EGR 322 Electronics II Project
Professor Sophie Liu
Fun with Resonance Using Operational Amplifiers to Build an
AM Radio Transmitter
Project demonstration due: April 24, 2019
Project report due: April 27, 2019
Please read this document before coming to do the project and do the
calculations in bold font in the notes of the construction steps before-hand.
This project is made based on the laboratory that was designed for the Laboratory Component of ENGN0520,
“Electrical Circuits and Signals” in the School of Engineering of Brown University by Professor Harvey
Silverman and used with his permission.
The project is partially based on material from:
1. Texas Instruments, Excerpts from “Op Amps for Everyone”,, Literature number SLOD006A.
2. Wayne Starr, “Basic Electronics Tutorials: #3 of 6: The Colpitts Oscillator”, ElectronicsTutorials.ws,
June 3 2012.
3. Wikipedia, “Amplitude Modulation”
4. Ron Mancini, “Design of Op Amp Sine Wave Oscillators”, Texas Instruments Inc., Analog
Applications Journal, August 2000.
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1. Goals
1. Learn how to read and use manufacturer’s datasheets
2. Learn how to wire and debug a complex system sequentially
3. Learn about designing several operational amplifiers and op amp circuits and analog processing
4. Have some fun in using your own radio station!
2. Introduction
We have talked about operational amplifiers in class and have spent some time using the assumptions for ideal
operational amplifiers to design active circuits and have even briefly discussed some of the properties of real,
non-ideal operational amplifiers. In this project, you shall gain some experience with using operational
amplifiers in several different configurations to put yourself on the radio! You shall make your own AM radio
transmitter and then listen to it as you broadcast to one of the AM receivers. (Even though Edwin Howard
Armstrong showed that FM has higher fidelity and essentially no static – surely you prefer listening to FM
stations over the AM ones for this reason —AM was the first modulation system and is easiest to implement
here. Besides, your transmitter is going to be very close to the receiver!)
Amplitude modulation (AM) is a technique used in electronic communication, most commonly for
transmitting information via a radio carrier wave. AM works by varying the strength of the transmitted signal in
relation to the information we want to send. For example, changes in signal strength may be used to specify the
sounds to be reproduced by a loudspeaker, or the light intensity of television pixels. Contrast this with
frequency modulation, in which the frequency is varied, and phase modulation, in which the phase is varied.
Suppose the signal that we what to broadcast – the music, the talk show, the news … -- is theoretically
characterized by a function of time called the modulation signal, 𝒎(𝒕). The modulation signal contains all the
information we ultimately want to get to the receiver. To allow for many stations over the allotted frequency
band, one has to transmit the information about a frequency that the AM station has been assigned. A sinusoid
at the allotted (much higher) frequency is called the carrier signal, c(t).
We model the carrier wave as a sine wave:
The constants 𝐴 and 𝜑𝑐 represent the carrier amplitude and initial phase, and are introduced for generality. For
simplicity, their respective values can be set to 1 and 0. For this analysis, we let m(t) be a simple sinewave
(although it could be a microphone signal or a video signal or …) and let the constant M represent its largest
magnitude
𝑚(𝑡) = 𝑀𝑐𝑜𝑠(𝜔𝑚 𝑡 + 𝜑).
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The AM modulation index 𝒉, is the measure of the amplitude variation surrounding an unmodulated carrier. As
with other modulation indices, in AM this quantity (also called "modulation depth") indicates how much the
modulation varies around its "original" level. For AM, it relates to variations in carrier amplitude and is defined
as:
So if ℎ = 0.5, carrier amplitude varies by 50% above (and below) its unmodulated level; for ℎ = 1.0, it varies by
100%. To avoid distortion, modulation depth must not exceed 100 percent. Transmitter systems will usually
incorporate a limiter circuit to ensure this. Variations of a modulated signal with percentages of modulation are
shown below for the sinusoidal modulation signal. In each image, the maximum amplitude is higher than in the
previous image (note that the scale changes from one image to the next).
