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- Chapter 9
- Sinusoidal Steady-State
Analysis
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- 9.1 Motivation
- 9.2 Sinusoids’ features
- 9.3 Phasors
- 9.4 Phasor relationships for circuit elements
- 9.5 Impedance and admittance
- 9.6 Kirchhoff’s laws in the frequency domain
- 9.7 Impedance combinations
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- A sinusoid is a signal that has the form of the sine or cosine function.
- A general expression for the sinusoid,
- where
- Vm = the amplitude of the sinusoid
- ω = the angular frequency
in radians/s
- Ф = the phase
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6
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- A phasor is a complex number that represents the amplitude and phase of
a sinusoid.
- It can be represented in one of the following three forms:
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9
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- Example 3
- Evaluate the following complex numbers:
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- Mathematic operation of complex number:
- Addition
- Subtraction
- Multiplication
- Division
- Reciprocal
- Square root
- Complex conjugate
- Euler’s identity
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- Transform a sinusoid to and from the time domain to the phasor domain:
- (time domain) (phasor domain)
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- Example 4
- Transform the following sinusoids to phasors:
- i = 6cos(50t – 40o) A
- v = –4sin(30t + 50o) V
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- Example 5:
- Transform the sinusoids
corresponding to phasors:
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- The differences between v(t) and V:
- v(t) is instantaneous or time-domain representation
V is the frequency or phasor-domain representation.
- v(t) is time dependent, V is not.
- v(t) is always real with no complex term, V is generally complex.
- Note: Phasor analysis applies only when frequency is constant; when it is applied to two or
more sinusoid signals only if they have the same frequency.
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- Example 6
- Use phasor approach, determine
the current i(t) in a circuit described by the integro-differential
equation.
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- In-class exercise for Unit 6a, we can derive the differential equations
for the following circuit in order to solve for vo(t) in
phase domain Vo.
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Notes