Huh, like this? Thank you Klaus, I will finally learn something here.
The Y value depends on number of points. The CCS is 1A.
C = 1/(2*pi*F*(Vin/I1)), C= 1/(2*pi*F*Z), this was your point ?
I have hoped this was clear, absolutely clear.
... I have to add that I really do not like the philosophical debates about engineering issues.
To eliminate amplifier effect, voltage is measured at amplifier output B and speaker input A and the ratio A/B shows the frequency response added by the cable.
Pavel, I've never checked if that kind of analysis is correct for transmission lines but I think it should be as for any normal networks it is applicable.
Before, and really right up to the first peak the load is capacitive (look at the phase of the pure impedance V(in)/1A) with a -90deg phase angle and increasing magnitude (reaching many nF), after the peak it turns inductive (+90deg), and so one, after each peak.
This is very equivalent to measuring the voltage drop accross the cable. Assuming symmetrically constructed cable, one side will do. The side grounded at the amp would apply and then this can be trivially be measured with a soundcard, may not even need balanced input.
Cable has resistance, speaker doesn't draw constant current vs. frequency --> voltage loss along the cable isn't constant, speaker's FR will change. Ohms Law, as simple as that.
@preload , @MrPeabody, you're overcomplicating things.
Pavel wanted to show that non-negligible impedance (primarily resistance) of a speaker cable, besides a general small level drop, causes a slight frequency response change when the speaker is not a constant load vs. frequency (neglecting current distortion here).
To better quantify the difference it is needed to factor out the (very small) response change seen already at the amp output which is not zero impedance -- but low enough to not disturb the general concept of the sim/measurement. Hence FR(load)/FR(amp) was computed to normalize out the amp's influence.
While it is true that the amp output impedance itself affects the effect it is small enough compared to the other impedance that it can be safely neglected. If it were the same magnitude than the cable the effect would be half as strong and if the amp were a current source there'd be zero effect on frequency response and level.
This whole thread is a bit lost....does it have an actual practical point to express?
It started off with the poster providing empiric data confirming that speaker cable can cause 0.2dB deviations in frequency response as a result of cable resistance/inductance driving a reactive load). But then it got obfuscated by additional argument about Mhz-frequency differences (sigh), and then all things just kind of went downhill from there.
It was still obscured in real circumstance usefulness if that's a thing. It boiled down to insignificant the way I read it. I'm starting to think pma is a cable charlatan "designer" myself.
I think the entire argument always boiled down to get cables that are thick enough. Can you do these tests with cables that are more reasonably close to what you would see as a recommendation. So 4mm2 vs 6mm2 at lets say 5 meters.Conclusion
It is impossible to say that "cables make no difference". It is not true. The cables depending on length, construction and speaker used may make an audible difference, even if they are as short as 2m. 5m of 2x1.5mm2 zipcord makes 0.2dB deviation at higher bass, into quite standard speaker load. This starts to be audible. The speaker cable should be as short as possible and monoblocks placed near the speaker are the best option in case of passive speakers.
Edit: the zipcord used was 2x1.5mm2, length 5m.