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RF Behavior of Passive Components

• Conventional circuit analysis– R is frequency independent

– Ideal inductor:

– Ideal capacitor:

• Evaluation– Impedance chart

LjX L ω=

CXC ω1=

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Impedance Chart(impedance of C & L vs frequency)

ZC=1/(2πfC)

ZL=2πfL

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How does a wire behave at high frequency?

• Example: Resistorσπ 2a

lRDC =

δ2/

aRR DC =

δω

2/

aRL DC =

µσπδ

f

1=

High frequency results in skin-effect whereby current flow ispushed to the outside

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How exactly is the current distribution as a function offrequency?

• Low frequency showsuniform currentdistribution

• medium to highfrequency pushescurrent to the outside

• RF “sees” currentcompletely restrictedto surface

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Impedance Measurement ExampleCapacitor going through resonance

CapacitorCharacteristics

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Equivalent Circuit Analysis