University of South Florida
Department of Electrical Engineering
Senior Design Project
Report:
“Design and Construction of a Superheterodyne Amplitude-Modulated Receiver”
by Charles P. Baylis II
Dr. Paris Wiley, Faculty
Supervisor
Fall 2002
I. ABSTRACT
The device that was designed
is a superheterodyne, fixed amplitude-modulated (AM) receiver. The receiver met its specifications to
receive an AM signal that is broadcast at 970 kilohertz (kHz), down-convert it
to an intermediate frequency of 455 kHz, and output an audio signal through a
speaker. This two-stage down-conversion
allows components with lower quality factors to be used in the circuit.
The signal enters the
receiver at the antenna, and is fed into a radio-frequency (RF) amplifier,
which has a gain of about 85 volts per volt (V/V) and a bandwidth of 43.4
kHz. This stage amplifies the signal
and removes the image frequency, the frequency which would be down-converted to
the same intermediate frequency as the signal being received. A local oscillator outputs about 3 volts (V)
peak-to-peak at approximately 1425 kilohertz.
This oscillator is mixed with the output of the RF Amplifier, providing
a signal at the intermediate frequency (IF) of 455 kHz, the difference of the
signal frequency and local oscillator frequency, to the IF amplifier. The IF amplifier gives a gain of over 100
and provides adjacent channel rejection with a bandwidth of 21.2 kHz. The signal is then demodulated, fed to an
audio amplifier, and output from a 0.5 watt, 8 ohm speaker.
Both the RF and IF
amplifiers use the cascode amplifier design; this design helps to prevent
Miller-effect oscillations. The local
oscillator is a common-base Colpitts oscillator and was tuned by the
cut-and-try method after initial design to achieve as close to 3 V
peak-to-peak, 1425 kHz as possible.
Each amplifier and the mixer contain a tuned circuit to remove unwanted
frequency components. The demodulator
consists of a diode and a lowpass filter, and the audio amplifier is constructed
from an LM386 power op-amp.
The cost for parts to
produce superheterodyne AM receiver is estimated at $66.60, while the cost per
unit for construction of one thousand units is estimated at $45.77. These costs could be reduced if the parts
were soldered together instead of being placed on a breadboard.
The societal impact of the
superheterodyne AM receiver is large, because it allows clear reception of
high-frequency channels. The clarity of
the superheterodyne receiver, originally introduced by Edwin Armstrong in the
time of World War I, opened the door to the development of frequency modulation
(FM) and allows the use of cellular phones, frequency modulation, and other
high frequency applications. Radio
communication today makes current information readily accessible to nearly
everyone.
The receiver designed works properly, providing a clear, distinguishable output of a local 970 AM broadcast.
II. ACKNOWLEDGEMENTS
The writer would like to
express deepest appreciation and gratitude to Dr. Paris Wiley, the faculty
supervisor for this project, for his knowledgeable assistance with theory and
design concepts in addition to fostering an understanding of non-ideal effects
that appeared during measurements.
Thanks is also given to Mr. Trung Nguyen and the departmental employees
of the Electrical Engineering Electronics and Equipment Repair Shop, who were
very helpful and accommodating in providing the necessary components to
construct the hardware for this project.
III. INTRODUCTION
This senior design project
consisted of the design and construction of a superheterodyne
amplitude-modulated (AM) receiver. The
purpose of the project was to receive an amplitude-modulated signal at 970
kilohertz (kHz) and output the audio waveform through a speaker device. Using a superheterodyne architecture, the
signal was received with an antenna, amplified, down-converted to an
intermediate frequency of approximately 455 kHz, amplified again, demodulated,
amplified, and output through the speaker.
The radio-frequency (RF) amplifier, local oscillator (LO), mixer, and
intermediate frequency (IF) amplifier were simulated using PSPICE following
design to test the feasibility of the design.
The design specifications are given in the table of Figure 1 and a system
block diagram is given in Figure 2. A
photograph of the finished receiver is shown in Figure 3.
|
Design Specification |
Met (Yes/No) |
|
Signal Reception with Antenna |
Yes |
|
Down-Conversion to Intermediate Frequency of
approximately 455 kHz (AM standard) |
Yes |
|
Audible Audio Output through Speaker |
Yes |
Figure 1. Table of Design Specifications.
Figure 2. System
Block Diagram.
Figure 3. Photograph of the Finished Receiver.
