1. Chapter 9 Sinusoids and Phasors
4/28/2017
Chapter 9 Sinusoids and Phasors
Phasor Relationships for circuit Elements.
Impedance and Admittance.
Kirchoff’s Laws in the Frequency Domain.
Impedance Combinations.
Applications.
Huseyin Bilgekul EENG224 Circuit Theory II Department of Electrical and Electronic Engineering Eastern Mediterranean University

2. Phasor Relationships for Circuit Elements
After we know how to convert RLC components from time to phasor domain, we can transform a time domain circuit into a phasor/frequency domain circuit.
Hence, we can apply the KCL laws and other theorems to directly set up phasor equations involving our target variable(s) for solving.
Next we find the phasor or frequency domain equivalent of the element equations for RLC elements.

3. Phasor Relationships for Circuit Elements
Phasor voltage and current of a resistor are in phase
Time Domain Frequency Domain

4. Phasor Relationship for Resistor
Frequency Domain
Time Domain
Voltage and current of a resistor are in phase

5. Phasor Relationships for Inductor
Phasor current of an inductor LAGS the voltage by 90 degrees.
Time Domain Frequency Domain

6. Phasor Relationships for Inductor
Phasor current of an inductor LAGS the voltage by 90 degrees.
Frequency Domain
Time Domain

7. Phasor Relationships for Capacitor
Phasor current of a capacitor LEADS the voltage by 90 degrees.
Time Domain Frequency Domain

8. Phasor Relationships for Capacitor
Phasor current of a capacitor LEADS the voltage by 90 degrees.
Frequency Domain
Time Domain

9. Phasor Relationships for Circuit Elements

10. Phasor Relationships for Circuit Elements

11. Impedance and Admittance
The Impedance Z of a circuit is the ratio of phasor voltage V to the phasor current I.
The Admitance Y of a circuit is the reciprocal of impedance measured in Simens (S).
Impedances and Admitances of passive elements.

14. Impedance as a Function of Frequency
The Impedance Z of a circuit is a function of the frequency.
Inductor is SHORT CIRCUIT at DC and OPEN CIRCUIT at high frequencies. Capacitor is OPEN CIRCUIT at DC and SHORT CIRCUIT at high frequencies.

15. Impedance of Joint Elements
The Impedance Z represents the opposition of the circuit to the flow of sinusoidal current. Z I + V -
The Reactance is Inductive if X is positive and it is Capacitive if X is negative.

16. Impedance as a Function of Frequency
As the applied frequency increases, the resistance of a resistor remains constant, the reactance of an inductor increases linearly, and the reactance of a capacitor decreases nonlinearly.
Reactance of inductor versus frequency
Reactance of capacitor versus frequency

17. Z

18. Admittance of Joint Elements
The Admittance Y represents the admittance of the circuit to the flow of sinusoidal current. The admittance is measured in Siemens (s) + V - Y I

19. Application of KVL for Phasors
The Kirchoff”s Voltage Law (KVL) holds in the frequency domain. For series connected impedances:
The Voltage Division for two elements in series is:

20. Parallel Combination for Phasors
The Kirchoff”s Voltage Law (KVL) holds in the frequency domain. For series connected impedances:
The Current Division for two elements is:

21. Z3 Z1

23. Application of Current Division for Phasors

24. Application of Current Division for Phasors

25. Example

28. Z1