# GIC's aplenty

#### The Electrician

Joined Oct 9, 2007
2,903
Most courses on analog electronics will include a segment on the GIC (generalized impedance converter). However, they seldom point out that there are variants on the standard topology. I've attached an image showing the 24 (possibly useful) variants on the GIC topology. The one designated A1A is a standard one.

Each one consists of 2 opamps and 5 admittances (not impedances). There are 5 nodes, which I number from 1 to 5, top to bottom.

For an exercise, calculate the driving point impedance (as seen at node 1, the top node) of circuit A1A in terms of the 5 admittances; assume the opamps are ideal with infinite gain. Having done that, calculate the same thing for circuit A1B, which is the same as A1A except that the opamp + and - terminals are reversed. Compare the impedances for a surprise. Compare the impedances of some more of the 24 topologies for a further surprise.

These circuits can be used to act as a synthetic inductor. If the opamps are not ideal, then any such synthetic inductor may exhibit different performance depending on which circuit is used. How shall we decide which circuit to use?

For those who are up to more difficult analysis, let the top opamp have a DC gain of A01, and a single pole gain function of A1 = A01/(1 + s t1), with t1 being the time constant of the roll off. Similarly, the bottom opamp has a non-ideal gain of A02/(1 + s t2). Calculate the impedance at node 1 with these non-ideal opamps and compare the performance of circuits A1A and A1B (and others if you like).

Those who enjoy analysis of opamp circuits will find this an intriguing puzzle. I'm sure knightofsolamnus will be one such person!

#### Distort10n

Joined Dec 25, 2006
429
I think these are similar to an op-amp gyrator. It simulates inductance. I will have to work out the math later...it is the weekend, and I deserve a break from work! 