```In 14/02/2013 07:18, Udo Lenz wrote:
```
```   Hi Antonio,
```
But this system has two resonances. Looking at the frequency response of the system, what I see is: At the poles the input impedance is never purely resistive, and is purely reactive in the unloaded case,
```inductive above and capacitive below.
```
At the central frequency the input impedance is purely resistive, with any resitive load at the output. Greater load widens the frequency range where the input impedance is approximately resistive.
```
```
I agree. I've carelessly equated the terms "pole frequency" and "ZCS frequency". As you have shown, they are not identical.. You should be able to run a coil with ZCS (i.e.the input being purely resistive) in the vicinity of the pole frequencies.
```
```
I was commiting an error in my previous frequency analysis, now corrected. Really, there are frequencies where the input impedance is resistive close to the two pole frequencies, but not exactly at them.
The center frequency at light loads and the central frequency at large loads have different properties. The first one will be more inductive below it and more capacitive above. The latter one is the other way around, behaving like a pole. So the frequency with the first behaviour does not exist anymore at large loads. A PLL, which corrects the frequency according to the phase between primary current and voltage can only lock onto one of these frequencies. It will be driven away from the other one.
This is interesting, and something that I was not observing due to my error. A PLL would really have problems. But in my time-domain simulations of the system, I used a simple comparator forcing the input voltage to have the same polarity of the input current, turned on after a few cycles. This control doesn't show instability with any load. It fails just if the current reverses with energy returning from the load, as happens if a burst is continued after a complete beat of the input current, in a lightly loaded case. But a PLL control controlled by the input current would also fail.
operate at a pole frequency, because both pole frequencies are identical, at the central frequency
```(with different Qs).
```
If you are using a PLL, compare the frequency where it operates at the end of a long burst with arc load with the two pole frequencies of the unloaded system. It's true that arc load adds capacitance to the secondary and changes the tuning of the system, so I would expect the final frequency to be somewhere below the central frequency. Or you can operate the system with
```small arcs, so the unloaded tuning is preserved.
```
In the case of a heavily loaded system with only a single ZCS frequency, this
```frequency will be close to the primary resonant frequency. The secondary
```
resonance will be wide at this point, as you have stated above, so that the value
```of that frequency will not matter as much as in the lightly loaded case.
```
```I agree.
I have updated my document, with some frequency response curves:
```everything is approximately linear.