Tony,
I missed this reply of yours earlier. I hadn't thought of the skin effect,
though given that is the result of penetration of fields, it must have some
reactive element, surely? I did actually look into this in some depth about
a year ago in relation to inductor design but more has flowed out than
remained. (Though I do remember nothing significant in phase angle within
the audio band. But to say it was near zero required about three
assumptions to be true which might have been a stretch.)
You also succinctly cover the radiation question that John does. ka = 2 is
considered the usual limit, incidentally, though on what grounds don't know.
ka = 1 might be flat and ka = 2 might give you a bandwidth. I have usually
regarded it as an experimental result - although the equations aren't that
difficult IIRC, there may be losses that leave the practical results a
little awry. But, as you say, plenty of reactive element in there.
Christian
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On 15 September 2011 20:43, Tony Casey <tony@...> wrote:
**
<snip>
--- In LTspice@..., Christian Thomas <ct.waveform@...> wrote:
Well, that's a question AG.
Might we not be looking at a naive question here? Ie. Can I please have a
resistor that changes with frequency but with none of those nasty
reactive
elements? If that's the case then looking in the s-plane is not the
answer
being sought.
In which case the answer needed is "No, you can't. Or at least you can't
have a full solution. (I think that must be right). But we do have some
useful reactive components that perform that function, and that's what
everyone else uses. C and L in LTSpice; and their s-plane behaviour is
built in."
CT
</snip>
Hello Christian,
I'm sure you ask the question tongue-in-cheek, because you surely must be
aware of instances where the real part of an impedance changes with
frequency without significant change in the reactance.
What about the resistance of straight length of wire? This increases due to
the skin effect, whereby as the frequency rises more and more of the current
travels closer to the outer (indeed for circular cross-section, the only)
surface of the wire, so in effect reducing the cross-sectional area of the
wire. In the limit, there is also a change in the inductance per unit length
too, but it is not significant compared to the change in resistance.
And although not strictly a "component", there is the free space acoustic
radiation resistance of a diaphragm, which also rises with frequency up to
the frequency where the circumference is approximately equal to the
wavelength. I will concede in this example that the reactive part of the
impedance also changes at a fair rate of knots over the same frequency
interval.
I'm sure you already knew all that. But it does illustrate why it is
perfect legitimate to seek frequency-dependent resistance models.
Regards,
Tony
