate the voltage diference between this coordinate and (is, js+1, ks), that is, moving one cell in the y direction (if Deltay is the discretization in the y direction this would be the voltage difference by moving Deltay in space. The following drawing shows how to do this:

In the cell (is, js, ks) you have the field Ey which lies on the vertex between (is, js, ks) and (is, js+1, ks). So the line integral becomes simply the product of the field Ey at coordinate (is, js, ks) and the spatial discretization Deltay.

If your voltage calculation is over a more complicated path, you should repeat this procedure over the whole path.

Best regards,

Andres

[Andres Altieri]

When I said "on the vertex" I mean "between the two vertices"....

[C Master]

Dear  Andres Altieri ,

Thank you very much for the explanation .

I'm sorry I'm not very familiar with electromagnetic field and electromagnetic wave.

If the position of my receiver is A, and the cell position before the receiver is B, Δ V= VA-VB = - E Δ y,I can calculate Δ v, then what method can be used to calculate the voltage value of point A. Just like in my .in file, the transmitter is a 1V voltage source. I want to know the voltage value at this point of the receiver.

Thank you again for your help.

C Master

[Antonis Giannopoulos]

Hi 

Thanks Andres for your very nice explanation of how to relate to a voltage via its definition from electromagnetic principles which is correct. In FDTD, as in all numerical methods, outputs are not continuous in space. The fields are known at specific locations and actually at these points are assumed constant. So, along a Yee cell edge the E field has a fixed value. There is no value at the nodes. However, if the fields vary smoothly then one can take averages to estimate such field values at nodes. The key here is the word "smoothly" which implies no discontinuities in media properties and not rapid variation of fields. 

So, as Andres have shown, If you want to find an equivalent voltage from say an Ey component then Vy = - Ey * Dy. Similarly you can find other components as needed.

If you want to delve more into circuit analogies then you either need to be modelling the circuit paths correctly (this can be tricky but doable) or interfacing a circuit simulator with the FDTD solver (this has been done for FDTD but gprMax does not do it) 

In essence this conversion in FDTD is just a scaling process and if you are trying to get experimental amplitudes to match with simulated ones there are many things that are not often included in the FDTD model that might affect the actual numbers. It can be done but you need to understand the theory and the way the linkage between field theory and simplified circuit concepts works.

Hope this helps

Antonis

[Andres Altieri]

Hi,

Thank you for your comment, Antonis!

C Master, voltage is defined between to points.

For example, the voltage source that you define generates a voltage difference  of an edge of the Yee Cell where you placed it. If you generate a fine geometry view you will see this edge in the cell.

At the receiver position you will have an electric field in the Y direction by Delta Y you will get the voltage difference across the edge of the cell like in the drawing I posted in the previous post.

If you say "I want the voltage at point B" you should try to be more specific. If you imagine that you place a voltage sensor between the vertices of the Yee Cell, this sensor will measure the

V = -Ey *  Delta Y

that is, this voltage will be simply the electric field at the point times the discretization. In this case, in most cases it would be the same to work with the field at the cell.

If you want the estimate the voltage B relative to another point in space, you should approximate the line integral of the previous post, by summing the field in every cell in the direction where you move and and multiplying by the discretization in that direction. I don't know how exact this would be.

Best regards,

Andrés

PD: in your script both the source and receiver are inside the PML.