1. Phasors, Impedance, SPICE, and Circuit Analysis
Phasor Analysis
Phasors, Impedance, SPICE, and Circuit Analysis
Kevin D. Donohue, University of Kentucky

2. Kevin D. Donohue, University of Kentucky
Impedance
The conversion of resistive, inductive, and capacitive elements to impedance for a sinusoidal excitation at frequency  is given by:
In general impedance is a complex quantity with a resistive component (real) and a reactive component (imaginary):
Kevin D. Donohue, University of Kentucky

3. Kevin D. Donohue, University of Kentucky
Phasors
Sources can be converted to phasor notation as follows:
This can be applied to all sources of the same frequency,
where  is used in the impedance conversion of the circuit.
If sources of different frequencies exist, superposition must
applied to solve for a given voltage or current:
1. Select sources with a common  and deactive all other sources.
2. Convert circuit elements to impedances.
3. Solve for desired voltage or current for selected .
4. Repeat steps 1 through 3 for new  until all sources have been applied.
5. Add together all time-domain solutions solutions obtain in Step 3.
Kevin D. Donohue, University of Kentucky

4. Kevin D. Donohue, University of Kentucky
Loop Analysis Example
Determine the steady-state response for vc(t) when vs(t) = 5cos(800t) V nF
6 kW
3 kW
vs(t)
+ vc(t) -
Show:
Kevin D. Donohue, University of Kentucky

5. Nodal Analysis Example
Find the steady-state value of vo(t) in the circuit below, if vs(t) = 20cos(4t):
10 
1 H ix + vo -
0.1 F vs
2 ix
0.5 H
Show: v0(t) = 13.91cos(4t º)
Kevin D. Donohue, University of Kentucky

6. Multiple Source Example
Find io if is = 3cos(10t) and vs = 6cos(20t + 60º) io
5  vs
0.01 F
0.5 H is
Show io = 0.54cos(20t+123.4º)+2.7cos(10t-153.4º)
Kevin D. Donohue, University of Kentucky

7. Equivalent Circuit Example
Find io steady-state using Norton’s Theorem, if vs(t) = 2sin(10t):
10  io vs
0.01 F
5 
.4 H
Show is(t)= .2sin(10t); Zth = 3-j = 3.2-18.4º;
io = 0.15cos(10t º)
Kevin D. Donohue, University of Kentucky

8. Equivalent Circuit Example
Find vo steady-state using Thévenin’s Theorem, if vs(t) = 20cos(4t):
10 
1 H ix + vo -
0.1 F vs
2 ix
0.5 H
Kevin D. Donohue, University of Kentucky