Why down-convert in two
stages? Why not simply convert the
signal to baseband with an antenna, diode, and tuned circuit? A primary reason is that the quality factor
of the circuits need not be as high in a homodyne (direct-down-conversion)
receiver. In a superheterodyne
receiver, adjacent channel rejection is performed in the IF amplifier,
requiring the RF amplifier to reject only the image frequency and interference
from the local oscillator. Because
quality factor Q is given by the equation
Q =
fo / W (1)
where fo is the center frequency of the
amplifier and W is the 3-decibel (dB) bandwidth of the amplifier, trying to
reject adjacent channels at the higher-frequency RF amplifier requires in a
higher quality-factor circuit.[1]
Another reason for using a
superheterodyne receiver is that the RF stage and local oscillator can be
adjusted to be synchronously tunable, while the IF, demodulator, and audio
amplifier stages can be fixed.[2] Keeping the
tuning of adjacent channel rejection stage (the IF) constant helps to keep the
gain (related to center frequency) and bandwidth of this stage consistent.
The concept of the
superheterodyne receiver system is a fundamental concept of communications
theory. Much of the challenge of this
project lay in the actual design of the electronic circuits. The key to successful design was designing
the electronics to avoid non-ideal occurrences that could degrade or eliminate
the desired message signal. Transistor
circuit operating points were designed to allow the message signal to receive
maximum gain before saturation or cutoff occurred. The mixer operating point was designed to allow maximum signal
swing. A knowledge of the principles of
the bipolar junction transistor (BJT) and the junction field-effect transistor
(JFET) were studied and applied to create a circuit with optimal response and
as little degradation of the message as possible. Amplifiers were designed to avoid unwanted oscillations. Careful tuning and adjustment of the
oscillator was also necessary; correct operation of the oscillator is a key to
optimal system behavior.
Several sources were
consulted during the design process.
The book Solid State Radio Engineering, written by Herbert L.
Krauss, Charles W. Bostian, and Fredrick H. Raab, contains much information
that was used for design of the RF and IF amplifiers, local oscillator, mixer,
and demodulator.[3] Microelectronic
Circuits, by Adel S. Sedra and
Kenneth C. Smith served as a reference relating to electronics calculations and
properties of the BJT and JFET.[4] The third
major source used for this project was Communication Systems, by A.
Bruce Carlson, Paul B. Crilly, and Janet C. Rutledge.[5] This book was consulted for communications
theory behind the superheterodyne receiver, and also provided the basic demodulator
design and explanation. Many other
various resources were consulted for necessary information pertaining to the
design of the individual stages.
IV. THEORY / DISCUSSION OF SIMULATION AND DESIGN METHODS
The design approach used in
this project was to design each component of the Figure 2 block diagram
individually. Simulations and testing
were also done by individual blocks in most cases. The first section following the antenna is the RF amplifier. The RF amplifier was designed with BJTs in a
cascode configuration for a gain of 100 volts per volt (V/V), or 30 dB. A general cascode amplifier circuit is shown
in Figure 4. This configuration
consists of a common-emitter BJT followed by a common-base BJT.
The values for L1
and C3 can be found using the formula
fo
= 1 / 2π√(LC) (2)
where fo is the resonant frequency. If the value of the inductor is known, the
value for the capacitor can be calculated or vice versa.
The formula for
common-emitter gain is given by
Av =
gmRC / (1 + gmRE) (3)
where RC is the total resistance between
the collector and ground and RE is the total resistance between the
emitter and ground. For the
common-emitter transistor in the cascode configuration, RC is
approximately equal to 1/gm because the base of the common-base
transistor is coupled to ground. RE
is zero because the emitter of the common-emitter transistor is coupled to
ground. Thus the gain for the
common-emitter circuit is approximately equal to 1. The formula for common-base gain is given by
Av
= rπgmRC / ( rπ + RB)
(4)
RB is the total
resistance between the base and ground.
Because the base is coupled to ground, RB is zero and the
total gain of the cascode amplifier is equal to gmRC.
Figure 4. General Cascode Amplifier Circuit.
The purpose for designing
the amplifier in the cascode configuration is the avoidance of oscillations
that could occur if a single-transistor circuit was used. In a common-emitter circuit, internal
transistor capacitance Cμ causes the circuit to suffer from the
Miller effect.[6] Cμ can complete a Colpitts
oscillator network with the tuned circuit at the output and unwanted
oscillations can occur. The cascode
configuration lessens the probability of oscillation by the use of a
common-base network, which does not experience the Miller effect, as the output
stage.
