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Transmission Lines & Resonators
1 1 Transmission Lines & Resonators Jeffrey Eldred Classical Mechanics and Electromagnetism June 2018 USPAS at MSU 1 1 1 1 1 1
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2 2 Lumped Circuit Model 2 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU 11/10/2018 2 2 2 2 2 2
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Lumped Circuit Transmission Line
We can investigate the frequency dependence with 3 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU 11/10/2018 3 3 3 3
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Lumped Circuit Transmission Line
The solutions then become: Characteristic Impedance Z0 4 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU 11/10/2018 4 4 4 4
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Transmission Line Without losses: Phase velocity: 5 5 5 5 5
Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU 11/10/2018 5 5 5 5
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Load on Transmission Line
The load impedance relates V and I at the z=0: Solve for V0-/ V0+ : Voltage reflection coefficient 6 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU 11/10/2018 6 6 6 6
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Load on Transmission Line
Voltage reflection coefficient Standing Wave Ratio Input Impedance 7 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU 11/10/2018 7 7 7 7
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Power Transmitted on Load
The reflected power takes away from the incident power. 8 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU 11/10/2018 8 8 8 8
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Load on Transmission Line
Voltage reflection coefficient Transmission Coefficient 9 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU 11/10/2018 9 9 9 9
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10 10 Resonators 10 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU 11/10/2018 10 10 10 10 10 10
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Parallel RLC Circuit Model
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Parallel RLC Circuit Model
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Parallel RLC Circuit Model
Resonance occurs when Wm = We, Zin = R: Quality factor Q is the ratio of power stored to power lost. Quality factor 13 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU 11/10/2018 13 13 13 13
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Quarter-Wave Resonator
Attenuation parameter λ small, kl close to resonance: 14 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU 11/10/2018 14 14 14 14
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Comparison to parallel circuit model
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