ece experiment

7/25/2019 ECE Experiment

1/13

Copyright 2014 GWU SEAS ECE Department ECE 2110: Circuit Theory

1

SCHOOL OF ENGINEERING AND APPLIED SCIENCEDEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

ECE2110:CIRCUIT THEORY LABORATORY

Experiment #11:Final Project Preparation Lab 1 Active Filter Design

EQUIPMENT

Lab Equipment Equipment Description

(1) DC Power Supply Agilent E3631A Triple Output DC Power Supply

(1) Function Generator Agilent 33522A Function/Arbitrary Waveform Generator

(1) Digital Multimeter (DMM) Keithley Model 175 Digital Multimeter (DMM)

(1) Digital Oscilloscope Agilent DSO1024A Digital Oscilloscope

(1) Breadboard Prototype Breadboard

(1) BNC T-Connector One input to two output BNC connector

(1) Test Leads Banana to Alligator Lead Set(2) Test Leads BNC to Mini-Grabber Lead Set

(1) BNC Cable BNC to BNC Cable

Table 1 Equipment List

COMPONENTS

Type Value Symbol Name Multis im Part Descripti on

Resistor --- R Basic/Resistor Various Values

Capacitor --- F C Basic/Capacitor Various Values

Op-Amp LM741 LM741 Basic/Analog/OpAmp/741 ---

Power Amp LM386 LM386 --- Audio AmplifierSpeaker 6 --- --- 18W Speaker

Table 2 Component List

OBJECTIVES

Understand the difference between active and passive filters

Design and build a band-pass filter using active components

Understand the limitations of the LM741

Understand what an LM386 is and why it is necessary

Build and measure a band-pass filter using LM741s and an LM386

Note: At this point, the final project should be introduced by the GTA. Ideally, an introduction to theproject will be given at the end of the last lab to prepare students for this prelab and lab. Students, pleasefind the final project specifications document on the ECE 2110 lab website under the Projects section..
http://www.seas.gwu.edu/~ece11/spec_sheets/equipment/powersupply_agilent_E3631A.pdfhttp://www.seas.gwu.edu/~ece11/spec_sheets/equipment/Agilent_33522A.pdfhttp://www.seas.gwu.edu/~ece11/spec_sheets/equipment/multimeter_keithley_175.pdfhttp://www.seas.gwu.edu/~ece11/spec_sheets/equipment/oscope_agilent_dso1024a.pdfhttp://www.seas.gwu.edu/~ece11/spec_sheets/equipment/oscope_agilent_dso1024a.pdfhttp://www.seas.gwu.edu/~ece11/spec_sheets/equipment/multimeter_keithley_175.pdfhttp://www.seas.gwu.edu/~ece11/spec_sheets/equipment/Agilent_33522A.pdfhttp://www.seas.gwu.edu/~ece11/spec_sheets/equipment/powersupply_agilent_E3631A.pdf


2/13

Experiment #11: Final Project Preparation Lab 1 Active Filter Design


2

SEAS

INTRODUCTION

This lab will introduce you to the concept of active filters and explain how they differ from passive filtersand why they are necessary. In Lab 10, you were introduced to passive filters. Passive filters consist ofonly passive components (inductors, capacitors, resistors). Because passive components cannot provideaverage power to a circuit, you cannot make a filter with a gain greater than 1 using only passive

components. In many situations, you may wish to create a filter with a gain greater than 1. For this, youmust incorporate an op-amp into the filter design.

Active 1st

Order Low-Pass Filter

Figure 1 Inverting Amplifier Figure 2 Active 1st Order Low-Pass Filter

Figure 1shows an inverting amplifier. From the lab on DC Operational Amplifiers, we know the gain ofthis amplifier is Vout/Vin= -Rf/Rin. Instead of using just resistors, we can substitute impedances Zfand Zin,and the gain becomes Vout/Vin= -Zf/Zin.

Figure 2shows the same amplifier, now with a capacitor inserted in the feedback path. Zinis still Rin, butZf is the impedance of the resistor and capacitor in parallel, so Zf = ZRf || ZCL: Substituting in theimpedances as shown in Figure 2:

1 / 1/ 1Typically, for filters, the transfer function of interest is the voltage gain, defined as T() = Vout/Vin. Sincethe voltage gain of the amplifier in Figure 2is Vout/Vin= -Zf/Zin, the transfer function for the filter becomes:

1

1What should be familiar is the expression in parentheses in the equation above, it is the transfer functionfor a low-pass filter. The expression outside of the brackets: -Rf/Rin, means this low-pass filter has gain!

