Calculating Impedance from ADC Outputs

Hi all,

I am developing a controller software for RF power Impedance matching Network for Plasma Technology. I am not good in electronics. My intention is to calculate impedance, Forward power, Reflected power and VSWR, where I am trying to match the source impedance with the load impedance through stepper motor. To detect Current, Voltage and Phase, I am using VI Sensor which has three outputs(RMS Current, RMS Voltage, and Phase) fed to built in ADC. I have done with all adc source code, but I am not really sure about procedures to follow in order to calculate impedance, Forward power, Reflected power and VSWR from adc outputs(RMS Current, RMS Voltage, and Phase ADC results). is there any one who may help me? I would extend a huge respect in advance.
Thank you

Don't know which quantities your "VI Sensor" is exactly measuring. To determine forward and reverse power unequivocally, you would use some kind of directional coupler.

FvM said:

Don't know which quantities your "VI Sensor" is exactly measuring. To determine forward and reverse power unequivocally, you would use some kind of directional coupler.

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Dear FvM,
The VI Sensor exactly measures RMS Voltage, RMS Current and Phase. I have already known digital values for these parameters. My question is, what are detail mathematical procedures to follow to calculate complex impedance, FWD&Reflected Power and how to implement? is there any power scaling needed to find an analogue power value?

Thank you Again

FvM said:

What is "phase" in this case? Phase angle between voltage and current?

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Hello dear FvM,
Yes, it is a phase difference between the voltage and current.
Thank you a lot

What is "phase" in this case? Phase angle between voltage and current?

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You can model the setup by a simple equivalent circuit:

- Generator with source voltage and output impedance Z0
- Complex load impedance Z1

Presumed R0 is known (usually real 50 ohms), you have three unknowns
- generator voltage V0 respectively forward power
- real and imaginary components of Z1

It should be determinable from three measured quantities. Setup a system of equations using elementary AC network calculus and try to solve it.

To design this, you really need an RF and process Engineer to define the characteristics and then choose a method suitable to the process variables.

Plasma imaginary impedance changes +/- reactance according the mix ratio of certain gasses used. It also changes according to the excitation frequency. but maximum power is transferred when reactance is minimized and the real impedance is matched to the source impedance. Typically 50 Ohms is used with Smith Chart analysis with swept frequencies.

In operation, conditions vary dynamically and of course there may be arcing interference noise while the power must be held constant with real impedance changing with current density according to the gap control and a stepper controlled vacuum air capacitor to balance phase. A working knowledge of Network Analyzers helps to understand how signals are generated, filtered, and noise rejected , in order to measure fundamental response apart from spurious noise and harmonics as well as induced resonance from spikes.

Always start any design with a well defined set of contraints, in this case for signal, noise and interference, as well as dynamic range of impedance, VSWR and current For this I suggest someone with RF engineer who also knows how to design the layout to avoid measurement errors, instrument the measurement system with drivers, detectors, directional couplers, mixers, filters, Balun, log amplifiers, then the measurement system is easier to define.

At the very minimum, you need a balun and directional coupler.

Otherwise you can expect fundamental problems. You aren't dealing with pure sine waves with constant voltage or current, here.

Dear FvM,
would you mention some how detail of a mathematical expression for complex matching impedance, Reflected power and forward power depend on the parameters above?
I really appreciate your genuine help.
Thank you


Dear SunnySkyguy,
I really like the fundamental points you mentioned. I would like to thank a lot. But, an optimized circuit and a PCB is already available for me. My problem is that I couldn't figure out a detail mathematical procedures to extract complex impedance, FWD power and Reflected power from aforementioned parameters softwarecally.
Thank you again

As said, I believe it can be calculated. But I don't plan to do your work.

The relation between complex load impedance and transmission and reflection is derived in RF engineering text books. See also:
https://en.wikipedia.org/wiki/Reflection_coefficient

Fikadu said:

Dear FvM,
would you mention some how detail of a mathematical expression for complex matching impedance, Reflected power and forward power depend on the parameters above?
I really appreciate your genuine help.
Thank you


Dear SunnySkyguy,
I really like the fundamental points you mentioned. I would like to thank a lot. But, an optimized circuit and a PCB is already available for me. My problem is that I couldn't figure out a detail mathematical procedures to extract complex impedance, FWD power and Reflected power from aforementioned parameters softwarecally.
Thank you again

Click to expand...

There is a helped me flag for each entry.

Consider that the V(t) and I(t) are very dynamic in plasma arc and sub-nanosecond avalanche times are possible, which results in broad spectral current proportional to the contact area and charge in the dielectric being discharged. The repetition rate of the plasma depends on many factors. The spectrum is limited by the rise time of current during avalanche effect with an unknown ESR and charge capacitance in the molecules, but very small.

It is important to realize the s parameters are only an average over the spectrum analyzed for repetitive impulse plasma, even at resonance or excitation frequency.

But the target control is still the maximum forward power that can be controlled while minimizing the reactance by controlling f and gas ratio to minimize Return Loss. But Return Loss is a scaler value, the s parameter reactance is the key to determining what needs to be altered by the phase , polarity and value of the reactive component which should be more sensitive to changes than the real part in a narrow range..

The non-linearity results in energy which may be real and/or reactive at harmonics of the both the repetition ratio and rise time of the avalanche effect up to the pulse width where there is a null, then recursive harmonics of the previous harmonics. These can be measured using THD.

In conclusion plasma impedance is very non-linear, but the linear relationship between the s parameters and linear impedance is well documented, as indicated by FVM.