1 Transmission Lines Resonators Jeffrey Eldred Classical Mechanics

2 Lumped Circuit Model 2 Classical Mechanics and Electromagnetism | June 2018 USPAS at

Lumped Circuit Transmission Line We can investigate the frequency dependence with 3 Classical Mechanics

Lumped Circuit Transmission Line The solutions then become: Characteristic Impedance Z 0 4 Classical

Transmission Line Without losses: Phase velocity: 5 Classical Mechanics and Electromagnetism | June 2018

Load on Transmission Line The load impedance relates V and I at the z=0:

Load on Transmission Line Voltage reflection coefficient Standing Wave Ratio Input Impedance 7 Classical

Power Transmitted on Load The reflected power takes away from the incident power. 8

Load on Transmission Line Voltage reflection coefficient Transmission Coefficient 9 Classical Mechanics and Electromagnetism

10 Resonators 10 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU 5/20/2021

Parallel RLC Circuit Model 11 11 Classical Mechanics and Electromagnetism | June 2018 USPAS

Parallel RLC Circuit Model 12 12 Classical Mechanics and Electromagnetism | June 2018 USPAS

Parallel RLC Circuit Model Resonance occurs when Wm = We, Zin = R: Quality

Quarter-Wave Resonator Attenuation parameter λ small, kl close to resonance: 14 14 Classical Mechanics

Comparison to parallel circuit model 15 15 Classical Mechanics and Electromagnetism | June 2018

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1 Transmission Lines & Resonators 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 5/20/2021

Lumped Circuit Transmission Line We can investigate the frequency dependence with 3 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU 5/20/2021

Lumped Circuit Transmission Line The solutions then become: Characteristic Impedance Z 0 4 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU 5/20/2021

Transmission Line Without losses: Phase velocity: 5 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU 5/20/2021

Load on Transmission Line The load impedance relates V and I at the z=0: Solve for V 0 -/ V 0+ : Voltage reflection coefficient 6 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU 5/20/2021

Load on Transmission Line Voltage reflection coefficient Standing Wave Ratio Input Impedance 7 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU 5/20/2021

Power Transmitted on Load The reflected power takes away from the incident power. 8 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU 5/20/2021

Load on Transmission Line Voltage reflection coefficient Transmission Coefficient 9 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU 5/20/2021

10 Resonators 10 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU 5/20/2021

Parallel RLC Circuit Model 11 11 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU 5/20/2021

Parallel RLC Circuit Model 12 12 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU 5/20/2021

Parallel RLC Circuit Model Resonance occurs when Wm = We, Zin = R: Quality factor Q is the ratio of power stored to power lost. 13 13 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU 5/20/2021

Quarter-Wave Resonator Attenuation parameter λ small, kl close to resonance: 14 14 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU 5/20/2021

Comparison to parallel circuit model 15 15 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU 5/20/2021