1. Chapter 9 – Sinusoids and Phasors
Sinusoid – a cosine or sine function
Vm = amplitude
ω = angular frequency = 2πf = 2π/T
Φ = phase angle  usually in degrees!

2. Sum of Sine and Cosine:

3. Phasor
A complex number representing the amplitude and phase angle of a sinusoid.
Complex Number Representation:
Rectangular
Polar
Exponential

4. Algebra of Complex Numbers:

6. Summary:
Addition or Subtraction: Rectangular
Multiplication, Division, Exponents and Roots: Polar or Exponential

7. How is a phasor related to a sinusoid?
Recall:
where:

8. Phasor Transformations:

9. Phasor Differentiation and Integration:

10. Example 1. Using the phasor approach find the solution to the integro-differential equation:

11. Complex Impedance
Element Impedance – ratio of phasor voltage to phasor current

12. Consider Parallel RLC
Time domain
Phasor

13. In General:
Element Admittance
In General:

14. Network Reduction:

15. Procedure:
Transform sinusoidal time functions to phasors, and convert element to complex impedance/admittance.
Apply network reduction, or other circuit principles (KVL, KCL, nodal, mesh, etc.) to determine desired response in phasor form.
Transform results to time functions.

16. Example2. Find:
vo(t)
Current in resistor.