[Amps] Resonance in PiNetworks

[2]

>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