To design for a gain, Rc
must be known so that gm can be calculated. Rc is the output resistance of
the transistor ro in parallel with the parallel equivalent resistance
Rp of the inductor having quality factor Q at the resonant frequency
fo, given by
Rp
= 2πQfoL (5)
The quality factor was measured by placing the tuned
circuit at the collector of a common-emitter network with a tuned circuit at
the collector (output). The frequency
of the input signal was varied until the output wave was at maximum amplitude
and using the assumption that transistor open-loop gain β is large, the
signal current through the collector was equated to the signal current through
the emitter:
ve
/ RE = vc / RC (6)
ve and vc, the signal
amplitudes at the collector and emitter, were measured. Since RE was known, RC
could be found by
RC = vc RE / ve (7)
Equation (5) was then used to find the quality
factor. Because RC was
known, to get a certain gain, gm should be calculated and forced in
the circuit. Because
gm
= 40IC (7)
it was found that by choosing a collector current,
the gain could be imposed. Assuming β
is large for both transistors, this current was forced by using a voltage
divider network with R1, R2, and R3, giving a
voltage at the emitter of the common-emitter transistor and choosing RE such
that the current is equal to one-fortieth of the desired value for gm. The exact values of R1, R2,
and R3 were determined by choosing a desired current through this
network.
For the local oscillator, a
common-base Colpitts network was used.
A general common-base Colpitts oscillator is shown in Figure 5. A feedback network is connected between the
collector and emitter of the BJT. The
capacitors are used in voltage-divider format to divide the output of
oscillation at the collector to about 3 Volts peak-to-peak, the optimum level
for the mixer input. The mixer load can
be measured once the operating point has been chosen for the mixer but can be
assumed to be fairly small, probably between 200 and 500 ohms. A loop gain of 2 to 3 is needed for steady
oscillations and should be achieved.
Ideally, a peak-to-peak voltage of 2Vcc should be developed at the
collector. Because Vcc was 15 Volts (V)
for this project, approximately 30 Volts was expected during optimal
oscillation. However, the actual value
for oscillation at the collector was 21 to 24 V peak-to-peak, due to the fact
that some of the voltage was lost due to RE and Remitter,
a resistor used to maintain a sinusoidal waveform.
The frequency of oscillation
is given by
fLO
= fRF + fIF (9)
Given the inductor value, the total equivalent
capacitance Ceq can be found from equation (2). To find C1 and C2, two
equations can be used. Assuming 21 V
peak-to-peak at the collector and desiring three volts across C2
gives, from voltage division,
21C1
/ (C1 + C2) = 3 (10)
The capacitors are considered as being in series for
purposes of the tuned circuit, so
C1C2
/ (C1 + C2) = Ceq (11)
These two equations were
used to determine the capacitor values.
Despite calculation, however, the tolerances in the capacitors and the
low load of the mixer required exact tuning of the circuit to be performed at
construction. Remitter, C1,
and C2 were adjusted to provide optimal output.
Figure 5. General Common Base
Colpitts Oscillator Circuit.
Mixing is based upon the
mathematical principle of the multiplication of two sinusoidal waves. Let f(t) = cos ω1t and g(t)
= cos ω2t. Then the
product f(t)g(t) is given by
f(t)g(t)
= cos ω1t cos ω2t
= ˝ cos (ω1 + ω2)t + ˝ cos (ω1
- ω2)t (12)
This shows that multiplication of two sinusoidal
waveforms gives a wave containing the sum and the difference frequencies. Thus, a nonlinear device which produces the
product of two waveforms (the RF amplifier and local oscillator outputs) can be
used as a mixer.
A JFET was used in the mixer
circuit, a general version of which is shown in Figure 6. The signal from the local oscillator is
represented by source V1 and the signal from the RF amplifier is
represented by V2. The
operating point can be set by choosing the source resistor RS. The equation governing the relationship
between the drain current ID and the gate-source voltage VGS
is given by
ID
= IDSS ( 1 – VGS /VP )2 (13)
This equation is nonlinear and thus produces the
product of the two waves, giving components with the sum and difference
frequencies. A tuned circuit can be
used to dampen the undesired components, leaving the difference frequency, the
intermediate frequency, as the output.
This equation and the obvious fact that
ID
= -VGS / RS (14)
give two equations in two unknowns. IDSS and VGS are
properties of the transistor and were measured before RS was chosen.
Figure 6. General Mixer Circuit.
Because R1 is not connected to Vcc, the
bias voltage at the source is zero regardless of the choice of R1. This can be chosen to be large to present a
large load resistance to the RF amplifier circuit. From equation (13), it can be seen that IDSS is the
current when the gate-source voltage is zero.
Thus the source and gate can be grounded and power applied to the
drain. The current through the source
is IDSS. A negative voltage
source can then be applied to the gate.
Beginning at zero volts, this source can be set continually more
negative until no current flows through the source. The negative voltage at which source current is zero is the
pinch-off voltage VP from equation (13).
