The George Washington University
School of Engineering and Applied Science
Department of Electrical and Computer Engineering
ECE 11 - LAB
Experiment # 11
Final Project Preparation Lab: Active Filters, LED Display, Intro to Power Amplifier
Equipment:
Lab Equipment
DC Power Supply
Function Generator
Digital Oscilloscope
Equipment Description
Agilent E3631A Triple Output DC Power Supply
Tektronix AFG3021B
Tektronix TDS460A
Table 1.1
Components:
Kit Part #
LM741 OpAmp
LM386 Power Amp
Resistors
Capacitors
8 Ω Speaker
Spice Part
Name
R
C
Symbol Name
Part Description
OpAmp
Power Amplifier (not an OpAmp)
Various values
Various values
Table 1.2
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 is is necessary
Build and measure a band-pass filter using LM741s and an LM386
(used in schematics
throughout this lab manual)
Prelab: (Submit electronically prior to lab meeting, also have a printed copy for yourself during lab)
Active Filters:
In lab 10 you were introduced to passive filters. Passive filters consist of only passive
components (inductors, capacitors, resistors). Because passive components cannot provide
average power to a circuit, one cannot make a filter with a gain greater than 1 using only passive
components. In situations one may wish to create a filter with a gain greater than 1. For this, one
incorporates an op-amp into the filter design.
First-Order Low Pass Active Filter:
Fig 1 – Inverting Amplifier
st
Fig 2 – Active 1 order lowpass filter
Figure 1 shows an inverting amplifier. From the lab on DC Operational Amplifiers we know the
gain of this amplifier is: VO / VI = -RF / RI. If instead of using just resistors, we can substitute
impedances (ZF and ZI) and the gain becomes: VO / VI = -ZF / ZI.
Figure 2 shows the same amplifier, now with a capacitor inserted in the feedback path. Zi is still
Ri, but ZF is the impedance of the resistor and capacitor are in parallel, so ZF = ZRf || ZCf:
Substituting in the impedances as shown in figure 2:
Typically, for filters, the transfer function of interest is the voltage gain, defined as T(w) = VO / VI.
Since the voltage gain of the amplifier in figure 2 is VO / VI = -ZF / ZI, the transfer function for the
filter in figure 2 becomes:
T ( w) 
Zf
Rf
VO


Vi
Zi
Ri

1

 1  jwC R
f
f





What should be familiar is the expression in brackets in the equation above, it is the transfer
function for a low-pass filter. But the expression outside of the brackets: –RF/RI, means this lowpass filter has gain!
The cutoff frequency for this low-pass filter is:
To design this filter, one chooses the appropriate resistors: RF and RI to set the gain. Then
determine CF for the desired cutoff frequency.
First-Order High Pass Active Filter:
st
Fig 3 – Inverting Amplifier
Fig 4 – Active 1 order high-pass filter
Figure 4 shows how we can make the inverting amplifier into a high-pass filter, by rearranging the
capacitor to be in series with the input resistor. The transfer function then becomes:
T ( w) 
Zf
Rf

VO

 
Vi
Zi
 Ri  1 / jwC i



When the frequency is low (e.g.: w -> 0), the transfer function approaches 0. As the frequency
gets higher and higher (e.g: w-> ∞) , the transfer function becomes -RF/RI. This is the behavior of
a high pass filter. The cutoff frequency for this filter can be derived as:
Creating a Band-Pass Active Filter by Cascading Filters:
When two filters are chained together this is called cascading. Passive filters can be cascaded
together, as can active filters. As a simple example, we can cascade the low-pass and high-pass
filters discussed above to create a band-pass filter as follows:
Rf1
Rf2
Ri1
Ri2
Rf3
Ri3
Fig 5 – Simple Active Band-pass filter w/ gain stage
What you should notice in figure 5 is the addition of a simple inverting amplifier shown as stage 3.
What is often done when cascading filters is to have the final stage provide all of the gain for the
system. In this example, we set the gain of our active low-pass filter (stage 1) to unity or 1. The
next stage, the high-pass filter (stage 2) also has a unity gain. But the final stage, the inverting
amplifier will set the gain for the system.
When amplifiers are cascaded, the gain of each stage is multiplied together to determine the
overall gain. To determine the transfer function for the system in figure #5, we multiply each
individual transfer function for each stage:
T ( w) 
 
