Rich Measures wrote:
>>>Sample problem: Part I: Ls = 200nH, Rs = 200 ohms, f = 100MHz. What
>>>is the Admittance, Y, Mr. White? A running description of your solution
>>>would be helpful.
>>
>>No, I won't bite. There is absolutely no need to drag admittance into
>>this discussion.
>>
>Then on to Part II: what is the parallel-equivalent resistance of 200nH
>in parallel with 200 ohms at 100MHz? (presumably using the method
>described below)
>
200 ohms, at ANY frequency, by definition - no calculation is required.
(Hopefully we are both assuming idealized components here, ie no
parasitic L or C in the resistor, and no parasitic R of C in the
inductor.)
Part III - it's my turn: what is the series-equivalent form, ie what are
Rs and Xs at 100MHz?
XL = 2*pi*100E6*200E-9 = 125.66 ohms
XL is equal to Xp by definition, because L and R are connected in
parallel.
R = 200 ohms = Rp by definition as we hopefully agreed above.
Then, using the equations I gave last time (out of the ARRL Handbook
since time immemorial):
Rs = Rp * Xp * Xp / (Rp * Rp + Xp * Xp)
= 56.61 ohms
Xs = Rp * Rp * Xp / (Rp * Rp + Xp * Xp)
= 90.10 ohms - at 100MHz that's 143.40nH
Q = Xs/Rs = 1.59
(Check arithmetic by calculating Q directly from the input values:
1/Q = Xp/Rp = 0.63, so Q = 1.59 which is correct.)
What do you make Xs, Rs and Q, Rich?
What does this mean in real-world terms?
It means that at exactly 100MHz, a network analyser or R-X bridge cannot
tell the difference between {200 ohms in parallel with 200nH} and its
series equivalent which is {56.61 ohms in series with 143.40nH}. The two
networks have exactly the same properties at that frequency. That's what
"equivalent" means in this context.
73 from Ian G3SEK Editor, 'The VHF/UHF DX Book'
'In Practice' columnist for RadCom (RSGB)
http://www.ifwtech.demon.co.uk/g3sek
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