The current-voltage characteristic
of the JFET is an increasing exponential curve with an equation given by
equation (13) between voltage values of VP and zero. Thus, a good point to bias the JFET for
maximum signal swing is the point at which VGS = ˝ VP. Placing this number into equation (13) gives
the corresponding value for ID.
Because the voltage at the gate is zero, the resistance of the source RS
to secure this operating point is given by
RS
= -VGS / ID (15)
This completes the circuit design of the mixer. The conversion gain of the mixer is given by
the following equation:
Conversion
Gain = Output Voltage at fIF / Input Voltage at fRF (16)
The conversion gain is limited by the quality factor
of the tuned circuit at the drain of the JFET.
A cascode network was used
for the design of the IF amplifier first stage. The value of the parallel equivalent resistance of the inductor
at the intermediate frequency was measured at the intermediate frequency in an
experiment similar to that for the inductor used in the RF amplifier. The amplifier design methods were very
similar to those used for the RF amplifier.
Like the RF amplifier, the IF amplifier was designed to give
approximately 30 dB of gain (100 V/V).
The IF amplifier second
stage was a common-collector emitter follower, designed to buffer the IF
amplifier from the lower input resistance of the demodulator. The circuit was designed to achieve a gain
close to the maximum common-collector gain of 1 and to present a large load
resistance to the IF amplifier.
The demodulator is used to
take its input signal, amplitude modulated at the intermediate frequency, and
demodulate it, passing only the envelope, which is the audio signal, to the
audio amplifier. This circuit is simply
a diode followed by a lowpass filter.
An AM signal with message x(t) is given by the equation
Xc(t)
= Ac[1 + μx(t)] cos ωct (17)[7]
where Ac is the carrier wave amplitude,
μ is the modulating index, and ωc is the angular frequency
of the carrier wave. Thus the
modulating signal “rides” on the positive and negative sides of the carrier
wave.
A general demodulator
circuit is shown in Figure 7. The diode
is used to provide nonlinearity, which results in several frequency components,
including a component at baseband. A
low pass filter follows the diode, removing all components except the baseband
component, which is the message. The
coupling capacitor allows the message to pass to the audio amplifier. A coupling capacitor blocks the DC component
of the signal, de-biasing the message.
The signal is then sent to the audio amplifier. The pole of the low pass filter was placed
at 20 kHz to allow all audible frequency components to pass. A capacitor can be chosen and the resistor
can be calculated using the following equation:
fp
= 1 / 2πRThC (18)
where fp is the pole frequency and RTh
is the Thevenin equivalent resistance seen at the terminals of the
capacitor.
Figure 7. General Demodulator Circuit.
The audio amplifier used for
this circuit was based upon a LM386 operational amplifier. This op-amp is designed to be operated on a
lower power supply and only has one power input of approximately four to eight
volts. The op-amp has a maximum gain of
20 V/V but can achieve higher gains if a coupling capacitor is connected
between pins one and eight. However, a
gain of 20 V/V was used with the configuration shown in Figure 8. The output of the op-amp is biased at half
of the power-supply voltage, so a large coupling capacitor must be placed at
the output to avoid forcing the op-amp to produce a large amount of current to
produce the DC component of the output voltage across the small load of the
speaker. A potentiometer controls the
input to the non-inverting op-amp and can be used as a volume control.
Figure 8. Audio Amplifier with LM386 Op-Amp.
Simulations were performed
on PSPICE for the RF amplifier, the local oscillator, the mixer, and the IF
amplifier. For the RF amplifier, the
designer is interested in finding the center frequency, the center-frequency
gain, and the 3-dB points. Therefore,
an AC analysis was used, showing the output on a linear scale and using cursors
to measure points of interest.
For the local oscillator,
the main features that needed to be seen in the simulation were the frequency
and peak-to-peak voltage of the waveform.
It was also desired to obtain a pure sine wave through adjusting the
resistance between the feedback-loop return point and the transistor emitter. Thus it was necessary to perform a Transient
Analysis on PSPICE, adjusting the time scale to view the sine wave
clearly.
The main characteristics
that needed to be obtained from the mixer simulation were the frequency content
of the output and the voltage level of the intermediate-frequency output
component relative to the RF input.
Finding these characteristics allows the simulated conversion gain to be
computed. A Transient Analysis was
used, allowing the output waveform to be seen in the time domain, and with use
of the Fast Fourier Transform feature, the frequency-domain output was also
viewed.
The IF amplifier simulation
was performed by taking an AC Analysis in a manner similar to the RF amplifier
simulation.
V. DESCRIPTION OF DESIGN
The RF amplifier, complete
with design values is shown in Figure 9.