Rf1 
 Rf 2
VO
1


 T1 ( w)  T2 ( w)  T3 ( w)  
Vi
Ri1  1  jwC1 R f 1   R i 2 1 / jwC 2
  Rf 3

 Ri 3

If we set the gain of stage 1 and stage 2 to unity, the transfer function simplifies to:
T ( w)  
 
Rf 3 
 Rf 2
1


Ri 3  1  jwC1 R f 1   Ri 2  1 / jwC 2




We see the overall gain for the system is set by the final stage (R f3 / RI3).
20 log (-Rf/Ri)
20 log (-Rf/Ri) – 3 dB
The low-pass section, stage 1, sets the upper cutoff frequency (w2). The high-pass section,
stage 2, sets the lower cutoff frequency (w1). The pass-band, or bandwidth of this band-pass
filter is simply w2-w1.
w2 
1
R f 1C1
w1 
1
Ri1C 2
To design an band-pass filter using this configuration, one first chooses the desired gain
and sets Rf3 and Ri3. Then one chooses Rf2 and Ri2 to have unity gain, similarly, Rf1 and Ri1
are chosen setting the gain of the first stage to 1 as well. Lastly, the cutoff frequencies are
chosen and the values of the capacitors: C1 and C2 are solved for using the cutoff
frequency equations.
Prelab Problem #1:
Using the procedure discussed above, design an active band-pass filter with a gain of -10, a
lower cuff-off frequency of 150 Hz and an upper cutoff frequency of 5 kHz.
Note: When choosing resistor values to set the gain for each stage, be certain to keep them in the
high kΩ range.
Lab:
Part I - Low-Pass Active Filter:
1. Using the LM741 op-amp, build the low-pass active filter section of the band-pass filter
you designed in prelab problem #1 in PSPICE. Simulate the following:
a. Use a +/- 12 VDC for the supply voltage for the LM741
b. Use a 300 mVRMS sine wave as input to the filter
c. Attach a 1 kΩ resistor as the load for the filter
d. Measure VOUT (in RMS voltage) across the 1kΩ load at the frequencies: 10 Hz,
150 Hz, 1 kHz, 4 kHz, 5 kHz, 6 kHz)
i. Using the peak output voltage of VOUT, calculate by hand the peak power
dissipated by the 1kΩ load resistor at each frequency.
ii. Calculate the current drawn by the 1kΩ load resistor at the peak output
power in each case.
iii. Record these values in table 1.1 below
e. Plot the magnitude and phase of VOUT/VIN (in dB) versus frequency from 10 Hz
to 7 kHz (your GTA will demonstrate how this is done in PSPICE)
i. Determine the -3dB frequency from this plot (record in table 1.1)
2. Build the low-pass active filter section on a breadboard. Make the following
measurements:
a. Show your GTA your setup prior to applying power
b. Use a +/- 12 VDC for the supply voltage for the LM741
c. Use a 300 mVRMS sine wave as input to the filter (using the function generator)
d. Attach a 1 kΩ resistor as the load for the filter
e. Measure VOUT (in RMS voltage) across the 1kΩ load at the frequencies: 10 Hz,
150 Hz, 1 kHz, 4 kHz, 5 kHz, 6 kHz)
i. Using the peak output voltage of VOUT, calculate by hand the peak power
dissipated by the 1kΩ load resistor at each frequency.
ii. Calculate the current drawn by the 1kΩ load resistor at the peak output
power in each case.
iii. Record these values in table 1.1 below
f. Adjust the frequency of the function generator until you find the exact -3dB
frequency of the filter (Where Vout = 1/sqrt(2) * max Vout), record in table 1.1
Vin (RMS)
Frequency
10 Hz
150 Hz
1 kHz
4 kHz
5 kHz
6 kHz
Sim.
Mes.
Sim.
Mes.
Vout (RMS)
Sim.
Mes.
Gain
(Vout/Vin)
Sim. Mes.
Pout (peak)
Sim.
Mes.
Iout (peak)
Sim.
-3dB Freq:
Table 1.1 – Output characteristics for low-pass active filter w/ 1kΩ load
Mes.
Part II - High-Pass Active Filter:
1. Using the LM741 op-amp, build the high-pass active filter section of the band-pass filter
