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ADV/TEC 5: Resonance

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ADV/TEC 5: Resonance

Introductory mini-lecture

- Mechanical: pendulum, Tacoma Narrows bridge
- Atomic transitions: frequency of photon matches the energy difference between two atomic levels
- Electrical: an LC circuit responds very sharply at a particular frequency

Resonance is a property of systems that have a natural frequency of oscillation. For example:

- Impedance of the capacitor decreases with frequency, so |iC| increases with frequency
- Impedance of the inductor increases with frequency, so |iL| decreases with frequency

- Impedance of inductor and capacitor in parallel:
- At resonance ZL + ZC = jωL – j/ωC = 0,
i.e.,|ZL|=|ZC |whenω2 =1/LC or

- Ztotal is (theoretically) infinite, so net current = 0,
i.e., iL= vL/ZL = –vC/ZC = –iC

- At resonance the vectors iL and iC are equal in magnitude but differ by 180⁰ in phase
- Input and output voltages are equal

- f1 and f2 are the frequencies at which |v2/v1| =
- Q = f0/(f2 – f1) measures the sharpness of the resonance
- Q measures the ratio of energy
stored to energy dissipated

- Q is proportional to R, so need
large R for high Q

- The Q of the resonance is also affected
by the resistance of the inductor RL

- We represent RL as an equivalent parallel resistance R'L so R and R'L form a simple resistive voltage divider at resonance