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Figure 1: Time Waveforms for AM Signal for a Sinusoidal Modulation Signal for 50%, 100% and 150%
Modulation
Note that for non-sinusoidal modulation signals such as speech from a microphone, one cannot use
trigonometry to get an analytic form. However, the AM signal on an oscilloscope will look about like those in
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Figure 1, except the low-frequency modulation signal will shape the high-frequency carrier signal by whatever
are its local values.
3. System Overview
Your task is to build, test and measure the performance of an AM transmitter over which you may broadcast to
the “world” wirelessly. (Clearly, the “world” would be much larger if you were allowed by the FCC to put a
whopping-big amplifier just prior to the antenna, but what is in the diagram should be more than sufficient to
reach the local receiver.) The block diagram for the transmitter is shown in Figure 3. You may notice that in
order to transmit, you will need an “antenna” – for this relatively low frequency system, a long wire will do and
we shall have some of these available in the room. You will also need a ground wire too that could be
connected to the ground for the AC in the room. These will be provided also.
The first of the four major components that need to be designed, wired and tested uses the LF353 general
purpose operational amplifier integrated circuit. The higher-frequency components, however, must use
components capable of these higher frequencies. The mixer is a totally different component, a four quadrant
multiplier. The reasons for these choices are explained below. The significant parts of the data sheets for each
of the integrated-circuits can be found from the Internet.
There are two parameters of operational amplifiers that often serve as difference makers relative to both cost
and overall capability. One is called the gain-bandwidth product (GBW) and the other is called the slew rate
(SR). The GBW is a constant for an amplifier indicating the potential tradeoffs between the designed gain and
the bandwidth of the signal passing through the amplifier. For example, if the GBW were 3MHz, then one
would expect that one design for a gain of 3 if the real bandwidth of the signal were 1MHz, or tradeoff and
design for a gain of 10, but the signal bandwidth could only be 300kHz. The SR is the maximum speed at
which the amplifier output can change, measured in Volts per microsecond.
The GBW and SR are values given by the manufacturer that can be used to assess the limiting performance of a
device. You may look up in the datasheet of LF353 from Internet under AC Electrical Characteristics where it
says that the LF353 has a minimum GBW of 2.5MHz and is typically about 4MHz and a typical SR of 12V/𝜇𝑠,
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while the AD817 has a typical GBW of about 50MHz and an SR of about 200V/𝜇s. In this project, you shall be
working with a carrier signal that is from 700-1000kHz, so you would be just about at the minimum GBW limit
if you were to use the LF353 for these frequencies with a gain near 2.5. Clearly the GBW of the AD817 is
more than sufficient for these purposes.
The SR, however, is a real issue for the frequencies of this project. If you want to use the equations included
below for design of an oscillator, the amplitude of the oscillation must be able to go full range, here about ±13𝑉.
This means that for a 1MHz oscillator, the output changes through 26V in a period of 1𝜇𝑠, implying a needed
average SR of at least 26V/𝜇𝑠. Clearly this is far larger than the maximum slew rate for the LF353!, so one will
have to use the AD817 for the oscillator. Unfortunately, we do not get something for nothing, as in 2019 for
hundreds quantities, the LF353 with two amplifiers in an IC costs $0.31, the AD817 with one amplifier per IC
costs $3.31! Also, note the AD633 multiplier is even more costly at $7.54, so if you burn something, burn an
LF353!! Further, you may notice that the SR of the AD633 is only 20V/𝜇𝑠, so will likely not fully support an
output modulated carrier that is faster than this. Thus, to use this IC, you cannot use it with full-scale output,
i.e., if the output is 2V P-P, at 1MHz the average SR will be about 4V/𝜇𝑠 which is pretty safe for this IC, but at
20V P-P, there will be some issues when you try to modulate the signal.