The RF amplifier was designed for a gain of 100. Using equation (2) and choosing a 100
microhenry inductor, the necessary capacitance for a resonant frequency of 970
kHz was found to be approximately 270 picofarads (pF). The measured resonant frequency for this
tuned circuit was approximately 1013.5 kHz, so a capacitance of 297 pF was used
for the quality factor measurement.
Using the process described in the above section, the parallel
equivalent resistance of the tuned circuit resulted in a parallel equivalent
resistance of 14,457.14 ohms and a quality factor of 23.918.
It was decided that the design would aim for 3 volts at the emitter of Q2, 5 volts at the emitter of Q1, and a current of 1 mA through the voltage divider network that is connected to the transistor bases. Assuming a base-emitter voltage of 0.6 for the transistors, values of R1 = 9.4 kilo-ohms, R2 = 2 kilo-ohms, and R3 = 3.6 kilo-ohms were obtained.
Figure 9. RF Amplifier Circuit With Design Values.
The voltage gain, equal to gmRC
= 40ICRC, was set equal to 100 and RC was set
equal to the parallel equivalent resistance of the tuned circuit. Because the output resistance ro
of the transistor was not taken into account, the actual gain was lower than
designed. The value necessary for IC
was found to be 0.1729 milliamperes (mA). This condition was forced upon the circuit by choosing the
emitter resistor of Q2 to be equal to 3/ 0.0001729 because the
voltage at this point is 3 volts due to the voltage divider network. The value obtained for the emitter
resistance was 17,351 ohms.
The designed local
oscillator is shown in Figure 10. Using
equation (9) and the knowledge that the frequency of the desired RF signal is
970 kHz and the intermediate frequency, as a standard, is 455 kHz for AM
broadcast, gives the frequency of the local oscillator as
fLO
= fRF + fIF (9)
fLO = 970 kHz +
455 kHz = 1425 kHz
Using 1425 kHz as the resonant frequency and
choosing an inductor of 100 microhenries, the equivalent capacitance was
calculated from equation (2) to be 124.7 pF.
Also, a voltage of 21 V peak-to-peak was assumed to be existent at the
collector and 3 V peak-to-peak was desired at the oscillator output. Using equations (10) and (11), two
expressions in two unknowns were obtained:
124.7
pF = C1C2 / (C1 + C2)
3 =
21C1 / (C1 + C2)
Solving these equations simultaneously, it was found
that C1 = 145.53 pF and C2 = 873.18 pF. The value of RE was chosen based
on the premise that approximately four times the power necessary to be
delivered to the mixer load (4 times the output voltage divided by the mixer
resistance squared) should be input to the circuit from the power supply
(measured by Vcc times the collector current.
However, this resistance was calculated for a previous local oscillator
design but was not altered when the design was changed. The local oscillator was found to still work
satisfactorily and this change was not necessary.
Figure 10. Local Oscillator Circuit With Design Values.
The value for Remitter was
determined by adjusting a potentiometer to obtain a sinusoidal waveform at
approximately 3 V peak-to-peak at the output.
This potentiometer was adjusted on a cut-and-try basis. After the waveform was determined to be
satisfactory, the value of the potentiometer was measured and a resistor
replaced the potentiometer in the circuit.
The mixer circuit with
design values is shown in Figure 11. A
3819 JFET was chosen for this mixer.
The output from the RF amplifier was injected into the gate, while the
local oscillator output was injected into the source. A large resistance of 1 mega-ohm was used for the gate resistance
to provide a large load resistance to the RF amplifier. The resistance Rp was placed in
the schematic to represent the equivalent parallel resistance of the inductor
at 455 kHz. An inductor valued at
approximately 100 microhenries was chosen, and a capacitance of 1187.901 pF was
calculated using equation 2 to complete the 455 kHz tuned circuit. This tuned circuit is present in an attempt
to dampen other frequency components so that the IF component is the strongest
at the input of the IF amplifier, which is connected to the output of the
mixer.
Figure 11. Mixer Circuit with Design Values.
To begin the operating-point
design, the characteristics of the 3819 JFET were measured. Using the techniques outlined in the
previous section, it was found that IDSS = 6.110 mA and VP
= 3.07 V. To set the operating point at
VGS = ˝ VP, it was found from the mixer characteristic
equation of equation (13) that the drain current ID = 1.5275
mA. To achive this drain current, the
source resistor RS was chosen using equation (15) to be 1004.910
ohms, or approximately 1 kilo-ohm. It
is important to note that the mere choice of this resistor determines the
operating point.
