>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.
>
? With a Pi-network Z-transformer, the peak in P output occurs when optimal
power transfers. Around this point, there is virtually no change in anode
current. The acid test is to use a dipmeter to determine the resonance of the
tank after max P transfer has been achieved.
>As a reality check of this,
? a dipmeter and a frequency counter is the ultimate reality check
>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.
>
? A famous amplifier "expert" I know tends to use the word "system" more and
more often the farther he gets out on a limb.
>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
Rich, AG6K, 805-386-3734, www.vcnet.com/measures
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