What's the Correct Way of Probing Currents? Conflicting Examples Exist.

[biergaizi]

I need to probe the voltages and currents manually in a non-standard simulation in openEMS, but I find the official examples show two conflicting approaches.

1. The first approach is to place a voltage probe on mesh line idx, and two current probes on mesh lines idx - 1, and idx. The true current (in phase with the voltage) is obtained by averaging both readings, so you can interpolate the current at idx - 0.5. But recall that in the Yee grid, the magnetic grid already has a built-in offset of 0.5 cells in the algorithm, so current at mesh coordinate idx - 0.5 is in fact located at idx.

   You can see an example of this approach in Coax_CylinderCoords.m. The voltage probe is located at z = 9, and the current probes are located at z = 8 and z = 9.

2. The second approach is to place a voltage probe at an exact mesh line, and place two current probes in the middle of this line and the previous/next mesh line (0.5 line offset). You average the adjacent probes to interpolate the current at the center, in alignment of the voltage probe on the grid line.

   You can see an example of this approach inside class MSLPort in python/openEMS/ports.py. MSLPort also uses finite-difference to extract the characteristic impedance, so it has additional probes, but the current calculate is performed as described here.

   

Both solutions look reasonable in isolation, but only one must be correct. Now there's the question - which calculation is the correct and rigorous one?

[gadiLhv]

Sorry if I deviated too much from your suggestions, but I feel like I need more info.

The way the current probes work, is they perform a mode matching integral along the given area (or there is another way). So instinctively, my first question would be, what line\s are you current probing? Microstrip? Differential? Co-planar waveguides?

That will help me answer a bit...

[biergaizi]

Lumped ports are good enough up until a rather high frequency. Why not use them?

In theory, MSLPort can help you to shape the electric field excitation using a custom weighing function, so that the discontinuity is minimized even if the port is electrically long. But this is in fact unimplemented... So yeah, there's currently little benefit of using it - besides automatically helping you to shift the excitation plane, reference plane, or drawing the line.

But... There is still a little-known benefit: The MSLPort can help you to extraction of of a microstrip characteristic impedance and propagation constant, without any prior knowledge. This is only made possible because PML as perfect termination on both sides, without lumped resistance anywhere. Internally, MSLPort differentiates the voltages and currents (from an additional probe) in adjacent mesh lines to obtain the complex Z0 and Beta.

This useful feature is completely undocumented, which I planned to do (also, if CalcPort is called without an explicit reference impedance, the extracted Z0 is used for classes that support them).

[thliebig]

You really do not need a custom weighting function if you place your probes a few cells away from the excitation... The correct MSL mode will have emerged by then... That is (one of) the reason why the MSL port is much better than a simple lumped port.

[gadiLhv]

In theory, MSLPort can help you to shape the electric field excitation using a custom weighing function, so that the discontinuity is minimized even if the port is electrically long

Yeah, that's what my PR is supposed to take care of...

But... There is still a little-known benefit: The MSLPort can help you to extraction of of a microstrip characteristic impedance and propagation constant, without any prior knowledge

This, as well...
I find time to concentrate scarce these days.

[biergaizi]

@thliebig: The correct MSL mode will have emerged by then...

Yes. When you're far enough from the excitation, the high-order modes die down. It's why I said "probe the voltage/current of the line at an offset away from the excitation plane (I believe it's to stay clear from the field at this discontinuity, getting a "clean" voltage and current)."

@gadiLhv: Could be that the +0.5 +1.5 shift was on purpose, could be just a design choice.

I think you misread the code. They're not +0.5 and +1.5 shifts. They're -0.5 and +0.5 shifts. The MSLPort creates 3 voltage probes and 2 current probes in like:

U1     I1     U2     I2     U3
-1    -0.5    0      0.5     1

Only U2, I1 and I2 are used to extract V+, V-, I+ and I- (0-based index here!).

    self.uf_tot = self.u_data.ui_f_val[1]
    self.if_tot = 0.5*(self.i_data.ui_f_val[0]+self.i_data.ui_f_val[1])

The remaining probes are used to extract characteristic impedance and propagation constant. This is for information only (optionally used for CalcPort if no ref_impedance is provided), and does not contribute to the voltage/current measurement.

    Et = self.u_data.ui_f_val[1]
    dEt = (self.u_data.ui_f_val[2] - self.u_data.ui_f_val[0]) / (np.sum(np.abs(self.U_delta)) * unit)
    Ht = self.if_tot # space averaging: Ht is now defined at the same pos as Et
    dHt = (self.i_data.ui_f_val[1] - self.i_data.ui_f_val[0]) / (np.abs(self.I_delta[0]) * unit)

    beta = np.sqrt( - dEt * dHt / (Ht * Et) )
    beta[np.real(beta) < 0] *= -1 # determine correct sign (unlike the paper)
    self.beta = beta

    # determine ZL
    self.Z_ref = np.sqrt(Et * dEt / (Ht * dHt))

[gadiLhv]

Woah, 3 probes is a bit of an over-kill. Stick with 2, I think it's solid... Since you are planning on probing in arbitrary locations, I'm guessing that evanescent mode aren't really an issue.

[thliebig]

Sorry I did not see this earlier as this is clearly a question I should answer.

Voltage probes integrate the electric field along a line to get the potential difference (aka voltage) between the start and stop points. Thus this probes start/stop is snapped to the primary (electric) mesh.

The current probes are a bit more difficult. They calculate the current through a surface by integrating the magnetic fields along a closed! loop (aka the closed edge of the surface the current flows through). That means ultimately this (edge) curve is snapped to the secondary/dual (magnetic) mesh (which is not shown to the user but calculated from the primary user-defined mesh).
This means in normal direction (current flow direction) it ideally should be defined in between the primary lines. If it is not, than it is snapped there, which is usually also just fine. Use the max. verbose mode to let openEMS tell you where the probes were snapped to. But be aware that the secondary/dual mesh also works with integer indices!
But in the other directions it is a good idea to define the current probe at the primary lines, because the "snapper" will always enlarge the surface towards the next secondary meh line. This allows to define a current probe even as a (1D) line which then will be enlarged to one cell width tangentially to the normal/flow direction.

This is always identical regardless of the mesh type (Cartesian vs cylindrical)

I hope this helps.

[thliebig]

Well small correction, the verbose mode shows the snapped mesh coordinates, not the indices.