The cutoff frequencyfor this low-pass filteris:

1Note: To design this filter, one chooses the appropriate resistors: Rf and Rin to set the gain, thendetermines CLfor the desired cutoff frequency (C).

inR

fR

V

Vin

out

inR

fR

V

Vin

out

LC


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3

SEAS

Active 1st

Order High-Pass Filter

Figure 3 Inverting Amplifier Figure 4 Active 1stOrder High-Pass Filter

Figure 4 shows how we can make the inverting amplifier into a high-pass filter by rearranging thecapacitor to be in series with the input resistor. The transfer function then becomes:

1/When the frequency is low (e.g. 0), the transfer function approaches 0. As the frequency getshigher and higher (e.g ), the transfer function becomes -Rf/Rin. This is the behavior of a high-passfilter. The cutoff frequencyfor this filter can be derived as:

1

inR

fR

V

Vin

out

inR

fR

V

Vin

out

HC


4/13

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5/13



5

SEAS

PRELAB

Part I Acti ve Band-Pass Filter Design

Figure P.1 Active Band-Pass Filter with Gain Stage

1. Using the procedure discussed in the Introduction, designan active band-pass filterwith again of -10, a lower cut-off frequency of 150Hzand an upper cutoff frequency of 5kHz. Be sureto show all work and mention any relevant assumptions or design decisions.

Note:When choosing resistor values to set the gain for each stage, be certain to keep them verylarge in the high krange.

1= 150Hz

2= 5kHz

Gain = -10

2. Save this design as you will need to simulate it later in this prelab.

in1R

f1R

Vin

LC

in2R

f2R

HC

in3R

f3R

Vout

+

-

+

-

Stage 1:Low-Pass Filter

Stage 2:High-Pass Filter

Stage 3:Inverter Gain Stage


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6

SEAS

Part II Active Low-Pass Filter Simulation

Figure P.2 Active 1stOrder Low-Pass Filter

1. Simulate the active low-pass filter section of the band-pass filter in Multisim using the LM741.

DC Supply Voltage (VCC+and VCC-): 12V

Vin: 300mVrmssine wave

Load: 1k

2. Run an AC Analysis from 10Hzto 6kHz. MeasureVout(in RMS voltage) across the 1kload atthe following frequencies: 10Hz, 150Hz, 1kHz, 4kHz, 5kHz, 6kHz

3. Usingthe peak output voltage of Vout, calculatethe peak power dissipatedby the 1kloadresistor at each frequency.

4. Calculatethe current drawn by the 1kload resistor at the peak output power in each case.

5. Recordthese values in Table P.2.

6. Plotthe magnitudeand phaseof Vout/Vin(in dB) versus frequency from 10Hz to 6kHz.

7. Determinethe -3dB frequencyfrom this plot.

Frequency Vin(rms) Vout (rms) Gain (Vout /Vin) Pout (peak) Iout (peak)

10Hz

150Hz

1kHz

4kHz

5kHz

6kHz

-3dB Freq.

Simulated

Table P.2 Low-Pass Filter Simulation Data

inR

fR

V

Vin

out

LC

300m 299.9961m .9999987 44.9988mu 299.9961mu

300m 299.8591m .99953 44.9577mu 299.8591mu

300m 294.0536m .98017 43.234mu 294.0536mu

300m 233.3358m .777795 27.2228mu 233.3358mu

300m 211.0610m .70354 22.2734mu 211.0610mu

300m 190.9126m .6365 18.224mu 190.9126mu

2.7924kHz


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7

SEAS

Part III Active High-Pass Filter Simulation

Figure P.3 Active 1stOrder High-Pass Filter

1. Simulate the active high-pass filter section of the band-pass filter in Multisim using the LM741.



Load: 1k


3. Usingthe peak output voltage of Vout, calculatethe peak power dissipatedby the 1kload

resistor at each frequency.4. Calculatethe current drawn by the 1kload resistor at the peak output power in each case.


