CIRCUITS and SYSTEMS part I Prof dr hab

CIRCUITS and SYSTEMS – part I Prof. dr hab. Stanisław Osowski Electrical Engineering (B. Sc. ) Projekt współfinansowany przez Unię Europejską w ramach Europejskiego Funduszu Społecznego. Publikacja dystrybuowana jest bezpłatnie

Lecture 6 Resonance phenomena

Definition Electrical resonance occurs in an electric RLC circuit at a particular frequency when in spite of RLC elements the phase shift between voltage and current at the input is zero (the reactive part of input impedance or admittance is zero). Series resonance occurs in series connection of RLC elements. Parallel resonance occurs in parallel connection of RLC elements.

Series resonance circuit Series resonance occurs when the imaginary part of Z, i. e. (Im(Z)=0 -> XL-Xc=0

Resonance frequency From ωL=1/(ωC) we get the resonance frequency

Phasor diagrams of circuit Before resonance At resonance frequency After resonance

Parameters of resonance • Quality factor • Characteristic resistance

Frequency characteristics of current • The current in the circuit • Frequency characteristics of current

Frequency characteristics of current

Voltages in RLC resonance circuit Frequency characteristics

Frequency characteristics of voltages

Current characteristics at different Q

Voltage characteristics at different Q

Parallel resonance circuit

Resonance equations Current-voltage relationship Resonance condition (Im(Y)=0)

Quality factor of parallel resonance circuit

Frequency characteristics of parallel circuit Frequency characteristics of voltage

Frequency characteristics of currents Frequency characteristics