7. ac analysis
DESCRIPTION
7. AC Analysis. CIRCUITS by Ulaby & Maharbiz. Overview. Linear Circuits at ac. Objective: To determine the steady state response of a linear circuit to ac signals. Sinusoidal input is common in electronic circuits - PowerPoint PPT PresentationTRANSCRIPT
7. AC ANALYSIS CIRCUITS by Ulaby & Maharbiz
Overview
Linear Circuits at acObjective: To determine the steady state response of a linear circuit to ac signals
Sinusoidal input is common in electronic circuits Any time-varying periodic signal can be represented by a
series of sinusoids (Fourier Series) Time-domain solution method can be cumbersome
Sinusoidal Signals tVtv cosm
f 2
fT 1
Useful relations
Phase Lead/Lag
Complex NumbersWe will find it is useful to represent sinusoids as complex numbers
jyxz jezzz
1j
Rectangular coordinatesPolar coordinates
sincos je j
Relations based on Euler’s Identity
yzxz
)Im(
Re
Relations for Complex Numbers
Learn how to perform these with your calculator/computer
Phasor Domain
1. The phasor-analysis technique transforms equationsfrom the time domain to the phasor domain.
2. Integro-differential equations get converted intolinear equations with no sinusoidal functions.
3. After solving for the desired variable--such as a particular voltage or current-- in the phasor domain, conversion back to the time domainprovides the same solution that would have been obtained had the original integro-differential equations been solved entirely in the time domain.
Phasor Domain
Phasor counterpart of
Time and Phasor Domain
It is much easier to deal with exponentials in the phasor domain than sinusoidal relations in the time domain.
You just need to track magnitude/phase, knowing that everything is at frequency .
Phasor Relation for Resistors
Time Domain Frequency Domain tRIiRv cosm
Current through a resistor
tIi cosm
Time domain
Phasor Domain
Phasor Relation for Inductors
Time Domain
Current through inductor in time domain
Time domain
Phasor Domain tIi cosm
Phasor Relation for Capacitors
Time Domain
Voltage across capacitor in time domain is
Time domain
Phasor Domain
tVv cosm dtdvCi
Summary of R, L, C
ac Phasor Analysis General Procedure
Using this procedure, we can apply our techniques from dc analysis
Example 1-4: RL Circuit
Cont.
Example 1-4: RL Circuit cont.
Impedance and Admittance
R = resistance = Re(Z)
Impedance is voltage/current
X = reactance = Im(Z)
Resistor
Inductor
Capacitor
RZ
LjZ
Cj/1Z
R/1Y
Lj/1Y
CjY
G = conductance = Re(Y)
Admittance is current/voltage
B = susceptance = Im(Y)
Impedance Transformation
Voltage & Current Division
Cont.
Example 7-6: Input Impedance (cont.)
Example 7-9: Thévenin Circuit
Linear Circuit PropertiesThévenin/Norton and Source Transformation Also Valid
Phasor Diagrams
Phase-Shift Circuits
Example 7-11: Cascaded Phase Shifter
Solution leads to:
Node 1 Cont.
(cont.)
Cont.
(cont.)
Example 7-14: Mesh Analysis by Inspection
Example 7-16: Thévenin Approach
Example 7-16: Thévenin Approach (Cont.)
Example 7-16: Thévenin Approach (Cont.)
Power Supply Circuit
Ideal Transformer
Half-Wave Rectifier
Full-Wave RectifierCurrent flow during first half of cycle
Current flow during second half of cycle
Smoothing RC Filter
Complete Power Supply
Example 7-20: Multisim Measurement of Phase Shift
Example 7-20 (cont.)
Using Transient Analysis
Summary