[Amps] Parasitics & Filament Sag

[Peter Chadwick]

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. R²+(XL-XC)², when at resonance = SQ.RT. R²= 
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