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Unformatted text preview: show that the impedance is ﬁnite at all frequencies. The
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only remaining possibility is circuit (g). This circuit is purely resistive at ω = 0, reduces to R j ωC for very
small frequencies, and asymptotes to j ω L at suﬃciently large frequencies — all of these characteristics are
in accordance with the given data. The impedance for circuit (g) is:
Z = j ωL + R
1 + j ω CR or R(1 − j ω CR)
R
CR2
=
+ j ω (L −
).
2 C 2 R2
2 C 2 R2
1+ω
1+ω
1 + ω 2 C 2 R2
Clearly, R = 1000Ω. It remains to solve for L and C . Use the measured impedance data to write two equations for these unknowns. For example, from the given data, the real part of the impedance is approximately
100Ω at f = 19 MHz. Hence
R
100 =...
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 Spring '08
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