Re: basic question about integrators in a loop (circle test)

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On 21/07/2025 11:11 pm, john larkin wrote:

On Sat, 19 Jul 2025 12:29:38 -0800, Christopher Howard
<christopher@librehacker.com> wrote:

<snip>

I was recently talking to my design center kids about differential
equations and circuits. All three are CE/EE grads or students. I
mentioned "initial conditions" and one of them recalled hearing the
term.  [1]

I got it drummed into my head during Pure Math 2, which was one of my second year undergraduate courses, It was entirely about integral and differential calculus, and remarkably tedious, but useful.

Your equation has an infinite number of solutions. One is Y=0, cold
and dead. One is a 1-volt sine wave. Another is a megavolt sine wave.
Which it does depends on the initial condition, what it's already
doing when you walk into the room. It will keep doing that. You can
Spice that.

Since Spice is designed to evaluate the sort of differential equations which described electronic circuit, this is a remarkably obvious assertion.

In real life, there are no ideal integrators, so the loop has
additional phase shifts, so there are different solutions to the
equation; specifically decaying or increasing sine waves.

The phase shifts control the frequency, not the amplitude, which is determined by component ratios which drift as the ambient temperature changes, or the components age.

To make a decent oscillator, you need an increasing amplitude circuit
and some sort of active amplitude limiter. Opamp clipping is the
cheapest limiter.

But it introduces harmonics of the sine wave being clipped.

[1] Computer Engineering is a kinda oxymoron.

Why? Computers are engineered devices, and designing them is definitely a branch of engineering. It strikes me as a sub-branch of electrical engineering, or perhaps of just electronic engineering (which is itself a sub-branch of electrical engineering).
An oxymoron embodies a contradiction. "Military intelligence" is the classic example.
"According to the Oxford Learner's Dictionary, oxymoron is defined as “a phrase that combines two words that seem to be the opposite of each other.” The Cambridge Dictionary defines an oxymoron as “two words or phrases used together that have, or seem to have, opposite meanings.”
--
Bill Sloman, Sydney