4. Implementation
Step 0: Set Up your Proto Board
This is a real electronics experiment which has circuits that can interfere with one another through their power-
supply attachments. Thus you should orient and tie your board into the ±15𝑉 power supplies in a structured
way:
1. Start your proto board with the RED line at the top (away from you) and progressively wire the steps
left to right. Consider the top + line of holes as +15VDC and the top – line of holes (near the blue
line) as GROUND.
2. Put in a jumper wire at the left of the board from ground at the top of the board (near the blue line) to
the + (next to the red line) at the bottom of the board. You now have two grounding places.
3. Assign the – (near the blue line) at the bottom of the board as the negative power supply 15VDC.
4. Use our pre-made twisted-pair power-supply wires to go from the power supply to the appropriate
place on the board. The color coding should be RED = +15V, BLACK = GROUND, and BLUE = -
15V.
5. To prevent noise from the power supply system, you should add a 10𝜇𝐹 “bypass capacitor” across
each supply. We have these available for you, but large microfarad capacitors are normally polarized.
These capacitors are labeled and the gray stripe is the negative side. Make sure the side with the gray
stripe goes to ground for the positive supply and the gray stripe goes to -15V for the bypass for the
negative supply.
Step I: Implement the Microphone Preamplifier
The first subsystem to implement is the microphone preamplifier. Its function is to appropriately host the
electret microphone and raise its signal level to one that is useful for modulating the AM carrier. Until the
recent advent of MEMS silicon microphones, electret microphones have been used in just about every
telephone, cell phone, recorders… The electret element is a plastic-like diaphragm material that has a metallic
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coating and acts like a capacitor. It is placed on a ring so it can vibrate. The vibration ultimately causes a small
voltage change corresponding to the sound vibrations on the diaphragm. However this change is very small, so
virtually all electrets contain a small FET transistor to bring their level up to about 20mV RMS when talking
closely. This means that the microphone requires some small amount of positive DC “phantom” power, about 1
- 2V across it and it draws about 0.5mA -1mA of current. The microphone and microphone preamplifier
circuit are shown in Figure 4. 𝑹𝑫 , a 22𝑘Ω resistor is included in Figure 4 for the voltage dropping. A simple
DC analysis should show that this value is proper for the voltage drop across the microphone to be 1.5±0.3𝑉
when the current drawn is 0.5mA. You will be asked to do this analysis for the write-up. However, in order to
do the design, you will have to calculate a reasonable value for the feedback resistor, 𝑹𝑭𝟏 , such that the overall
gain will be about 40dB.
Notes:
1. Power the microphone and check if you have a valid microphone output by whistling into the microphone. A
whistle should produce a near sinusoidal output. Do not whistle too close or too loudly as this may saturate
the microphone output.
2. We can use the inexpensive LF353 for the preamplifier because 40dB is a factor of 100, and a speech signal
is limited to about 8000Hz, so the GBW is 800,000, significantly below the minimum value in the
specifications for the IC.
3. You need to determine the value of 𝑹𝑭𝟏 , the feedback resistor for the amplifier
4. The resistor and capacitor on the left of the circuit is a simple one-pole low-pass filter to eliminate higher,
unwanted, frequencies from the power supply. You are using a quality power supply, so this circuit should
play no role here.
5. Figure 5 shows the pin assignments for the LF353.
6. Just to eliminate any DC offset, a 0.1𝜇𝐹 coupling capacitor is used to block it from the next stages.
7. IMPORTANT: Make all measurements on the oscilloscope with the probes set for 10X.
8. Remember there is more to build, so keep your circuit neat and compact!
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Step II: Implement the Oscillator that Creates the Carrier Wave
Some Theory for Oscillators
In Figure 6 the very-high-level block diagram of a negative feedback system is shown, where for an op amp, A
is the amplifier and 𝛽 is the feedback path. It should not be hard to deduce that
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This equation becomes unstable when 𝐴𝛽→−1 , or 1+𝐴𝛽→0 which is called the Barkhausen criterion. In
terms of complex numbers, this corresponds to 1∠180°. This implies that in order to satisfy the Barkhausen
criterion, and thus build an oscillator, we must feed back 𝑉out with a phase shift of 180°.