6. Plotthe magnitudeand phaseof Vout/Vin(in dB) versus frequency from 10Hz to 6kHz.

7. Determinethe -3dB frequencyfrom this plot.


10Hz

150Hz

1kHz

4kHz

5kHz

6kHz

-3dB Freq.

Simulated

Table P.3 High-Pass Filter Simulation Data

inR

fR

V

Vin

out

HC

300m 20.0485m .06683 200.973n 20.0485mu

300m 212.6401m .70880 22.6097mu 212.6401mu

300m 296.7496m .98916 44.0302mu 296.7496mu

300m 299.8064m .99935 44.9479mu 299.8064mu

300m 299.8668m .999556 44.96mu 299.8668mu

300m 299.8896m .999632 44.9669mu 299.8896mu

264.5417Hz


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8

SEAS

Part IV Active Band-Pass Filter Simulation

Figure P.4 Active Band-Pass Filter with Gain Stage

1. Simulate the cascaded active band-pass filter, including the inverter gain stage, in Multisimusing the LM741.



Load: 1k





6. Plotthe magnitudeand phaseof Vout/Vin(in dB) versus frequency from 10Hz to 6kHz.7. Determineboth the lower and upper -3dB frequenciesfrom this plot.


10Hz

150Hz

1kHz

4kHz

5kHz

6kHz

Lower -3dB Upper -3dB

SimulatedTable P.4 Band-Pass Filter Simulation Data

in1R

f1R

Vin

LC

in2R

f2R

HC

in3R

f3R

Vout

+

-

+

-




300m 200.4703m .668 20.0942mu 200.4703mu

300m 2.1307 7.102 2.2584m 2.1307m

300m 2.9084 9.695 4.2293m 2.9084m

300m 2.3294 7.765 2.7131m 2.3294m

300m 2.1063 7.021 2.2181m 2.1063m

300m 1.9040 6.347 1.8126m 1.9040m

66.5 440000


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9

SEAS

LAB

Part I Active Low-Pass Filter

Figure 1.1 Active 1stOrder Low-Pass Filter

1. Buildthe active low-pass filter section on a breadboard. Show the GTA your setup beforeapplying power.

DC Supply Voltage (VCC+and VCC-): 12V Vin: 300mVrmssine wave

Load: 1k

2. MeasureVoutusing the DMM (RMS voltage) across the 1kload at the following frequencies:10Hz, 150Hz, 1kHz, 4kHz, 5kHz, 6kHz



5. Recordthese values in Table 1.1.

6. Adjustthe frequencyof the function generator until you find the exact -3dB frequencyof the

filter, where max.Frequency Vin(rms) Vout (rms) Gain (Vout /Vin) Pout (peak) Iout (peak)

Sim. Meas. Sim. Meas. Sim. Meas. Sim. Meas. Sim. Meas.

10Hz

150Hz

1kHz

4kHz

5kHz

6kHz

-3dB Freq.

Simulated

Measured

Error

Table 1.1 Low-Pass Filter Output Characteristics with 1kLoad

inR

fR

V

Vin

out

LC

300mV 255mV 299.9961mV 247mV .9999987 44.9988W 299.9961A 247A

300mV 319mV 299.8591mV 312mV .99953 44.9577W 299.8591A

300mV 279mV 294.0536mV 267mV .98017 43.234W 294.0536A

300mV 292mV 233.3358mV 234mV .777795 27.2228W 233.3358A

300mV 298mV 211.0610mV 215mV .70354 22.2734W 211.0610A

300mV 302mV 190.9126mV 196mV .6365 18.224W 190.9126A

5.1835kHz

~5kHz


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10

SEAS

Part II Active High-Pass Filter

Figure 2.1 Active 1stOrder High-Pass Filter

1. Buildthe active high-pass filter section on a breadboard. Show the GTA your setup beforeapplying power.



Load: 1k





6. Adjustthe frequencyof the function generator until you find the exact -3dB frequencyof the

filter, where max.Frequency Vin(rms) Vout (rms) Gain (Vout /Vin) Pout (peak) Iout (peak)


10Hz

150Hz

1kHz

4kHz

5kHz

6kHz

-3dB Freq.

