Foster’s reactance theorem states that any reactance increases as a function of frequency

Unfortunately, this can’t be done over a large range, because as Foster’s reactance theorem states, as soon as you deviate a little from your center frequency, both the inductive reactance of your antenna and the reactance of whatever you’re using to cancel it (most likely a capacitive element) both increase (go toward **up** by some amount **also** goes up by some amount

If you had a Non-Foster element, the reactance of your tuning element would go **down** by some amount

Most attempts to do this have required the use of active elements (such as gyrators) so synthesis a negative impedance. However, I’m wondering if a switched-capacitor circuit can be used to synthesize this Non-Foster reactance. Most analyses of switched-capacitor circuits show that they are synthetic resistors at frequencies far below the switching frequency. However, what does the impedance look like *near* the switching frequency?

Well, since you’re pumping current into the circuit at exactly the rate of switching, you should see a large voltage. As a result, it should look like a high-impedance near the switching frequency. I would tend to believe that the switching function takes the usual

The upshot of all this mixing is that just below the switching frequency, one would have a reactance that’s decreasing. (I’m doing a considerable amount of hand-waiving here, excluding such things as aliases of the switching harmonics.) What’s even cooler about this reactance is that the Non-Foster region is determined by the switching frequency–so, one could move it around just by changing the switching frequency. You’d effectively have a digitally-tunable antenna.

There are a number of problems with this scheme, most notably the radiation of switching noise and any switched-capacitor noise effects. However, I think it’s worth looking at and building upon.