# Help in understanding proposed circuit to measure plasma current

I am working with a plasma where we bias an electrode with a voltage and the plasma acts as a source of current to the electrode. We calculate the plasma current by measuring the voltage across a resistor of known resistance situated between the electrode and the power supply maintaining the voltage (see image, left, where I have treated the plasma like a current source between the electrode and left a gap as sometimes the plasma is there and sometimes it isn't).

The plasma current is not constant: there is a relatively constant current and then fast changes that occur on microsecond timescales. Ideally I'd like to know the current as a function of time (near DC current AND fast changing current), and it seems to me one could with the setup on the left. However, I was reading a paper where another group made the circuit at the right to measure the fast-changing signal.

I do not understand what this circuit on the right is doing. The capacitance makes me think that it's acting like a filter so that they are only measuring the fast changes. Could someone help me understand what the circuit at the right is changing in the voltmeter's measurement and why it is necessary to measure the fast changes?

• These simplified circuit diagrams lack details. In right-most circuit, if V is an ideal DC voltage source, then C, R2 do nothing useful. Commented Aug 6 at 15:23
• What details would be helpful? If it is any help, the paper which discusses using this circuit said "capacitor C acts as a charge storage to enable measurements of fast current transients and R2 is the capacitor discharge resistor." Another paper discussed using C=4.7 uF, R1 = 1 Mohm and R2 = 1 kohm. V is a power supply, so I assume this doesn't count as an ideal DC voltage source. Commented Aug 6 at 16:11

The circuit on the right is just a more practical implementation of the block diagram on the left. These “circuits” are just high level representations. The actual circuits with performance that you need are quite a bit more involved.

C on the right decreases the AC impedance of the source as visible to the plasma. R2 on the right preloads the power supply so that the low-frequency AC and DC impedance is lowered as well. The conductance of the series pass element in the supply increases with current usually.

Those are practical ways of improving the performance of a power supply that needs to supply fairly low but very high bandwidth currents. The circuit on the left would have all those tricks added too in practice. They are just different levels of simplification of a practical circuit.

If you took an identical regulated power supply and connected it to the simple circuit on the left and on the right, the one on the right will have lower impedance as seen by the plasma current, and will maintain the bias voltage the plasma is subjected to much more stable into high frequencies. The left circuit’s bias voltage will fluctuate more when exposed to fast changing plasma load, compared to the circuit on the right.

But - again - those are simplifications, potentially vast simplifications - depending on the average and peak currents needed, and the bandwidth of the AC current. There is a lot of practical consideration in translating these simple ideas into real circuits that perform well, and everything depends on the specs.

If you want to hear more details about how a real circuit would look, please edit the question to include at least the following specifications needed to build such a supply:

• voltage range,
• maximum average current,
• maximum peak current,
• maximum slew rate of the current (from plasma physics), assuming zero impedance bias source
• maximum allowed source impedance vs. frequency presented by the supply to the plasma, or the maximum voltage amplitude allowed (load regulation error) vs. frequency under peak loading at maximum slew rate,
• duty cycle parameters of the supply - how long does it have to continuously operate, and how long will it have at minimum to cool down between operating periods (continuous duty is of course possible but costs more due to thermal demands)
• This was very helpful. Thank you! We already have a power supply that is maintaining the voltage 24 hours a day (and has been for 10+ years). I'm working to get the specs and will append my question when I have that information. Thank you, again. Commented Aug 6 at 21:03