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i got a book about amateur radio electronics from the 70's and i was hoping it'd teach me some basics, but alas, i failed the knowledge check on the first page.

back to the high school level texts it is. should also either get a bag of random parts to experiment with or resurrect the tiny kiddie lab i got like 15 years ago. sans a burnt out LED it should still be in working condition.

@Shufei @grainloom

Here are a couple analogies that might be helpful:

If you think of resistance sources as long jumps and capacitance sources as high jumps, they make a right triangle. The magnitude of the hypotenuse reflects the energy involved clearing the two obstacles in sequence. That is called impedance, or at least it's a good way to visualize why it's calculated with Pythagorean theorem

A more accurate analogy would be that a circuitis like a roadway. Resistance is like narrow places in the road and capacitance is like traffic lights. They both reduce the flow of traffic, but they do so in different ways, which means the total effect on traffic is a geometric mean (impedance) instead of being the sum

@grainloom V/I = R = 1/jωC = jωL for AC signals in steady state

@grainloom It's complex number notation, basically instead of writing the actual voltage as a function of time:

A*cos(ωt+ φ)

you can turn this into a complex notation

A*exp(jωt+ φ)

Then you do a Laplace transform which turns everything from time domain into frequency domain.

There are three types of impedances:

Resistive (R)

Capacitive (C)

Inductive (L)

and in terms of what they do, the capacitor works as a derivative of the signal, and the impedance as an integral.

@grainloom So in time domain you have

I(t) = R V(t)

I(t) = C dV(t)/dt

I(t) = L ∫ V(t) dt

In the frequency domain this becomes what I wrote. The use 'j' rather than 'i' for the imaginary part of the complex number to avoid confusion with the current.

But so you see that by putting R, C and L in a circuit, you can shape your signal, that is how you make filters etc.

@grainloom Oops, made a mistake there, you need to swap I and V🤦♂️

Anyway, of your signal is a cosine then the derivative is a sine, which is just a cosine with a 90 degree phase shift. The same for the integral, but the phase shift is in the other direction.

d(exp(jωt))/dt =

jω.d(exp(jωt))/djωt =

jω.exp(jωt)

Sure! Introduce the spinny things!

@grainloom

My grandfather was a ham radio operator who tried to introduce me to electronics at 8yo. I only remember impedance because I'd independently constructed Pythagorean theorem by studying the pattern of the wallpaper in my room

@xmanmonk yup, that's what the book said too. so that's a pretty well educated guess.

Rain 🚱@grainloom@cybre.spacelike, apparently there are "ohm resistors" and "inductive resistors" ?? and the latter doesn't heat up or something??? but does some funky stuff with AC phases?????

i'm pretty sure i won't need to know this stuff until i find out what the hecc an "impendance" is.