Figure 7 shows the Bode plot phase-shift results for one to four cascaded, one-pole RC lowpass filters having
the same cutoff frequency and assumed to be independent of each other. (For completeness, Figure 8 shows a
cascade of three such filters.) Note from Figure 7 that one could try to use two RC sections to achieve the
needed phase shift, but predicting the frequency for which that would be achieved and the frequency stability of
the resulting oscillator would be very poor. However, using three sections, one can see that the phase shift is
−180° just below a normalized frequency of 2, where the normalized frequency corresponding to 1 is 𝜔=1 / 𝑅𝐶.
More precisely, under the assumption of independence of the sections to each other,
Implying that the phase shift of each section is just -60° as tan (60°) = √3 ≈ 1.732, the frequency for which total
phase shift is -180° is:
The phase-shift oscillator thus should produce a fundamental frequency of about 𝑓𝑜𝑠𝑐 𝐻𝑧, the uncertainty due to
the fact that the sections DO interact. 𝑓𝑜𝑠𝑐 𝐻𝑧 would be more a more precise prediction if one inserted op-amp
buffers at points A and B in Figure 8.
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Is a Phase-Shift Oscillator a possible implementation???
You are welcome to try to design the oscillator as a phase-shift oscillator using the circuit of Figure 8 as the
phase shifter for an inverting amplifier with some gain. However, even with the high GBW amplifier,
professor Sophie Liu has not been able to achieve good results for frequencies above 500kHz, which is what
you need for the carrier frequency!!! This was true even for the “improved” case in which a buffer amplifier
was placed between the first and second and the second and third phase-shift stages. The full circuit is shown in
Figure 9. You should note that the gain for 𝛽 at the “phase unstable” point is (1/2)^3 so the gain of the
amplifier has to be eight in order for the overall gain to be 1, but, without any buffers, it has to be much higher
than this. You could select Rin > 𝑅 so as not to load the phase shift circuit. You want to select components R
and C such that the carrier frequency is between 600 and 1000kHz (I could not do it!) You might find that this
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oscillator has some significant harmonic distortion even for the lower frequencies that were obtainable. The
moral of the story is DO NOT DO THIS!
A Simpler, Working Implementation for the needed AM Radio Band: 550kHz-1600kHz
The Colpitts Oscillator
Another implementation of an oscillator also uses a third-order low-pass filter to give the needed phase shift.
This implementation is better suited for a higher-frequency oscillator and does work in the needed range.
However, the circuit requires the use of an inductor and two capacitors, rather than the more simple idea of
three RC one-pole filters. The Colpitts Oscillator is shown in Figure 10. Here, 𝐺 is the gain of the amplifier and
is a value you will need to determine. Note that his analysis is an ideal one in which the (quite important)
resistance of the inductor is considered to be zero, and the values of the capacitors the same. As part of the
write-up, you will validate that the open-loop transfer function for the oscillator is third-order as follows:
If we use these open-loop solutions to determine the denominator of the closed-loop system, 1+𝐴𝛽, then we
have, after making a common denominator,
This is more easily analyzed using the Barkhausen criterion and our knowledge of linear, constant coefficient
systems. A third-order system has three poles. For oscillation, at least one of the poles must be on the 𝑗𝜔 axis.
In fact, if the oscillation frequency is not zero, then there must be poles at
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precisely ±𝑗𝜔, where 𝜔 is the frequency of oscillation. This means the denominator of Equation (2) would
factor as
Comparing the denominator of (2) to (3) would imply,
Notes:
0. For this step you will be using the AD817 op-amp, the pin assignment for this chip is significantly
different from the LF353 op-amp that we used before. Check the figure 11 for the correct pin assignment.