The IF Amplifier with design
values is shown in Figure 12. Like the
RF Amplifier, the IF Amplifier was designed for a gain of 100. The first stage was designed for 3 V at the
emitter of the Q2, 5 V at the emitter of Q1, and 1 mA
through the voltage divider network at the transistor bases. Unlike the RF Amplifier, the output
resistance ro of the transistor was measured with the curve tracer
as 18,500 ohms and taken into account in the design by setting the collector
resistance equal to the equivalent inductor resistance in parallel with ro. The measured results, as expected, were
more accurate.
Figure 12. IF Amplifier Circuit With Design Values.
Using RC =
6510.42 || 18,500 = 4815.70, because the gain is equal to gmRC,
the necessary collector current was found to be 0.5191 mA. Because 3 V exists at the emitter of Q1
and assuming that β is large, the necessary value for RE was
found to be 5678.59 ohms.
For the emitter follower
used as the second stage, the DC voltage divider network of R6 and R7
was designed to conduct a current of approximately 0.01 mA. This allows the load resistance of the first
stage to appear large regardless of the actual load resistance presented by the
demodulator. As stated in the above
section, the highest possible gain of the common collector circuit is one. This occurs when the value for AC emitter
resistance is large. RE was
chosen as 10 kilo-ohms so that it would not substantially lower the value of
emitter resistance when a small load resistance is attached.
The demodulator circuit with
design values is shown in Figure 13.
The low pass filter consisting of C1 and R1 was
designed for a pole frequency of 20 kHz.
A 1 microfarad capacitor was used for the coupling capacitor C2. A is a coupling capacitor to prevent A capacitor value of 1 nanofarad (nF) was
chosen and the Thevenin resistance value seen by this capacitor was calculated
using equation (18). A Thevenin
resistance value of 7957.74 ohms was calculated. The Thevenin resistance seen by C1 is simply R1||R2. R2 was used as 100 kilo-ohms at
the time the calculation was made; however, a value of about 2 to 3 kilo-ohms
would have been more appropriate.
However, at this time, it was not known that the volume control
potentiometer would be placed at this location and that a lower load value
would be sufficient for correct operation.
The use of 100 kilo-ohms for R2 gave R1 = 8645.75
ohms.
Figure 13. Demodulator Circuit With Design Values.
The audio amplifier was
designed just as shown in Figure 8, with Rspeaker = 8 ohms. A gain of 20 in the op-amp was found to be
sufficient to drive the 8 ohm, 0.5 watt speaker, as the power through the
speaker is given by the following formula:
P =
V2 / Rspeaker
0.5
= V2 / 8
V =
2 V rms
An RMS voltage of 2 V gives a necessary signal
peak-to-peak voltage of 5.66 V to run the speaker at rated load. The amplifier was powered by 6 volts, a
theoretically sufficient voltage to avoid cutting off the signal. A 5 kilo-ohm potentiometer was used for the
variable Rpot, varying the input signal level and thus serving as a
volume control. Because the 3819 op-amp
automatically biases the output signal at half of the supply voltage, a 470
microfarad capacitor was connected between the op-amp and the speaker to
prevent the speaker from drawing DC current.
Without this capacitor, the voltage supply had to be lower because of
the large current used, causing the signal to distort.
A complete schematic of the
AM superheterodyne receiver design is given as Appendix A at the conclusion of
this report. The values shown in the
schematic are the actual values used for the parts and may differ slightly from
the parts shown in the above graphs.
For example, capacitance values were often changed at the testing to
improve tuning.
The antenna used for this
experiment was an approximately 15 foot strand of 10 AWG machine tool wire. This wire was stretched out and attached to
the input to the circuit. A
quarter-wave antenna, though optimal, is not practical for an AM receiver; its
length would be approximately 300 feet.
A tuned circuit tuned to 970 kHz was placed at the input of the system
to remove stray interference such as local oscillator interference.
VI. MEASURED AND SIMULATED RESULTS
Measurements were taken on
each individual system as it was constructed.
Finally, the system was integrated and measurements were taken simply to
check proper operation. For the RF
amplifier, measurements of center frequency, center frequency gain, and 3-dB
attenuation points were taken. From
these measurements, it was possible to compute the bandwidth and the quality
factor of the amplifier. Key
measurements and their discrepancies with simulated values are shown in the
table of Figure 14. A probable reason
for the discrepancy in center-frequency gain is that the output resistance ro
of the transistor was not taken into account when designing for a gain of
100. Consequently, both the measured
and simulated gains were lower than 100.
