ELECTRIC CIRCUITS
ECSE-2010
Spring 2003
Class 36
ASSIGNMENTS DUE
•
Today (Thursday):
•
•
•
Will do Experiment # 9 in Class (EP-9)
Whole Class is Experiment #9 – Lissajous
Figures
Next Monday:
•
•
•
•
Homework #13 Due
Will do Experiment #10 in Class (EP-10)
Activity 37-1 (In Class)
Next Tuesday/Wednesday:
•
•
Will do Computer Project #5 in Class (CP-5)
Activities 38-1, 38-2 (In Class)
REVIEW
• Bode Plots:
Factor H(s) into Known Functions
H(s)  K H1 (s) x H 2 (s) x H 3 (s) x ....
Define g( )  20 log10a( );
g  db gain
Define g K  K db  20 log10 K ;
K  / K
g( )  g K  g1  g 2  g 3  ....
 ( )   K  1   2   3  ....
Graphically Add Known Bode Plots
REVIEW
• Known Functions:
N
s
H rN (s; W)  N ; Ramp
W
N
W
H lpN (s; W) 
; Low Pass
N
(s  W)
N
s
N
H hp
(s; W) 
; High Pass
N
(s  W)
H q (s;  0 ,Q) 
0
2
s  (  0 Q) s   0
2
2
; Quadratic
FREQUENCY RESPONSE
 Plots of a( ) and  ( ) vs. 
 Method of s-plane vectors - Small n
 Maple - Large n
 Plots of g  20 log10 [a( )] and  ( ) vs. log10 
 Bode Plots
 Semi-log Graph Paper
 Now Wish to Develop an Experimental Technique
 Lissajous Figures
LISSAJOUS FIGURES
• Experimental Technique for Determining
Amplitude Ratio a( ) and Phase Shift
 ( ) of Sinusoids
• Use Scopes in “X-Y” Mode
• Drive x axis of Scope with x(t)
• Drive y axis of Scope with y(t)
LISSAJOUS FIGURES
Let x(t)  X m cos ( t  x )
y(t)  Ym cos ( t  y )
Ym
Want to measure: a( ) 
Xm
 ( )   y   x
LISSAJOUS FIGURES
y
X m  Ym ; a  1
x   y    0
Slope  1
yx
x
LISSAJOUS FIGURES
y
x
X m  Ym ; a  1
x  y    180
Slope  1
y  x
0
LISSAJOUS FIGURES
If: X m  Ym and x  y :
What would you see on scope in X-Y mode?
 Straight Line, Slope  1
(y  x)
If: X m  Ym and y  x  180 :
o
What would you see on scope in X-Y mode?
 Straight Line, Slope  1 (y  x)
LISSAJOUS FIGURES
y
Ym  Xm
Circle
Xm  Ym
Xm  Ym ; a  1
x  y    90
0
x
LISSAJOUS FIGURES
If X m  Ym and y  x    90
o
What would you see?
 Circle!
If X m  Ym and  90o    90o
What would you see?
 Ellipse in 1st and 3rd Quadrants!
LISSAJOUS FIGURES
If X m  Ym and  90o    270o
What would you see?
 Ellipse in 2nd and 4th Quadrants!
LISSAJOUS FIGURES
See Notes on Lissajous Figures
y(t)  Ym cos( t  y ); y max  Ym , y min  Ym
 Peak to Peak Vertical Excursion  2Ym  A
 Can Measure A from Scope
x(t)  X m cos( t  x ); x max  X m , x min  X m
 Peak to Peak Horizontal Excursion  2X m  C
 Can Measure C from Scope
LISSAJOUS FIGURES
x  0 when  t 0  x  900 ;  t 0  900  x
y when x  0  Ym cos( t 0  y )
 Ym cos(  900  x  y )
 Ym cos(  900 )
  Ymsin
 B  2Ym sin  A sin
 Can Measure B on Scope
LISSAJOUS FIGURES
Ym A
a( )  Amplitude Ratio  H(j ) 

Xm C
 ( )  Phase Shift  y  x  /H(j )
B
  sin
;
A
1
 90o    90o
B
 180  sin
;  90o    270o
A
o
1
LISSAJOUS FIGURES
 Drive x-axis with Input; y-axis with Output
 Make Measurements of A,B,C from
Lissajous Figures at several values of frequency
 Calculate a( ) and  ( ) at each frequency
 Sketch a( ) and  ( ) vs 
 Experiment #9a
EXPERIMENT 9
 Part a); Phase Shift Network
 v b has a different Amplitude
and different Phase than v a
 Measure the amplitude ratio and phase shift
by observing the Lissajous figures
EXPERIMENT 9a


VA
VB


EXPERIMENT 9b
.47  F
VB
C
C
C
R
Vout
VA
R
R
RF
Phase Shift Oscillator
Use 100k Pot
EXPERIMENT 9
 Part b); Phase Shift Oscillator
 Add Op Amp
 Circuit will oscillate with NO input if V out  V a
 Op Amp has Phase Shift of  1800
 At some frequency, the Phase Shift of the
Phase Shift Network will also be  1800  f osc
741 LAYOUT
VDC
Used for Offsets
vp
v out
vn
Note Pin Layout
VDC
OP AMP PIN LAYOUT
VDC v out
8 7 6 5
Note Indentation
For 741
1
2
vn
3
4
v p VDC