I built a simple resonant circuit for use with the EOM consisting of:
- A 1:16 turn ratio RF transformer
- A tunable inductor
- That's it
The schematic of the full circuit including the EOM is:
The principle of operation is that the impedance Z of the LC circuit in parallel with the secondary transformer coil becomes very high on resonance. The transformer makes this impedance look like Z/(16^{2}) to an input signal, and the circuit is optimized when this value is 50 Ω so that the impedance is matched and there is maximal power coupling. Meanwhile, the voltage is stepped up by a factor of 16, so the ultimate result is a gain on resonance. The transformer is useful in its own right in the case where the load impedance is not adjustable, in order to match this with the input impedance. In that case, one chooses the appropriate turn ratio to make Z/n^{2} = 50 Ω (for RF applications). In our case, we make Z as high as possible, and in doing so we need to increase n, which in turn increases the voltage gain---pretty neat!
The measurement setup is the same as here. Below is the measured voltage transfer function, with the effect of the attenuators from the source to the circuit (to avoid power reflection, as detailed in the linked post) subtracted out.
It seems like either the inductor I am using is not quite what it says it is, or that the capacitance of the EOM is not the roughly 12 pF it is supposed to be. The latter is not very likely as I got roughly the same resonant frequency of ~26 MHz when simulating the EOM with a mica capacitor. In any case, I am going to replace the inductor with a slightly smaller one and try to adjust the frequency to 33 MHz.
I wanted to plot the LISO prediction for this circuit along with the measured transfer function, but I am running into trouble with getting the Q quite right. The resonant frequency and gain come out to about the same, but the shape was much broader. I realized that I had the coupling efficiency of the mutual inductance line set to unity (ideal), and when I changed this to 0.9 the Q magically increased, resulting in a very sharp spike. I am not sure if I am doing something wrong, but I will either figure it out or just use something to model it analytically. |