A possible reason for the difference is that the parameters for the
Q2N3904 transistor in PSPICE may not have been identical to those of the
transistor used in the circuit. The
quality factor and center-frequency gain measurements were reasonably close to
simulation results. A PSPICE graph from
the AC analysis is included in Appendix B.
|
Category |
Simulated |
Measured |
Percent Discrepancy |
|
Center
Frequency (kHz) |
964.045 |
974.3 |
1.064% |
|
Center Freq. Gain (V/V) |
91.997 |
87.188 |
-5.227% |
|
Bandwidth (kHz) |
41.573 |
43.4 |
4.395% |
|
Quality Factor |
23.189 |
22.45 |
-3.187% |
Figure 14. Measured and Simulated RF Amplifier Results.
For the local oscillator,
the parameters of interest are the frequency of oscillation and the
peak-to-peak voltage of the output waveform.
A comparison of simulated and measured values for the local oscillator
is given in the table of Figure 15. A
probable reason for discrepancies is that the measurements were taken from a
circuit that had been improved during the testing the process to account for
non-ideal factors. This was a necessary
step because proper operation of the local oscillator is critical to obtaining
a properly functioning device.
|
Category |
Simulated |
Measured |
Percent Discrepancy |
|
Freq.of
Oscillation (kHz) |
1375.516 |
1423 |
3.45% |
|
Output
Voltage (V p-p) |
3.251 |
3.060 |
-5.88% |
Figure 15. Measured and Simulated Local Oscillator Results.
Mixer results were measured
by inputting the local oscillator at the local oscillator input and inputting
1.250 V peak from the function generator to the RF input. The mixer circuit for simulation is shown in
Figure 11 and a comparison of mixer measurements with simulation results is
shown in Figure 15. Discrepancies may
be due to the fact that the measurement techniques are difficult for the mixer
output, due to the fluctuations of the signal from the mixing of different
frequency components.
|
Category |
Simulated |
Measured |
Percent Discrepancy |
|
Conversion
Gain (V/V) |
0.827 |
0.704 |
-17.4% |
|
Center
Frequency (kHz) |
469.799 |
461.1 |
-1.892% |
Figure 16. Measured and Simulated Mixer Results.
The parameters of interest
for the IF amplifier (Figure 12) are the same as for the RF amplifier. A comparison of results is given in Figure
17. All percent discrepancies are
fairly small. Unlike the RF Amplifier,
transistor output resistance ro was taken into account in the design
procedure. As a result, the simulated
and measured gains were higher for the IF amplifier.
|
Category |
Simulated |
Measured |
Percent Discrepancy |
|
Center
Frequency (kHz) |
454.546 |
459.7 |
1.134% |
|
Center
Freq. Gain (V/V) |
106.108 |
109.36 |
3.065% |
|
Bandwidth
(kHz) |
21.718 |
21.2 |
-2.385% |
|
Quality
Factor |
20.929 |
21.88 |
4.544% |
Figure 17. Measured and Simulated IF Amplfier Results.
Figure 18. RF Amplifier Output.
Following design of these
four major components and the demodulator, the system was integrated and
tested. After the audio amplifier was
added and a working system was achieved, measurements were taken of signal
levels and frequencies throughout the circuit.
For the RF Amplifier, the output peak-to-peak voltage was measured as
1.05 V. A picture of the 970 kHz
amplitude-modulated signal at the output of the RF amplifier as seen on the
oscilloscope is shown in Figure 18.
During system operation, the
local oscillator output was measured at 3.064 Volts peak-to-peak at
approximately 1430 kHz. The local
oscillator output as measured by the oscilloscope during complete system
operation is shown in Figure 19.
Figure 19. Local Oscillator Output.
The mixer was seen to
produce an output of 692 millivolts (mV) during system operation, yielding a
conversion gain of 0.659 (-3.622 dB).
The mixer output is a combination of several frequency components. The most prominent are the 455 kHz
difference component and the 1425 kHz local oscillator feedthrough
component. The mixer output is shown in
Figure 20.
Figure 20. Mixer Output.
The IF amplifier output is
shown in Figure 21 and demonstrates that most of the other frequency components
have been removed by filtering, leaving the 455 kHz component as the
predominant component. The frequency of
the output was measured to be 467 kHz, with a peak-to-peak voltage of 7.32
Volts.
Figure 21. IF Amplifier Output.
The output wave of the
demodulator is shown in Figure 22. The
455 kHz carrier has been removed, leaving only the message envelope. This message was found to have a
peak-to-peak voltage of 4.80 Volts. The
output of this was fed to the audio amplifier, whose output (to the speaker) is
shown in Figure 23. Notice that
amplification occurs between the demodulator output and the audio amplifier output. Some saturation is also observed in the
audio amplifier output, however, the signal is still easily intelligible and a
pattern can be readily observed in the graph.
Figure 22. Demodulator Output.
Figure 23. Audio Amplifier Output to the Speaker.
