"Stretching" an inductor

Huh? Won't a parallel tank do what you want? Although you're saying reactance, rather than "real".

...Jim Thompson

There may be some version of a generalized impedance converter that produces a resistive impedance proportional to frequency squared. I have seen some that produce a negative resistance inversely proportional to frequency squared, i.e. -1/D*w^2, where D is a constant based on resistor and capacitor values in the circuit.

Huh?? If I put 100nH in series with 30pF, at 100MHz the net reactance is +j9.78 ohms; at 200MHz, it's +j99.14 ohms. Last time I checked, 99 is more than twice 9.8, not less. In general, if you double any frequency above the resonance, you get a reactance more than twice as high, though the effect is the strongest for starting frequencies near the resonance.

Cheers, Tom

Joel Kolstad wrote:

That's an FDNR, (Frequency Dependant Negative Resistor), and can be realised with the basic four-op-amp gyrator circuit using two capacitors and three resistors. You can get a negative resistance that either increases or decreases as the square of the frequency, depending where you put the capacitors, but I've never found a way of doing anything useful with this circuit.

You can make a frequency dependant voltage divider with an FNDR and a resistor, but the circuit goes through a phase inversion, the point of inflection being at the frequency where -R = R

Make that "two-op-amp gyrator circuit".

You wrote, ". . . but I've never found a way of doing anything useful with this circuit."

If as you wrote in the paragraph after that, you put it in series with a resistor, you get a circuit that behaves much like a series resonant circuit. Not only does it go through a phase inversion, but it goes through zero resistance. Similarly if you put it in parallel with a resistor, you get something that behaves much like a parallel resonant circuit: where the gyrator negative resistance equals the parallel positive resistance, the net resistance goes to infinity. If you think of C-R-L circuits (or better, 1/sC, R, sL) as having components that contribute in quadrature, with 90 degrees going from C to R and R to L, you see that you can have the same effect with three components that behave as R, sL and s^2Gyrator; you've just multiplied everything by s. Or you can have a {1/s^2Gyrator, 1/sC, R} set. And you can expand your filtering horizons by having a set {1/s^2Gyrator, 1/sC, R, sL, s^2Gyrator} . . . that lets you implement higher order filters in simpler topologies (if only the gyrator were a simple passive two-lead part!)

Gyrators don't seem to be used very often, but I have seen them used to (presumably) keep the op amp out of the direct signal path, in an attempt to have it contribute less distortion in the passband.

Cheers, Tom

TuT wrote:

Thanks Tom, that'll certainly do it. When I said "small capactior," in my case I was thinking "below resonance" -- as you say, when you're above resonance the reverse is true. I should have thought it through some more before posting.

---Joel

Hmm... in fact... ignore that bit about above vs. below resonance too -- turns out I dropped a minus sign in my original calculations. :-(

Check out the Sept 14 EDN Magazine, "design ideas" Brick-wall lowpass audio filter for a practical circuit which uses three gyrators.

I don't care much for EDN, but occasionally a contributor sends them something really good. This is one.

Don

Cute. But my favorite filter book, Herrero & Willoner, has techniques where you simply enter pass and stop bands and go directly to Laplace, thence to active filter, gyrator or otherwise.

...Jim Thompson