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.

· brutaldon · · ·

like, 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.

@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

@wim_v12e i really wish i knew what the things after the second = mean. gonna find out soon enough i guess. (not tonight tho, tonight is Plan 9 night)

@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)

@wim_v12e
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.

@grainloom I think this is just - a resistor is just supposed to, uh, resist the flow of current. But an easy way to do that is to have a really long bit of wire. Unfortunately if you coil it up to make it fit in a reasonable space now it's a coil and coils ("inductors") are kind of magical for alternating current. So resistors that aren't coil-y are nicer.

@grainloom if you put a coil or a capacitor in a circuit, now it's response depends on how things change with time (capacitors accumulate energy for later; coils resist change, using stored energy to do that) save everything is complicated. But if what you are feeding in is a single sine wave, time-dependence just produces phase shifts, and you can fake that with complex numbers. So instead of a coil being time-dependent, now it's a resistor with an imaginary resistance.

@grainloom complex-number resistances for coils and capacitors and random components are called "impedance" - they resist but also shift in phase the input voltages. Using complex numbers, sad mind as you stick to a single frequency, the math is not as bad as it sounds.

@grainloom also the are much more coherent explanations elsewhere, in engineering texts of you prefer a practical attitude or physics textbooks if you prefer a more abstract approach. ｃｙｂｒｅｓｐａｃｅ: the social hub of the information superhighway jack in to the mastodon fediverse today and surf the dataflow through our cybrepunk, slightly glitchy web portal support us on patreon or liberapay!