1. ECE 1270: Introduction to Electric Circuits
Lecture 19:
Kirchoff's Laws
(Revisited)
Chapter 9: Sinusoidal Steady-State Analysis
Section 9.5

2. Phasors
Phasor Transform or
Phasor Representation
1) A phasor is a complex number that represents the amplitude and phase of a sinusoid
2) Phasors provide a simple means of analyzing linear circuits excited by sinusoidal sources

3. Frequency Domain Representation for Inductor and Capacitor
1) A Capacitor will create -90 deg phase shift (waveform shifted by 90 deg to the right)
2) An Inductor will create +90 deg phase shift (waveform shifted 90 deg to the left)

4. Frequency Domain Representation for Inductor and Capacitor
Let's plot impedance of an Inductor and Capacitor
Use Matlab or Graphic Calculator or Multisim or LTSpice
What happens to the impedance of inductor and capacitor at low and high frequencies?

5. Example 9.6

6. AP 9.7
In Class
Plot in Matlab or Multisim
and look for imag(Zab)=0

7. Problem 9.22
Find Zab

8. Significance of Impedance
Impedance in a circuit: either inductor or capacitor or both
Impedance, Z is a complex number in frequency domain
magnitude (amplitude) & phase or real & imaginary
Magnitude gives us scaling factor between voltage and current
Phase tells us by how many degrees voltage will lead/lag current
Zero phase=zero imaginary part=no phase shift=resistive
Power
When current passes through resistor, power is always absorbed or lost
When current passes through impedance, power is not necessarily lost: it is simply delayed or stored
Power is resonated: it bounces back and forth without being absorbed number

9. Problem 9.24 (AC Sweep plot in Multisim)
(a) Find ω (angular frequency in rad/s) at which Zab is purely resistive
(b) Find the value of Zab at this frequency