Frequency Analysis with SPICE
Phasors, Impedance, Frequency
Sweep, and SPICE
Kevin D. Donohue, University of Kentucky
1
Recall Loop Analysis Example
Determine the steady-state response for vc(t) when vs(t) =
5cos(800πt) V
+ vc(t) 3 kΩ
vs(t)
114.86 nF
6 kΩ
Result:
π

Vˆc = 2.5000 - j1.4434 = 2.8868∠ − 30o ⇔ vc (t ) = 2.8868 cos 800πt −  V
6

Kevin D. Donohue, University of Kentucky
2
SPICE Solution
Steady-State Analysis in SPICE is performed using the .AC
(frequency sweep) option in the simulation set up. It will
perform the analysis for a range of frequencies.
You must indicate the:
1. Scale for uniform frequency increments
2. Starting frequency
3. Ending frequency
4. Number of frequencies used in the given range.
Sources in the AC analysis must be set up in “edit simulation
model” menu to:
1. Identify source as sinusoidal
2. Check the “use AC” option
3. Provide a magnitude and phase
Kevin D. Donohue, University of Kentucky
3
SPICE Example
Find the phasor for vc(t) for vs(t)= 5cos(2πft) V in the circuit
below for f = 100, 200, 300, 400, 500, …..1000 Hz
IVm
C
114.86n
R1
3k
V
R2
6k
ex16-Small Signal AC-2-Table
FREQ
MAG(V(IVM))
(Hz)
(V)
+100.000 +3.299
+200.000 +3.203
+300.000 +3.059
+400.000 +2.887
+500.000 +2.703
+600.000 +2.520
+700.000 +2.345
+800.000 +2.182
+900.000 +2.033
+1.000k
+1.898
Kevin D. Donohue, University of Kentucky
PH_DEG(V(IVM))
(deg)
-8.213
-16.102
-23.413
-30.000
-35.817
-40.893
-45.295
-49.107
-52.411
-55.285
4
Plotting Frequency Sweep Results
Choices for AC (frequency sweep simulation)
¾ For frequency ranges that include several orders of
magnitude, a logarithmic or Decade (DEC) scale is more
practical than a linear scale
¾
The magnitude results can also be computed on a
logarithmic scale referred to a decibels or dB defined as:
M dB = 20 log10 ( M )
Kevin D. Donohue, University of Kentucky
5
Plot of Magnitude
Linear Magnitude, Log Frequency
Circuit1-Small Signal AC-5
+1.000
+10.000
+100.000
dB Magnitude, Log Frequency
Frequency (Hz)
+1.000k
Circuit1-Small Signal AC-6
+10.000k
+1.000
+10.000
+100.000
Frequency (Hz)
+1.000k
+10.000k
+3.000
+0.000e+000
+2.000
+1.000
-20.000
+0.000e+000
MAG(V(IVM))
DB(V(IVM))
Linear Magnitude, Linear Frequency
u14ex1.ckt-Small Signal AC-7
+10.000k
+20.000k
+30.000k
dB Magnitude, Linear Frequency
u14ex1.ckt-Small Signal AC-8
Frequency (Hz)
+40.000k
+10.000k
+50.000
+20.000k
+30.000k
Frequency (Hz)
+40.000k
+50.000
+3.000
+0.000e+000
+2.000
+1.000
-20.000
+0.000e+000
MAG(V(IVM))
DB(V(IVM))
Kevin D. Donohue, University of Kentucky
6
Plot of Phase
Linear Frequency, in Degrees
u14ex1.ckt-Small Signal AC-8
+10.000k
+20.000k
+30.000k
Frequency (Hz)
+40.000k
+50.000
+0.000e+000
-50.000
PH_DEG(V(IVM))
Log Frequency, in Degrees
u14ex1.ckt-Small Signal AC-9
+1.000
+10.000
+100.000
Frequency (Hz)
+1.000k
+10.000k
+0.000e+000
-50.000
PH_DEG(V(IVM))
Kevin D. Donohue, University of Kentucky
7
Recall Nodal Analysis Example
Find the steady-state value of vo(t) in the
circuit below, if vs(t) = 20cos(4t):
10 Ω
vs
0.1 F
ix
1H
2 ix
+
vo
0.5 H
-
Show: v0(t) = 13.91cos(4t + 198.3º)
Kevin D. Donohue, University of Kentucky
8
SPICE Example
Find the phasor for vc(t) when vs(t)= 20cos(4t) V in
the circuit below (note f = 2/π =0.6366)
R
10
L
1
vAm
L0
.5
FCCCS
V
0
IVm
C
.1
FREQ
MAG(I(VAM))
PH_DEG(I(VAM))
MAG(V(IVM))
PH_DEG(V(IVM))
+108.440
+13.912
-161.560
(Hz)
+636.600m +7.589
Kevin D. Donohue, University of Kentucky
9