1. Select 𝝎𝒐 to be the radian/sec equivalent to about 750 kHz. However, if we allow the poles to go into the
right-half plane, rather than restrict them to the 𝒋𝝎 axis, the circuit will still oscillate, but at a slightly
higher frequency.
2. We have a stock of only four inductor values: 𝟏𝝁𝑯, 5𝝁𝑯, 10𝝁𝑯,𝒂𝒏𝒅 𝟏5𝝁𝑯. Any of these should be
useful for this project. You will need to select one of these values.
3. 𝝎𝒐 is only an estimate. In our equations we assumed an ideal inductor, but a real inductor will have
resistance and also have properties that change some with frequency, so we expect the estimate to be off by,
hopefully, less than about 5% of what you might measure.
4. For equations (4) to be true, one can see that the gain G would be one. However, since we ignored
several real issues using the ideal analysis above, you will likely need to increase the gain to just
beyond 2 to make the circuit oscillate. Increasing the gain allows the poles to go into the right-half
plane. The gain is easily increased by increasing the feedback resistor.
5. It is best if R is relatively small as compared to r. Selecting 𝑹 ≈ 𝟏𝟎𝟎𝛀 and 𝒓 ≈ 𝟏𝟎𝒌𝛀 are good starting
choices.
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6. You would like as nearly a sinusoidal output as possible. With poor choices of the resistor values, the signal
could almost be a square wave. You will need to experiment a bit to have the signal fairly sinusoidal, but
with about 20V peak-to-peak output. You should use the FFT function on the oscilloscope to jot down the
amplitudes of the fundamental and worst harmonic. You might also note that taking the output as the
𝑉𝑓 signal in Figure 10 is better than taking the Vo signal. For the basics of using FFT on an oscilloscope, you
may refer to the video at https://www.youtube.com/watch?v=oRf-IpG6XAw.
7. While the AM receiver in the stereo receiver is digitally tuned, you will likely use an old fashioned analog-
tuned AM receiver to make your life easier! If you used the digitally tuned receiver, then it expects precise
carrier frequencies that are multiples of 10 kHz, e.g., 720 KHz or 970 kHz, and not 725 kHz. The analog-
tuned receiver can adjust for in-between, so you will not have to fiddle with the carrier to make it perfect for
the digital tuner. However, AMJ radio was known for its susceptibility to noise, so expect some squeals and
such.
8. Take a picture of the carrier frequency and its FFT (you will need to calculate the Total Harmonic Distortion
in this signal)
Step III: Implement the Modulator and Attenuation Networks
The simplest way to amplitude modulate a sinusoidal carrier is with a multiplier. Here we shall use the AD633
from Analog Devices which is advertised as a four-quadrant multiplier. Important: Your multiplier IC is
packaged as an 8-pin PDIP and the pin outputs (top view), taken from the datasheet, are listed in Figure
12.
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You should see that the multiplier has the two power pins for ±15𝑉, five inputs X1,X2,Y1,Y2,Z, and one
output, W, and implements the equation,
Note that the factor of 10 is needed to keep the output in the linear range (-10V, 10V) if the inputs can also be
within that range.
You have already generated the carrier signal, 𝑪(𝒕) and the modulation signal 𝑴(t), both with no DC
component. You want the output of the multiplier to give the AM modulated signal,
Equations (5) and (6) should tell you how to wire the modulator.
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Unfortunately, this is a real system and some practical issues need to be resolved. Due to the frequency at
which you are working and the 20𝑉/𝜇𝑠 maximum slew rate of the multiplier, the following is true: (1) A
sinusoid changes most rapidly about zero at a rate of its full amplitude in a quarter of its period; (2) for an
800kHz carrier of 10V peak amplitude the necessary slew rate would be 10𝑉∗4∗800,000𝐻𝑧=32V/𝜇𝑠 which is
out of range. Thus you will need to attenuate the carrier signal before the multiplier to keep its output
amplitude below, say, 5V.
have a peak voltage of 10V then it is easy to see that 𝑲 ≤ 𝟎.𝟐𝟓. You can use a simple voltage divider on the
output of the oscillator making the lower resistor 1k𝛀 (this value is selected to make the oscilloscope
measurements accurate.)
