Jeffrey Eldred Classical Mechanics and Electromagnetism June 2018 USPAS at MSU 2 Lumped Circuit Model 2 Classical Mechanics and Electromagnetism June 2018 USPAS at MSU 2 6112018 We can investigate the frequency dependence with ID: 676006
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Transmission Lines & Resonators
Jeffrey Eldred
Classical Mechanics and Electromagnetism
June 2018 USPAS at MSU Slide2
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Lumped Circuit Model
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Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
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We can investigate the frequency dependence with
3Lumped Circuit Transmission Line
Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
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The solutions then become:
4Lumped Circuit Transmission Line
Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
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Characteristic Impedance Z
0Slide5
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Transmission LineClassical Mechanics and Electromagnetism | June 2018 USPAS at MSU
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Without losses:
Phase velocity:Slide6
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Load on Transmission LineClassical Mechanics and Electromagnetism | June 2018 USPAS at MSU
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The load impedance relates V and I at the z=0:
Solve for V
0
-/ V0+ :
Voltage reflection coefficientSlide7
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Load on Transmission LineClassical Mechanics and Electromagnetism | June 2018 USPAS at MSU
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Voltage reflection coefficient
Standing Wave Ratio
Input ImpedanceSlide8
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Power Transmitted on LoadClassical Mechanics and Electromagnetism | June 2018 USPAS at MSU
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The reflected power takes away from the incident power.Slide9
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Load on Transmission LineClassical Mechanics and Electromagnetism | June 2018 USPAS at MSU
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Voltage reflection coefficient
Transmission CoefficientSlide10
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Resonators
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Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
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Parallel RLC Circuit ModelClassical Mechanics and Electromagnetism | June 2018 USPAS at MSU
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Parallel RLC Circuit ModelClassical Mechanics and Electromagnetism | June 2018 USPAS at MSU
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Resonance occurs when Wm = We, Zin = R:Quality factor Q is the ratio of power stored to power lost.
13Parallel RLC Circuit Model
Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
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Quality factorSlide14
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Quarter-Wave ResonatorClassical Mechanics and Electromagnetism | June 2018 USPAS at MSU
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Attenuation parameter
λ
small, kl close to resonance:Slide15
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Comparison to parallel circuit modelClassical Mechanics and Electromagnetism | June 2018 USPAS at MSU
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