you designed in prelab problem #1 in PSPICE. Simulate the following:
a. Use a +/- 12 VDC for the supply voltage for the LM741
b. Use a 300 mVRMS sine wave as input to the filter
c. Attach a 1 kΩ resistor as the load for the filter
d. Measure VOUT (in RMS voltage) across the 1kΩ load at the frequencies: 10 Hz,
150 Hz, 1 kHz, 4 kHz, 5 kHz, 6 kHz)
i. Using the peak output voltage of VOUT, calculate by hand the peak power
dissipated by the 1kΩ load resistor at each frequency.
ii. Calculate the current drawn by the 1kΩ load resistor at the peak output
power in each case.
iii. Record these values in table 1.2 below
e. Plot the magnitude and phase of VOUT/VIN (in dB) versus frequency from 10 Hz
to 7 kHz
i. Determine the -3dB frequency from this plot (record in table 1.2)
2. Build the high-pass active filter section on a breadboard. Make the following
measurements:
a. Show your GTA your setup prior to applying power
b. Use a +/- 12 VDC for the supply voltage for the LM741
c. Use a 300 mVRMS sine wave as input to the filter (using the function generator)
d. Attach a 1 kΩ resistor as the load for the filter
e. Measure VOUT (in RMS voltage) across the 1kΩ load at the frequencies: 10 Hz,
150 Hz, 1 kHz, 4 kHz, 5 kHz, 6 kHz)
i. Using the peak output voltage of VOUT, calculate by hand the peak power
dissipated by the 1kΩ load resistor at each frequency.
ii. Calculate the current drawn by the 1kΩ load resistor at the peak output
power in each case.
iii. Record these values in table 1.2 below
f. Adjust the frequency of the function generator until you find the exact -3dB
frequency of the filter (Where Vout = 1/sqrt(2) * max Vout), record in table 1.2
Vin (RMS)
Frequency
10 Hz
150 Hz
1 kHz
4 kHz
5 kHz
6 kHz
Sim.
Mes.
Sim.
Mes.
Vout (RMS)
Sim.
Mes.
Gain
(Vout/Vin)
Sim. Mes.
Pout (peak)
Sim.
Mes.
Iout (peak)
Sim.
-3dB Freq:
Table 1.2 – Output characteristics for high-pass active filter w/ 1kΩ load
Mes.
Part III - Band-Pass Active Filter:
1. Using the LM741 op-amp, build the complete band-pass active filter you designed in
prelab problem #1 in PSPICE. Simulate the following:
a. Use a +/- 12 VDC for the supply voltage for the LM741
b. Use a 300 mVRMS sine wave as input to the filter
c. Attach a 1 kΩ resistor as the load for the filter
d. Measure VOUT (in RMS voltage) across the 1kΩ load at the frequencies: 10 Hz,
150 Hz, 1 kHz, 4 kHz, 5 kHz, 6 kHz)
i. Using the peak output voltage of VOUT, calculate by hand the peak power
dissipated by the 1kΩ load resistor at each frequency.
ii. Calculate the current drawn by the 1kΩ load resistor at the peak output
power in each case.
iii. Record these values in table 1.3 below
e. Plot the magnitude and phase of VOUT/VIN (in dB) versus frequency from 10 Hz
to 7 kHz
i. Determine the -3dB frequency from this plot (record in table 1.3)
2. Build the complete band-pass active filter on a breadboard. Make the following
measurements:
a. Show your GTA your setup prior to applying power
b. Use a +/- 12 VDC for the supply voltage for the LM741
c. Use a 300 mVRMS sine wave as input to the filter (using the function generator)
d. Attach a 1 kΩ resistor as the load for the filter
e. Measure VOUT (in RMS voltage) across the 1kΩ load at the frequencies: 10 Hz,
150 Hz, 1 kHz, 4 kHz, 5 kHz, 6 kHz)
i. Using the peak output voltage of VOUT, calculate by hand the peak power
dissipated by the 1kΩ load resistor at each frequency.
ii. Calculate the current drawn by the 1kΩ load resistor at the peak output
power in each case.
iii. Record these values in table 1.3 below
f. Adjust the frequency of the function generator until you find the exact -3dB