Notes:
1. Wire carefully and please do not blow up the multiplier! – it costs many times more than does an
amplifier IC.
2. The calculations of this step can all be done before you come into the lab. You should have your
wiring diagram for the multiplier and voltage dividers ready to go before you start.
3. From about one foot from the microphone, whistle (the human sine wave) and capture the signal on the
oscilloscope similar to one of those in Figure 1 to show the modulated signal and to estimate the
percentage modulation in the write-up.
Step IV: Add an RF Amplifier
The output power of the transmitter is limited by output capability of the multiplier (about 30 ma) if you were to
connect the antenna directly to the multiplier output. You can get a gain of two or more by adding a simple
inverter with some voltage gain as the final stage of the system using an additional AD817 (GBW prevents the
use of the LF353 again). It can drive about 50ma. This will require an additional IC and two resistors. It is
shown in Figure 13.
Step V: Add the Antenna Circuit
To make your circuit really broadcast well, you should use the idea of resonance to help you to make the
antenna effective. To do this the network shown in Figure 13 is recommended for the loop antenna you shall
use. We have carefully measured all the antennas and have found that each has an inductance, L, of about
10𝜇𝐻 and a resistance 𝑝 ≈ 0.23Ω. To make certain there is no overload to the buffer amplifier, you should
make 𝑅 = 100Ω. Thus all you have to do now is select some values for the two capacitors C1 and C2 and the
damping resistor, r. However, getting the circuit to have resonance at your carrier frequency is a bit tricky. You
really only have a few choices for r, 0.0Ω, 1.2Ω, 1.5Ω, 1.8Ω, or 2.2Ω, assuming you want to use only a single
resistor here. If you select 𝑟 = 0Ω, you will have the highest gain from the resonant network, but it will make
the bandpass characteristic very narrow, implying it will be difficult to find perfect capacitors. If you make 𝑟,
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many times larger than 𝑝, then the gain of the network is reduced as the value gets larger, but the peak is
broader so it will be easier to find matching capacitors.
For carrier frequencies between 600800 kHz, you can probably begin and end using 𝐶1 = 0.022𝜇𝐹. Then all
you have to do is find a value of C2 such that the resonant frequency of the matching network is the same as the
carrier frequency you are generating. To match well, you may have to use several capacitors in series and/or
parallel. You can do this in three ways:
1. Trial and error – try a lot of C2 values until the output voltage peaks– you can measure at the + side
of Vout to ground. This may take some time and be messy with lots of series/parallel capacitor
groups.
2. Model the matching network in KCIRC changing the value of C2 until the peak matches the carrier
frequency.
3. I have solved the circuit analytically and made a MATLAB program that tells you all the important
parameters – including the output frequency and the gain in dB. The program is a MATLAB m-file
and is called solve_antenna_circuit (C1, C2, R, r), i.e., it has four parameters. I have put this file on
D2L. You will likely change only C2 and look at the resulting resonant frequency until you know the
correct matching value for your carrier.
Measure the actual gain from the antenna-matching circuit by finding the ratio of its output voltage to its
input voltage.
Step VI: Transmit and Tune Into Your AM Station
Then, after reading the carrier frequency on which you are transmitting, you can tune the receiver to the nearest
normal AM frequency. UNFORTUNATELY, unlike all stations today, your carrier generator is not crystal
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controlled, and so it is difficult to get exactly on one of the digitally-selected AM carrier frequencies. However,
an old-fashioned analog-tuned receiver shown in Figure 14 will help you a lot. If you have one , please bring it
to the lab and try it and see how far away you can transmit.
Figure 14: Old-fashioned Analog-tuned Receiver
Demonstrate your AM radio to your instructor – this will contribute toward your project grade.
Congratulations!!! You have just built an AM radio station
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