Adv tec 5 resonance
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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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Adv tec 5 resonance

ADV/TEC 5: Resonance

Introductory mini-lecture


Resonance in physical systems

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:


Parallel lcr circuit

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


Lcr circuit at resonance

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


Vector representation

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


Quality factor q of a resonant circuit

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


Quality factor q of a resonant circuit1

Quality factor Q of a resonant circuit


Non ideal inductor

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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