Peter is certainly right.
I vividly remember a "dreaded" University professor that still required the
late 70's electronics engineering student to account in detail for the six
cases of "resonance" that could be derived for a low-Q resonant circuit.
From memory these were:
1. Frequency of oscillation when excited by an external source of energy; lower
in frequency when Q is lowered;
2. Highest RF voltage over the capacitor; higher in frequency when the Q is
lowered;
3. Highest RF voltage over the inductance; lower in frequency when the Q is
lowered;
4. Phase angle = 0; losses are accounted for as a series resistance in the
inductance; lower in frequency when the Q is lowered;
5. Phase angle = 0; losses are accounted for as a parallel resistance over the
capacitor; higher in frequency when the Q is lowered;
And finally
6. Xc = Xl which only held for parallel circuits that were unloaded and lossless
This was an expansion of the reasoning by i.a. Terman that wrote in "Radio
Engineering"
(my 1st edition 8th printing p.55):
"The resonant frequency of the parallel circuit is sometimes taken as the point
of minimum line current, sometimes as the condition that makes the impedance a
pure resistance, and sometimes the frequency for which omegaL = 1/omegaC.
These three definitions of resonance in parallel circuits lead to resonant
frequencies that are different by such a very small fraction of 1 percent when
the circuit Q is at all large..."
The paragraph was underlined by the previous owner of my book, so it seems
likely that 30's/40's electrical engineering
educators also found it necessary to point this out.
When Q is large enough it may be quite safe to neglect the differences, but
when coming to i.a. load-lines and
phase-gain characteristics of low-Q networks, it may be good practice to apply
rigorous analysis.
Another area would be the design of a convergent servo tuning system for an RF
power amplifier.
73/
Karl-Arne
SM0AOM
----- Original Message -----
From: "Peter Chadwick" <g3rzp@g3rzp.wanadoo.co.uk>
To: "Mike Sawyer" <w3slk@uplink.net>; <g3rzp@g3rzp.wanadoo.co.uk>; "R L
Measures" <r@somis.org>
Cc: <amps@contesting.com>
Sent: Monday, September 04, 2006 3:22 PM
Subject: Re: [Amps] Parasitics & Filament Sag
> Mikey said:
> >Peter,
> Show me concrete evidence that the voltage and current are not in phase
> when XL=XC. Basic AC theory demonstrates that resonance is the point where
> all that's left is Z=R, where R is the DC resistance left in the circuit.
> Unless the formula has gone through a radical change since my classroom
> days, its always been Z= SQ.RT. RÂ+(XL-XC)Â, when at resonance = SQ.RT.
> RÂ=
> R. Now where am I going wrong here?<
> Because the 'XL' is really sq.rt (XL^2 + RL^2) and the 'XC' is really sq.rt
> (XC^2+ RC^2) where RL and RC are the series resistances of the inductor and
> capacitor respectively. If you take the case where Q=5, then the 'XL'
> becomes an impedance of 1.1XL with a phase angle of 78.7degrees, rather than
> 90. Thus the 'XL -XC' has to be done vectorially as ZL-ZC. Terman goes into
> this - 3rd Edition Sec 3-2, page 49 et seq. He says:
> "In the general case when the circuit Q is low, a curve of circuit impedance
> as a function of frequency still tends to have the shape of a resonance curve
> unless the circuit Q approaches or is less than unity, but the maximum
> impedance does not necessarily occur at the frequency of series resonance,
> and the condition for unity power factor does not necessarily occur at the
> frequency of series resonance or when the impedance is a maximum. The actual
> behaviour depends not only upon the circuit Q, but also the division of
> resistance between the inductive and capacitive branches......"
> The XL=XC definition works fine for a series resonant circuit, but not a
> parallel one unless you neglect the effects of Q. That you can do if Q is
> high (typically >15 or so is a good rule of thumb) because you approximate
> anyway. But analysing something like a Foster Seeley running low Q for
> linearity leads to some pretty wild errors if you assume XL = XC. Similarly,
> a tank ciruit where you're worried about phase shift because of feedback - or
> the effect on IMD of an elliptical load line. Another area where it makes a
> lot of difference is in low Q coupled circuits, especially where you need
> kQ>1.
> We got something like 25 hours of lectures on resosncne and coupled circuits
> etc when I was at college: a good chunk has stuck, mainly because I've used
> it. These days, students don't seem to get taught anything about resonance
> and tuned circuits - maybe because people don't generally use coils in
> integrated circuits!
> 73
> Peter G3RZP
> _______________________________________________
> Amps mailing list
> Amps@contesting.com
> http://lists.contesting.com/mailman/listinfo/amps
>
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