Simulation Results & Discussion

Using a plasma equivalent circuit with a resonant frequency of 4.47 MHz, great care has been taken to simulate the return analyzer circuitry, including the electrometer, comparators, and phase detector.  The relative phase difference between the active collector signal and the driven guard reference is very important to the PFP mode of operation.  Figure 6 below is a plot of the relative phase difference between those two signals during a simulated DDS frequency sweep from 100 kHz to 100 MHz.

Figure 9: Relative phase difference profile for PFP operation

The plasma resonant frequency is represented by the zero relative phase difference at 4.588 MHz which is roughly the 4.47 MHz frequency expected.  From this plot it was possible to test the actual response of the comparators and phase detection circuitry.

For one simulation, a transient analysis was performed with a DDS output of 1 MHz.  According to the relative phase difference plot above, this should have a pretty high (off resonance) phase difference response.  Figure 7 below is a plot of the active collector return and driven guard reference signals in their form following the comparators.  Also included in the plot is a display of the XOR phase detector system output.

Figure 10: PFP mode transient analysis at max phase low

This verifies that the reference signal indeed leads the return signal from the active collector in its inductive reactance response.  Also, these signals are as much out of phase as the relative phase difference plot above indicates they should be.  The XOR digital output response at the top of this plot is easily connected to a loop filter to yield the previously discussed 0-5 Volt signal proportional to the relative phase difference between the return and reference signals.

            Figure 8 below is a result of a simulation with the DDS output frequency almost equal to the resonant frequency of the plasma.

Figure 11: PFP mode transient analysis at resonance

Notice that the two signals are almost perfectly in phase and the output from the XOR gate, if sent through a loop filter, would be practically 0 Volts.

            At the higher extreme, the following is the same type of simulation with a DDS output frequency of 10 MHz, which is well above the resonant frequency of the plasma.

Figure 12: PFP mode transient analysis at max phase high

Here again it is clear that the signals are out of phase.  The plasma return signal from the active collector is now leading the reference signal due to the switch to capacitive reactance on the higher side of the plasma resonant frequency.

So overall, the electrometer, comparators, and phase detection circuitry simulates as expected.