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Unformatted text preview: source and load resistances must be transformed down to 5 Ω by the
shunt capactors. The √
series resistance of the branch consisting of 100 ΩjXo is 100/(1 + Q2 ), so we need
2
1 + Q = 20, or Q = 19 = 4.36. Thus Xo must be −100/4.36 = −23 Ω (rounding to the nearest Ohm).
To resonate the system, the net capacitive reactance must be −50 Ω, so we need −23 − 23 + XC = −50, or
XC = −4 Ω. The ﬁnal circuit is shown in the Figure. j 50Ω −j 4Ω 100Ω −j 23Ω Vs −j 23Ω 100Ω Since an explicit center frequency is not speciﬁed, we can scale the ﬁlter to any center frequency. If the
center frequency is chosen to be 100 MHz, then the component values are as shown in the Figure below. 398 pF 100Ω
79.6 nH
69.2 pF Vs 69.2 pF 100Ω The magnitude of the voltage across the output resistor is shown below, forVs = 1 Volt, at frequencies near
the center frequency. The center frequency is slightly shifted away from 100 MHz because the component
values have been rounded. 0.5 0.4 0.3...
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 Spring '08
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