Kevin D. Donohue, University of Kentucky

1

Frequency Analysis with SPICE

Phasors, Impedance, Frequency Sweep, and SPICE

Kevin D. Donohue, University of Kentucky

2

Recall Loop Analysis Example

Determine the steady-state response for vc(t) when vs(t) = 5cos(800t) V

Result:

V 6

800cos8868.2)( 302.8868 j1.4434 - 2.5000 ˆ

ttvV cc

114.86 nF

6 k

3 k

vs(t)

+ vc(t) -

Kevin D. Donohue, University of Kentucky

3

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 increments2. Starting frequency3. Ending frequency4. 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 sinusoidal2. Check the “use AC” option3. Provide a magnitude and phase

Kevin D. Donohue, University of Kentucky

4

SPICE Example

Find the phasor for vc(t) for vs(t)= 5cos(2ft) V in the circuit below for f = 100, 200, 300, 400, 500, …..1000 Hz

V R2 6k

R1 3k

IVm

C114.86n

ex16-Small Signal AC-2-TableFREQ MAG(V(IVM)) PH_DEG(V(IVM))(Hz) (V) (deg)+100.000 +3.299 -8.213+200.000 +3.203 -16.102+300.000 +3.059 -23.413+400.000 +2.887 -30.000+500.000 +2.703 -35.817+600.000 +2.520 -40.893+700.000 +2.345 -45.295+800.000 +2.182 -49.107+900.000 +2.033 -52.411+1.000k +1.898 -55.285

Kevin D. Donohue, University of Kentucky

5

Plotting Frequency Sweep Results

Choices for AC (frequency sweep simulation) For frequency ranges that include several orders of

magnitude, a logarithmic or Decade (DEC) scale is more practical than a linear scale

The magnitude results can also be computed on a logarithmic scale referred to a decibels or dB defined as:

)(log20 10 MM dB

Kevin D. Donohue, University of Kentucky

6

Plot of Magnitude

Linear Magnitude, Linear Frequency

dB Magnitude, Log FrequencyLinear Magnitude, Log Frequency

dB Magnitude, Linear Frequency

MAG(V(IVM))

Frequency (Hz)Circuit1-Small Signal AC-5

+0.000e+000

+1.000

+2.000

+3.000

+1.000 +10.000 +100.000 +1.000k +10.000k

DB(V(IVM))

Frequency (Hz)Circuit1-Small Signal AC-6

-20.000

+0.000e+000

+1.000 +10.000 +100.000 +1.000k +10.000k

MAG(V(IVM))

Frequency (Hz)u14ex1.ckt-Small Signal AC-7

+0.000e+000

+1.000

+2.000

+3.000

+10.000k +20.000k +30.000k +40.000k +50.000k

DB(V(IVM))

Frequency (Hz)u14ex1.ckt-Small Signal AC-8

-20.000

+0.000e+000

+10.000k +20.000k +30.000k +40.000k +50.000k

Kevin D. Donohue, University of Kentucky

7

Plot of Phase

Linear Frequency, in Degrees

Log Frequency, in Degrees

PH_DEG(V(IVM))

Frequency (Hz)u14ex1.ckt-Small Signal AC-8

-50.000

+0.000e+000

+10.000k +20.000k +30.000k +40.000k +50.000k

PH_DEG(V(IVM))

Frequency (Hz)u14ex1.ckt-Small Signal AC-9

-50.000

+0.000e+000

+1.000 +10.000 +100.000 +1.000k +10.000k

Kevin D. Donohue, University of Kentucky

8

Recall Nodal Analysis Example

Find the steady-state value of vo(t) in the circuit below, if vs(t) = 20cos(4t):

vs

10

2 ix

1 H

0.5 H0.1 Fix

Show: v0(t) = 13.91cos(4t + 198.3º)

+vo

-

Kevin D. Donohue, University of Kentucky

9

SPICE Example

Find the phasor for vc(t) when vs(t)= 20cos(4t) V in the circuit below (note f = 2/ =0.6636)

FREQ MAG(I(VAM)) PH_DEG(I(VAM)) MAG(V(IVM)) PH_DEG(V(IVM))

(Hz)

+636.600m +7.589 +108.440 +13.912 -161.560

V0

R 10

L1

L0.5

C.1

FC

CC

S

vAm

IVm