Experiment # 3

EE 312 Basic Electronic Instrument LaboratorySeptember 13, 2000

See Lecture 5 Filters on 1999 EE 312/352 Websitewww.ee.buffalo.edu/~whalen/ee352

Objectives:• Design and assemble of Resistance-

Capacitance (RC) and Resistance-Inductance (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:

R

j

C

j L

Impedance

Rj

C

R

j LHigh-Pass RL Filter

Low Pass RL Filter

High-Pass RC Filter

Low-Pass RC Filter

High

Low

Low

High

time0

time

Vout(t)

Rj

C

0

Vin(t)

Example: Low-Pass RC Filter

0

A tV t

V t

out

in( )

( )

( ) ? & Phase shift ?

time0

time

Vout(t)

Rj

C

0

Vin(t)Low-Pass RC Filter

Calculation for a High Pass Filter(Steady State Response)

)1()(1

1

)(

)(

2

22

R

Xj

RX

jXRXR

R

jXR

jXR

jXR

R

jXR

R

V

V

C

C

C

C

C

C

C

Cin

out

R

-jXc

CfXC

2

1

X

R fCR

fRC

X

R

f

f

V

V f

f

jf

f

c

x

c x

out

in x

x

1

2

1

2

1

11

2

( )( )

but

Define crossover frequency, fx, as

Then

so

First, look at this factor

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

1 jf

f

x?

1 1

1

1

2 2

2

2

( ) cos ( ) sin

( ) (cos sin )

( )

f

fj

f

f

f

fj

f

fe

x x

x

x j

1

1 2 ( )f

f

x

f

f

x

tan f

f

x tan ( )1 f

f

xPhase shift

V

V f

f

f

fe

V

V f

f

e

out

in x

x j

out

in x

j

1

11

1

1

2

2

2

( )( )

( )

so:

or

Amplitude

Phase

V

V f

f

eout

in x

j

1

1 2( )

When f >> fx, Amplitude 1, 0

Thus, this is high pass

When f << fx, Amplitude 0, 90

Low frequencies are blocked

Step ResponseHigh-Pass Low-Pass

Vin

Vout Vout

Vin

Voltage on capacitor cannot change instantaneously. So Vout = Vin initially.

Voltage on capacitor cannot change instantaneously. So Vout = 0 initially.

Vin Vout Vin Vout

RC

Fall Time

Vout

time

1.00.9

0.1 10%

90%

100%

1/e~37%

et

RC

Fall Time & Time Constant ( )

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

RFunction Generator

oscilloscope

Filter ScopeOscillator

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/(2RC) is well within FG frequency range. E.G. fx ~ 3 kHz.

Comment:

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 high-pass RC filter using a square wave

• 6- Measure time constant and rise time in a low-pass RL filter using a square wave

1- Internal Impedance of Function Generator

Filter impedance >> Generator impedanceRload > 10 X Rinternal

Rinternal

RLoadFunction Generator

Step 2- Measure the decreased amplitude of the output signal and Ix with 100 ohms resistor

Rinternal

Function Generator

oscilloscope 1M

Step 1- Set Vp-p=10V

Step 3- Determine Rinternal

Rinternal

100Function Generator

oscilloscopeIx

2- Low-Pass RC Filter

~

CRO CH2CRO CH1

Assemble a low-pass RC filter having a Crossover frequency of about 3 kHz

fRC

x 1

2

R

C

~

CRO CH2CRO CH1

Vp-p=10V Vout

VoutFrequency..

fx..

a) b)

Use Digital CRO to readout directly phase difference between input and output

3- Low-Pass RL Filter

~

L=1 mH

R VoutVin

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

to oscilloscope

Vout

Vin R

C

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

R VoutVin

Measure the time constant and fall time.Use Digital CRO to readout directly fall time.Use Digital CRO Cursors to determine T = L/R