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:

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

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

9. Phasor Transformations:

10. Phasor Differentiation and Integration:

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

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

14. Consider Parallel RLC
Time domain
Phasor

15. In General:
Element Admittance
In General:

16. Network Reduction:

17. 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.

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