1. 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

2. Lecture 6
Resonance phenomena

3. 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.

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

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

6. Phasor diagrams of circuit
At resonance frequency
After resonance
Before resonance

7. Parameters of resonance
Quality factor
Characteristic resistance

8. Frequency characteristics of current
The current in the circuit
Frequency characteristics of current

9. Frequency characteristics of current

10. Voltages in RLC resonance circuit
Frequency characteristics

11. Frequency characteristics of voltages

12. Current characteristics at different Q

13. Voltage characteristics at different Q

14. Parallel resonance circuit

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

16. Quality factor
Quality factor of parallel resonance circuit

17. Frequency characteristics of parallel circuit
Frequency characteristics of voltage

18. Frequency characteristics of currents