1. Transmission Lines & Resonators1 1
Transmission Lines & Resonators
Jeffrey Eldred
Classical Mechanics and Electromagnetism
June 2018 USPAS at MSU 1 1 1 1 1 1

2. 2 2
Lumped Circuit Model 2
Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
11/10/2018 2 2 2 2 2 2

3. 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

4. Lumped Circuit Transmission Line
The solutions then become:
Characteristic Impedance Z0 4
Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
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5. Transmission Line Without losses: Phase velocity: 5 5 5 5 5
Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
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6. 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

7. 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

8. Power Transmitted on Load
The reflected power takes away from the incident power. 8
Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
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9. Load on Transmission Line
Voltage reflection coefficient
Transmission Coefficient 9
Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
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10. 10 10
Resonators 10
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11. Parallel RLC Circuit Model11
Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
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12. Parallel RLC Circuit Model12
Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
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13. 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
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14. Quarter-Wave Resonator
Attenuation parameter λ small, kl close to resonance: 14
Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
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15. Comparison to parallel circuit model15
Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
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