Simulated

Measured

Error

Table 2.1 High-Pass Filter Output Characteristics with 1kLoad

inR

fR

V

Vin

out

HC

300mV 267mV 20.0485mV 11.3mV .06683 200.973nW 20.0485A

300mV 315mV 212.6401mV 228mV .70880 22.6097W 212.6401A

300mV 282mV 296.7496mV 279mV .98916 44.0302W 296.7496A

300mV 307mV 299.8064mV 304mV .99935 44.9479W 299.8064A

300mV 302mV 299.8668mV 300mV .999556 44.96W 299.8668A

300mV 300mV 299.8896mV 297mV .999632 44.9669W 299.8896A

264.5417Hz

160.57Hz


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11

SEAS

Part III Active Band-Pass Filter

Figure 3.1 Active Band-Pass Filter with Gain Stage

7. Buildthe active low-pass filter section on a breadboard. Show the GTA your setup beforeapplying power.



Load: 1k





12. Adjustthe frequencyof the function generator until you find the exact -3dB frequencies (upperand lower) of the filter, where max.



10Hz

150Hz

1kHz

4kHz

5kHz

6kHz


Simulated

Measured

Error

Table 3.1 Band-Pass Filter Output Characteristics with 1kLoad

in1R

f1R

in

LC

in2R

f2R

HC

in3R

f3R

Vout

+

-




298mV 288mV

315mV 2.07V

293mV 3V

293mV 2.5V

300mV 2.33V

303mV


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12

SEAS

Part IV Active Band-Pass Filter wi th Small Load

1. For the band-pass filter you have simulated and measured, calculatethe amount of current a 6load would draw at the highest valueof Voutyou recorded in Table 3.1.

a. Whatis the value in mA? Include this in your lab write-upb. Canthe LM741 op-amp provide this much current to a 6load?

i. Downloadthe LM741 specification sheet from the lab website.

ii. Lookfor the electrical parameter: Output Short Circuit Currentiii. Isthis value moreor lessthan the amount of current a 6load would draw?

c. Replacethe 1kload in your Multisimsimulation with a6load.i. Run an AC Analysis from 10Hzto 6kHz. MeasureVout(in RMS voltage) across

the 6load at the following frequencies: 10Hz, 150Hz, 1kHz, 4kHz, 5kHz, 6kHzii. Whatdo you notice about your results?

2. From Step 1 you should realize that the LM741 cannot supporta small loadlike 6.a. We need an amplifierfor the 3

rdstage of our band-pass filter that can provide enough

current to our 6load.b. For this, we will replace Stage 3 of our amplifier with a power amplifier called the LM386.

i. The LM386 is not an op-amp. It is a self-contained amplifier that can provide agreat deal of current to small loads.

ii. Downloadthe LM386 specification sheet from the lab website.

3. On page 5 of the LM386 specification sheet a sample configuration is shown.a. Replacethe 3

rdstageof your amplifier with this sample configuration.

b. Instead of a 6load, use the speakerprovided in your kit.

4. MeasureVoutusing the DMM (RMS voltage) across the speaker at the following frequencies:10Hz, 150Hz, 1kHz, 4kHz, 5kHz, 6kHz

5. Usingthe peak output voltage of Vout, calculatethe peak power dissipatedby the speaker ateach frequency.

6. Calculatethe current drawn by the speaker at the peak output power in each case.


8. Adjustthe frequencyof the function generator until you find the exact -3dB frequencies(upper

and lower) of the filter, where max.Frequency Vin(rms) Vout (rms) Gain (Vout /Vin) Pout (peak) Iout (peak)


10Hz

150Hz

1kHz

4kHz

5kHz

6kHz


Simulated

Measured

Error

Table 4.1 Band-Pass Filter Output Characteristics with 6Load


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13

SEAS

POST-LAB ANALYSIS

Be certain to include:1. Your calculationsfor how you designed the band-pass filter.

2. The Multisimschematicfor the band-pass filter.

3. The Multisimoutputshowing Vout/Vin(in dB) versus frequency for the low-pass filter, high-pass

filter, and finally the band-pass filter.

Answer the following questions and provide some discussion on the following:1. Whywas the LM741 incapable of driving a 6load?

2. Whyis the LM386 capable of driving the 6load?

3. Whydid we use the speaker instead of a 6resistor in Part IV?

REFERENCES

[1] Thomas, Roland E., Albert J. Rosa, and Gregory J. Toussaint. The Analysis and Design of LinearCircuits. 7

thed. Hoboken, NJ: Wiley, 2012.

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