Foster’s reactance theorem states that any reactance increases as a function of frequency . This is true of the impedance looking into an antenna, where the reactance may be a large part of the overall impedance. The task in matching the antenna (for maximum power transfer and therefore maximum SNR) is to cancel the reactance (or susceptance) and match the resistance.
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 ). So, for every change in frequency from the center frequency, your antenna reactance goes up by some amount , but your matching element’s reactance 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 , compensating for the increased reactance of the antenna. You would then have a broadband (or broader) match.
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? Read More
My other blogs & plans for the future
It used to be that I’d post just about anything here. However, after a few months of posting circuit design articles, I developed a consistent readership and decided that most of you aren’t interested in my daily life and/or the tech hobbies that I might be up to. As a result, I separated my personally-centered blogs from this blog.
I just wanted to quickly mention that if anyone is interested, I have two other blogs:
Personal Blog
Tech (software/computer) Blog
Also, you’ll notice that Google Ads are prominently displayed on this blog. I wanted to recoup the hosting costs of running this blog. Unfortunately, that didn’t end up being as profitable as I thought. So, as soon as I hit $100 of ad revenue (which is the minimum to cash out of my Google AdSense account), I’ll remove the ads. I’ll essentially be eating the hosting cost (in addition to the time I’ve put into the blog).
Unless I change my mind. Which is unlikely.
Also, I might try out some more social features on the web site. If I get the time. Which is also unlikely.