The following facts about Pi Networks, especially those in typical HF power
amplifiers, can be readily deduced by analyzing the circuit using
straightforward circuit theory.
1. The network transfer function contains three poles, as you would expect
from three non-degenerate reactances (C1,C2, and L). These three poles occur at
frequencies very close to the resonances you would observe with simple LC
circuits of (C1,L), (C2,L) and (C1+C2,L).
2. The peak of the power transfer for this network occurs at the 3rd of
these. Namely, at omega=1/sqrt(Cseries x L) where Cseries=C1+C2. Since this is
the
peak in the response of the network, it is the dominant resonance.
3. The other two resonances are also present but of little significance.
Conclusion: the tuned PINET is a highly resonant network with resonant
frequency as I stated above. If it wasn't, you would never see the type of
peaking
that happens as the optimum plate resistance is reached.
As a reality check of this, I analyzed a number of typical PINETs using
values from both my own designs and from the ubiquitous ARRL Handbook charts.
As
suspected, they all showed a dominant resonance at a frequency within about 2%
of the simple omega formula (C1+C2,L).
I would like to offer one opinion relevant to all discussions of resonance.
Namely, there is no universal definition of resonance that holds for all
systems. The "resonant frequency" of a simple LC or mechanical circuit is
universally accepted (it is the peak or null of some network parameter, such as
the
impedance) but more complex systems may contain numerous resonances. The only
generally accepted definition of resonance is an extreme value (max or min) of
some system quantity.
In the case of an amplifier with a PINET tank, the most important of such
quantities is the transmission coefficient of the network, which occurs at the
dominant resonance frequency.
Eric von Valtier K8LV
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