Transcript No Slide Title

Experiment # 3
EE 312 Basic Electronic Instrument Laboratory
September 13, 2000
See Lecture 5 Filters on 1999 EE 312/352 Website
www.ee.buffalo.edu/~whalen/ee352
Objectives:
• Design and assemble of ResistanceCapacitance (RC) and ResistanceInductance (RL) filters.
• Measure the frequency response
(magnitude & phase) of RC and RL filters.
• Examine the time-domain responses of
these filters to a square-wave voltage .
Background:
Impedance
R
j

C
j L
High-Pass RC Filter
R
Low-Pass RC Filter
j

C
High
Low
Low Pass RL Filter
High-Pass RL Filter
R
Low
jL
High
Example: Low-Pass RC Filter
Vin(t)
Vout(t)
R

0
j
C
time
0
0
time
Low-Pass RC Filter
Vin(t)
Vout(t)
R

0
j
C
time
Vout (t )
A(t ) 
Vin(t )
0
?
&
time
Phase shift
?
Calculation for a High Pass Filter
(Steady State Response)
1
XC 
2   f  C
Vout
R

Vin
R  jX C


R  jX C
R
(
)
R  jX C
R  jX C
R2
R
( R  jXC )
2
 XC
1
XC

(1  j
)
XC 2
R
1 (
)
R
R
-jXc
but
Xc
1

R 2fCR
Define crossover frequency, fx, as
1
fx 
2RC
Then
fx, roughly speaking, is the
frequency that separate the
frequency range for which a
filter passes signals from the
range for which the filter
attenuates signals
Xc fx

R
f
so
Vout
1
fx

 (1  j )
Vin 1  ( fx )2
f
f
First, look at this factor
fx
1 j  ?
f
fx 2
fx 2
 1  ( ) cos   j 1  ( ) sin 
f
f
fx 2
 1  ( ) (cos   j sin )
f
fx 2
j
 1 ( )  e
f
fx
f

1
fx
tan  
f
Phase shift
fx
  tan ( )
f
1
fx 2
1 ( )
f
so:
or
Vout
1
fx 2 j

 1 ( ) e
Vin 1  ( fx )2
f
f
Vout
1
j

e
fx 2
Vin
1 ( )
f
Amplitude
Phase
Vout

Vin
When f >> fx, Amplitude
1
e j
fx 2
1 ( )
f
1, 
0
Thus, this is high pass
When f << fx, Amplitude
0,

90
Low frequencies are blocked
Step Response
Low-Pass
High-Pass
Vin
Vin
Vout
Vin
Vin
Vout
Vout
Voltage on capacitor cannot
change instantaneously. So
Vout = Vin initially.
Vout
Voltage on capacitor cannot
change instantaneously. So Vout
= 0 initially.
Fall Time & Time Constant
( )
Vout
1.0
0.9
100%
90%
1/e~37%
0.1

e
t
RC
  RC
10%
time
Fall Time
Relationship Between Time Constant T & Rise-Time or Fall-Time
T = RC or L/R
Rise-Time (Fall-Time) = T X ln9 = 2.2T
Components:
• Resistor Substitution Box
• Capacitor Substitution Box
• 1 mH Inductor
• 100 Ohms Resistor
Comment:
Function
Generator
Oscillator
R
Filter
oscilloscope
Scope
FG has 50 ohm internal resistance- keep R high enough so that
crossover freq. has no more than a 10% dependence upon it. e. g. R >
500 ohm
CRO has 1 M input impedance - keep R low enough so that crossover
freq has no more than a 10% dependence upon it. R < 100k
Choose C so that crossover frequency fx = 1/(2RC) is well within
FG frequency range. E.G. fx ~ 3 kHz.
Procedures:
• 1- Determine internal impedance of the function
generator which is expected to be ~50 ohms
• 2- Measure low-pass RC filters characteristics
• 3- Measure low-pass RL filters characteristics
• 4- Simulate RC & RL low-pass filters (Bell 242)
• 5-Measure time constant and fall time in a highpass RC filter using a square wave
• 6- Measure time constant and rise time in a lowpass RL filter using a square wave
1- Internal Impedance of Function Generator
Rinternal
Function
Generator
RLoad
Filter impedance >> Generator impedance
Rload > 10 X Rinternal
Step 1- Set Vp-p=10V
Rinternal
Function
Generator
oscilloscope
1M
Step 2- Measure the decreased amplitude of
the output signal and Ix with 100 ohms
resistor
Rinternal
Function
Generator
Step 3- Determine Rinternal
100
Ix
oscilloscope
2- Low-Pass RC Filter
CRO CH1
CRO CH2
R
C
~
Assemble a low-pass RC filter having a Crossover
frequency of about 3 kHz
1
fx 
2RC
CRO CH1
CRO CH2
~
Vout
Vp-p=10V
a)
Frequency Vout
.
.
fx
.
.
b)
Use Digital CRO to
readout directly phase
difference between input
and output
3- Low-Pass RL Filter
L=1 mH
Vin ~
R
Vout
Repeat the procedure in step 2 for
an appropriate crossover frequency
in the range 100 kHz to 150 kHz.
4- Simulation
(PSpice)
• Simulate the RC and RL low-pass filters
in parts 2 and 3. Do so in Bell 242.
• Perform an ac sweep between frequencies
of 1Hz and 1 MHz (or from fx/100 to 100
fx) with 20 to 50 data points per decade.
• Display experimental and PSPICE values
for the magnitude (dB) and phase of the
output voltage on the same graph.
5- Time Constant and Fall Time in a High-Pass RC Filter
C
Vout
Vin
R
to oscilloscope
Measure the time constant and fall time.
Use Digital CRO to readout directly fall time.
Use Digital CRO Cursors to determine T =
RC
6- Time Constant & Rise Time in a Low-Pass RL Filter
L=1 mH
Vin
R
Vout
Measure the time constant and fall time.
Use Digital CRO to readout directly fall time.
Use Digital CRO Cursors to determine T = L/R