Re: Analyzing Stub Matching with Reflection Coefficients

K7ITM wrote:
. . .
The analogy may not be prefect, but I think it's a lot like the
usefulness of the idea of a "virtual ground" at the inverting input of
an op amp. But it's a virtual ground only under specific conditions:
strong negative feedback is active, and the non-inverting input is at
(AC, at least) ground potential. For it to be a useful concept
without too many pitfalls, the person using it has to be aware that
the conditions that make it a good approximation don't always hold.
Similarly for a "virtual short" on a line.
>. . .

Let me relate a story. . .

Years ago at Tektronix, I transferred to a different group. Across the aisle was a very bright engineer, fresh from school with a Masters or PhD degree -- I don't recall which. I recall that his advanced education had specialized in nonlinear control systems, very much a mathematically complex and challenging field. His entirely academic background had been very different from mine, so I was often enthralled by his attempts to reconcile reality with the idealized world he had, until very recently, occupied.

One day I found him muttering, trying this and that, until he asked for some help with his test setup. He was driving an inverting op amp circuit with a square wave, and he was seeing sharp pulses at the "virtual ground" summing junction with his 'scope. He had tried moving his probe grounds, replacing the op amp, bypassing, and everything else he could think of, to rid his display of this obvious erroneous artifact. The voltage at the summing junction, he explained, should always be zero, since it's a virtual ground. Those spikes shouldn't be there.

I tried to explain to him how a "virtual ground" was created: An input signal initially generates a voltage at the op amp input. The op amp responds by sending an inverted signal back to the summing junction which adds to the initial voltage to produce very nearly zero at the input. I explained that it can never be zero, but at best is the op amp output voltage divided by its open loop gain. But more to the point, the op amp isn't infinitely fast, so it takes some time for it to respond to that initial voltage or any changes. And during that lag, the summing junction voltage can move a great distance from zero. So the spikes are occurring during the time it takes the op amp to respond to changes in the input stimulus.

Well, he didn't get it. He just couldn't make the transition from the idealized, infinitely fast and infinite gain op amps of his academic models to the real things he had to work with. And looking back on it, I think the basic problem was that he never really fully understood just how that virtual ground came about even in an idealized world.

After a number more frustrating and unresolved collisions with reality, he wisely quit and got a teaching job. I'm sure he did well in the academic world.

Those many models we use daily to keep calculations, concepts, and analyses manageable are just that -- models. It's imperative to constantly be aware of the range over which those models are valid, and alert to any situation which might make the model invalid. People solving routine problems can, unfortunately, often get along for a long time without realizing the limitations of their models, and can be lulled into a belief that they're not models at all but reality. But in the environment where I've spent most of my time, this carelessness leads you very quickly into places which can be very difficult to get out of.

Roy Lewallen, W7EL
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