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# ADV/TEC 5: Resonance - PowerPoint PPT Presentation

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

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