Chapter 9 – Sinusoids and Phasors

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Presentation transcript:

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!

Sum of Sine and Cosine:

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

Algebra of Complex Numbers:

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

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

Phasor Transformations:

Phasor Differentiation and Integration:

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

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

Consider Parallel RLC Time domain Phasor

In General: Element Admittance In General:

Network Reduction:

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.

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