I am delivering power to my device using a VNA with frequency ranging from 300kHz to 8GHz. I am trying to figure out the current that passes through my sample, or DUT. I can set the output power of the VVNA and measure the S11. Here is my approach.
Since the total current (the sum of the incident and reflected waves) at the DUT can be expressed as:
I=V0/Z0 (1-Gamma)
then, use P0=I*V0, so current becomes
I=sqrt(P0*(1-Gamma)/Z0), where Gamma=10^(S11/20)
Is this approach current? Another method that I thought of is to first measure the DC resistance, R. Then, the current can be derived as:
I=sqrt(P0*(1-Gamma^2)/R).
Is any of these correct? Any help is much appreciated.
Your approach is close, but not correct. You need to include the phase in the reflection coefficient. You don't get the phase from Gamma=10^(S11/20).
Gamma can be complex and it can be +1 or -1. For example, if it is +1 (open circuit) there is no current, and if it is -1 (short circuit) the current is twice as much as in the incident signal. It should be possible to set the VNA to give you the real and imaginary parts of Gamma, or the magnitude and phase.
The current is the sum of the input current and the reflected current, represented as complex numbers. Its magnitude is the length (absolute value) of that complex number.
I think also that the current you calculate will be the RMS value.
I think you should not use the DC value of resistance.
Thank you Malcolm for your response.
Thank you for pointing out the phase information, I overlooked this issue. If I measure S11 in complex number ie. S11=a+ib, and Gamma=Real(10^(a+ib/20))
that should incorporate the phase information? Previously I was just using the S11 's magnitude, and I will use a+ib in the future.
Also, I just noticed I probably shouldn't use P0=I*V0, instead, I should be using P0=V0^2/Z0. So, the formula becomes:
I_rms=sqrt(P0*(1-Gamma)^2/Z0), Gamma=Real(10^(a+ib/20))
If gamma is a complex number it is already in the form you want. The S11 you started with is actually S11(dB) which is 20*log10(abs(a+ib)).
S11(complex) is a+ib.
Sometimes a and b are not available in a data file, but S11(dB) is and also the phase S11(radians) or S11(degrees), so you can still get the complex number.
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