frequency of the filter (Where Vout = 1/sqrt(2) * max Vout), record in table 1.3
Vin (RMS)
Frequency
10 Hz
150 Hz
1 kHz
4 kHz
5 kHz
6 kHz
Sim.
Mes.
Sim.
Mes.
Vout (RMS)
Sim.
Mes.
Gain
(Vout/Vin)
Sim. Mes.
Pout (peak)
Sim.
Mes.
Iout (peak)
Sim.
-3dB Freq:
Table 1.3 – Output characteristics for band-pass active filter w/ 1kΩ load
Mes.
Part IV - Band-Pass Active Filter w/ Small Load:
1. For the band-pass filter you’ve simulated and measured, calculate the amount of current
an 8 Ω load would draw at the highest value of Vout you recorded in table 1.3.
a. What is the value in mA?
i. Include this in your lab write-up
b. Can the LM741 OpAmp provide this much current to an 8 Ω load?
i. Download the LM741 spec-sheet from the lab website
ii. Look for the electrical parameter: “Output Short Circuit Current”
1. Include this in your lab write-up
iii. Is this value more or less than the amount of current an 8 Ω load would
draw?
c. Replace the 1 kΩ load in your SPICE simulation with an 8 Ω load
i. Find VOUT (in RMS voltage) across the 1kΩ load at the frequencies: 10
Hz, 150 Hz, 1 kHz, 4 kHz, 5 kHz, 6 kHz)
ii. What do you see?
iii. Your GTA will help you understand your results.
2. From step 1 you should realize that the LM741 cannot support a small load like 8 Ωs.
rd
a. We need an amplifier for the 3 stage of our band-pass filter that can provide
enough current to our 8 Ω load.
b. For this we will replace stage 3 of our amplifier with a power amplifier called the
LM386 (this is in your kit).
i. The LM386 is not an op-amp, it is a self-contained amplifier that can
provide a great deal of current to small loads
ii. Download the LM386 spec-sheet from the lab website
3. On page 5 of the LM386 spec-sheet a sample configuration is shown
rd
a. Replace the 3 stage of your amplifier with this sample configuration
b. Instead of an 8 Ω load, use the speaker in your kit
c. Show your GTA your setup prior to applying power
d. Use a +/- 12 VDC for the supply voltage for the LM741 and the LM386
e. Use a 300 mVRMS sine wave as input to the filter (using the function generator)
f. Measure VOUT (in RMS voltage) across the 8 Ω speaker at the frequencies: 10
Hz, 150 Hz, 1 kHz, 4 kHz, 5 kHz, 6 kHz)
i. Using the peak output voltage of VOUT, calculate by hand the peak power
dissipated by the 8 Ω load resistor at each frequency.
ii. Calculate the current drawn by the 8 Ω load resistor at the peak output
power in each case.
iii. Record these values in table 1.3 below
g. Adjust the frequency of the function generator until you find the exact -3dB
frequency of the filter (Where Vout = 1/sqrt(2) * max Vout), record in table 1.4
Frequency
10 Hz
150 Hz
1 kHz
4 kHz
5 kHz
6 kHz
Vin (RMS)
Vout (RMS)
Mes.
Mes.
Gain
(Vout/Vin)
Mes.
Pout (peak)
Iout (peak)
Mes.
Mes.
Mes.
-3dB Freq:
Table 1.4 – Output characteristics for band-pass active filter w/ 8Ω load
Lab Write-up
The informal lab report write-up style should be used for this lab. Be certain to include:
1) Your calculations for how you designed the band-pass filter.
2) The SPICE schematic for the band-pass filter.
3) The SPICE output showing Vout/Vin (in dB) versus frequency for the low-pass filter, highpass filter, and finally the band-pass filter.
4) Tables 1.1 – 1.4, add a column showing % error for each simulated/measured value.
Answer the following questions and provide some discussion on the following:
1) Why was the LM741 incapable of driving an 8Ω load?
2) Why is the LM386 capable of driving the 8Ω load?
3) Why did we use the speaker instead of an 8Ω resistor in part IV?