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## [AMPS] More L-net/Series to Parallel questions

 To: [AMPS] More L-net/Series to Parallel questions jono@enteract.com (Jon Ogden) Tue, 16 Feb 99 16:09:23 -0600
 ```OK, more questions on series to parallel conversions and L-nets. Let's try this one on for size: Assume a resonant RLC circuit. The input impedance is 4600 Ohms. C is conected to ground at 7.6 pF. L is 1 uH and is in series with Rout. L and Rout are connected in parallel to C. This is a standard L-net type circuit. Freq: 28 MHz OK, find Rout. According to the design tables in "Solid State Radio Engineering" by Krauss, Bostian and Raab (page 76), we have the following: Q = wL/Rout = wCRin (1) Rin = L/(CRout)=Q/(wC) (2) = Rout(Q^2+1) (3) wL = (1/wC)*(Q^2/(Q^2+1)) (4) OK: w=2*pi*28MHz = 175929600 >From (1) above, we get: Q= w*C*Rin = 175929600*7.6E-12*4600 = 6.02 Also from (1) we can say that: Rout = wL/Q = 175929600*1E-6/6.02 = 29.24 Ohms >From (2) we can say that Rout = L/(C*Rin) = 1E-6/(7.6E-12*4500) = 29.24 Ohms However, using (3): Rout =Rin/(Q^2+1) = 4500/((6.02)^2+1) = 4500/37.24 = 120.83 OK I GIVE UP!!!! WHY DO THE EQUATIONS NOT JIVE?????? I can derive equation (3) from the other equations given, but I cannot figure out why the numbers can show up different. I must be doing something obviously wrong or the book has an error in its formulas. So can someone please tell me why? Yes, I'll feel like an idiot, but at least I'll have my error corrected. And secondly, no one has yet explained my L-network vs. series -> parallel transformation question. With all this brain power here, someone has got to know how to answer both of these. Or is the brain power only existent when theory is discussed and not real mathematics? 73, Jon KE9NA -------------------------------------------------------------------------- Jon Ogden jono@enteract.com www.qsl.net/ke9na "A life lived in fear is a life half lived." -- FAQ on WWW: http://www.contesting.com/ampfaq.html Submissions: amps@contesting.com Administrative requests: amps-REQUEST@contesting.com Problems: owner-amps@contesting.com Search: http://www.contesting.com/km9p/search.htm ```
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