I have done the simulations to find the s-parameters of EM waves for metallic (copper) wire array system ion COMSOL. The EM waves is reflected back and there is hardly any transmission. However, the phase of the transmission coefficient is greater than zero (figures attached). Can anyone explain why is that so?
There will always be phase when the signal magnitude is not exactly zero. Phase is the angle whose tangent is the ratio of the imaginary part to the real part. If either part is not exactly zero there will be a phase. If you plot the data on a polar chart there is only one point where the amplitude is zero, at the centre, and here the phase is not zero, but indeterminate (0/0).
Maybe you want to know why the phase isn't zero for the transmission. Assuming that you have set it up so that transmission through air would give zero phase, perhaps the wires in the array are introducing inductive loading which results in extra phase, and more at higher frequencies. Does positive phase in your plot represent extra distance or less distance?
To add to what Malcolm answered, actually I ran into this phenomenon myself. If your signal amplitude is very small, and both the real and the imaginary parts are "vanishingly" close to zero, lo and behold, you'll get a phase angle of 45 degrees (or 135, 225, 315, depending on signs).
Phase angle = arctan(imaginary / real)
This is only an esthetic problem. So what I did, below a certain amplitude, along the real and/or the imaginary axis, I forced the imaginary value to be way smaller than the real value. Something like,
IF abs(imaginary) < .0001 THEN imaginary = 10E-30
IF abs(real) < .0001 THEN real = 10E-20
That way, when signal amplitude is "essentially zero," in my formatted output for phase angle, I got a phase angle of also zero. Everyone was pleased with this way of showing the model results. (Of course, the assumption here is that for whatever signal you're talking about, this value of 0.0001 was vanishingly small. If not, just redefine those IF statements to what makes sense.)
But really, it's purely for esthetic purposes.
The effect is produced by tiny rounding errors that add up when the amplitudes are very small. The cause is ultimately the math. co-processor in the computer.
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