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ADV/TEC 5: Resonance

ADV/TEC 5: Resonance. Introductory mini-lecture. Resonance in physical systems. Mechanical: pendulum, Tacoma Narrows bridge Atomic transitions: frequency of photon matches the energy difference between two atomic levels

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ADV/TEC 5: Resonance

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  1. ADV/TEC 5: Resonance Introductory mini-lecture

  2. Resonance in physical systems • 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:

  3. Parallel LCR circuit • Impedance of the capacitor decreases with frequency, so |iC| increases with frequency • Impedance of the inductor increases with frequency, so |iL| decreases with frequency

  4. LCR circuit at resonance • 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

  5. Vector representation • At resonance the vectors iL and iC are equal in magnitude but differ by 180⁰ in phase • Input and output voltages are equal

  6. Quality factor Q of a resonant circuit • 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

  7. Quality factor Q of a resonant circuit

  8. Non-ideal inductor • 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

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