u/DenkSnek

Hello, I hope you all are having a great day. There's a TL;DR at the bottom with a context paragraph above it. I also want to point out that my field-understanding is very casual & limited so far.

From my understanding, stray capacitance & inductance form between a system & a foreign object unintentionally (or intentionally? Would a touch screen & a human finger be an intentional example?) They impact the system such that:

I_c = C(dv_c/dt)
and
V_L = L(di/dt)

This is due to the nature of capacitance (geometric capacitance formula) and inductance (Wheeler's formula):

C = (eA)/d
and
L = (k(n^2)(d^2))/(18d + 40L)

That's to say any two objects of distance d (capacitance) or L (inductance) will exhibit capacitance and inductance between them as a function of their physical dimensions.

This is due to their local electromagnetic field divergences & curls affecting one another per the Maxwell/Heaviside equations (still learning about this relationship.)

Therefore, as the individual divergences & curls create a net divergence & curl across the field shared by the system & foreign object, there will be a voltage (applied voltage - inductively induced voltage, due to Faraday's Law of Induction) and a current in part to capacitance

So ultimately, any two objects insulated from each other will, given a fast changing voltage, carry current. This changing current in turn attenuates the fast-changing voltage by inducing a backwards-polarity voltage. This is so that the current remains as constant as possible.

As miniscule as these voltages & currents may be, every pair of objects exhibit stray capacitance & inductance that influences their localized field characteristics. I suppose that also explains leakage inductance in a transformer? The miniscule-detail may not be right because there does need to be a fast changing voltage or current to cause this & ionize the insulating material.

TL;DR: I'm trying to understand what stray capacitance & inductance is from the perspective of field interactions. My previous paragraph is how my current perspective is, but it doesn't sound quite right?

Hello,

I hope you all are having a great day! I may be in over my head with this question, so I apologize if the wording is off.

I'm reading the Art of Electronics 3rd ed., which in Chapter 1.7.9 (RC lowpass filter, pg. 51), the authors pose a question of designing filters that can have differing amplitude & phase responses. They deny this possibility quoting the laws of causality & referencing the Kramers-Kronig relations. I've done brief research on these topics, but I'm not connecting how it relates to the impracticality of designing such filters (or perhaps why amplitude and phase are dependent on each other; I may be missing a fundamental concept here).

I see that the real components of the complex amplitudes & phases make up the energy dispersion spectrum, whereas the imaginary components make up the energy absorption spectrum. I'm not sure where to go from here, though.

Below is the quote from the textbook:

"An interesting question is the following: is it possible to make a filter with some arbitrary specified amplitude response and some other arbitrary specified phase response? ... no: the demands of causality force a relationship between phase and amplitude response of realizable analog filters (known officially as the Kramers-Kronig relation)."

Thank you! I appreciate it.