VII. COST ANALYSIS
A key component in the
design of a system is the cost of production.
A cost analysis has been performed on the AM superheterodyne receiver to
determine the cost of producing one unit and the cost of producing one thousand
units. A table given in Figure 24 shows
the quantities of the different components used in the construction of the
device and the costs per unit and any special bulk quantity costs that may
exist.
|
Part Type |
Cost |
No. per Unit |
Bulk Rate (if applicable) |
Cost for One Unit |
Cost for 1000 Units |
|
Resistor |
$4.99/50, $5.99/100 |
29 |
$11.99/500 |
$4.99 |
$695.42 |
|
1 uF Coupling Capacitor |
$7.92/10 |
19 |
$396/1000 |
$15.84 |
$7524.00 |
|
470 uF Electrolytic Capacitor |
$0.69 |
1 |
$173/1000 |
$0.69 |
$173.00 |
|
Other Capacitor (Assorted Values) |
$3.99/100 |
14 |
|
$3.99 |
$558.60 |
|
Inductor (100uH RF Choke) |
$0.99 |
4 |
|
$3.96 |
$3960.00 |
|
Inductor (1 mH) |
$3.75 |
1 |
$1011/1000 |
$3.75 |
$1011.00 |
|
2N3904 Bipolar Junction Transistor |
$0.21 |
6 |
$176.00/5000 $47.52/1000 |
$1.26 |
$223.52 |
|
Potentiometer (Volume Control) |
$0.80 |
1 |
|
$0.80 |
$800.00 |
|
3819 JFET |
$1.60 |
1 |
|
$1.60 |
$1600.00 |
|
LM386 Op-Amp |
$0.74 |
1 |
$123.75/500 |
$0.74 |
$247.50 |
|
22 AWG Wire |
$3.36/225ft |
3 feet |
|
$0.05 |
$47.04 |
|
10 AWG Machine Tool Wire |
$61.67/1000ft |
15 feet |
|
$0.93 |
$925.05 |
|
0.5W,8ΩSpeaker |
$3.00 |
1 |
|
$3.00 |
$3000.00 |
|
Proam Breadboard |
$25.00 |
1 |
|
$25.00 |
$25,000.00 |
|
Total Costs |
|
|
|
$66.60 |
$45,765.13 |
Figure 24. Cost Analysis.[8]
The cost analysis indicates
that the price of producing one unit is $66.60. This may initially seem a bit expensive for an AM receiver, but
major factors in this price are the cost of all the coupling capacitors
necessary for the system to run properly and the breadboard, which together
comprise 61.32 percent of the cost.
Producing the product in a quantity of 1000 reduces the cost per unit to
$45.77, a substantial difference. The
cost could be decreased massively by soldering the parts together instead of
using a breadboard; a breadboard alone costs $25.00. Taking these ideas into consideration, this receiver is
definitely economically feasible.
VII. SOCIETAL AND ENVIRONMENTAL IMPACT
Edwin Armstrong devised the
superheterodyne receiver for military applications in an attempt to create a
more clear reception of high-frequency signals.[9] The devising of this new method for
receiving signals allowed the use of higher frequencies for frequency
modulation (FM) transmission and other applications that now function in the
higher-frequency bands. This has had a
tremendous impact upon society because it opened the door for the introduction
of applications such as FM radio (which requires a wider transmission
bandwidth) and cellular phones. Most
importantly, it allowed more frequencies to be effectively utilized, an
important concept because of the many applications that fill the airwaves.
The impact upon society of
this design project is that an AM receiver has been created that is fixed to a
news-radio station. Through this
design, listeners can hear updates on news, weather, and traffic; all events that
affect the everyday lives of people across the world. This radio device will help to make the world a smaller place,
allowing the transfer of information over a distance. It can also be used for leisure, as the station to which it is
tuned carries baseball games on a regular basis. This receiver could also receive critical emergency broadcast
messages in times of crisis.
If this project ceased to
function correctly, it would mean that the user would be less in touch with the
world and the events that daily surround him.
It could also be disastrous in the case of emergency, if this were the
person’s only radio. Radio is a
critical part of today’s communication system and personal radio systems must
be working properly for that communication system to remain intact.
As far as environmental
impact is concerned, this device does not pollute the environment by using
gasoline, but is powered by electricity.
The use of rechargeable batteries for this device should be easily
possible, reducing waste due to battery disposal.
VIII. CONCLUSIONS AND RECOMMENDATIONS
The device designed works
incredibly well, receiving an amplitude-modulated signal at 970 kHz and
outputting the message through a speaker in audio form. The output is very clear and distinguishable
and can be easily heard over the noise floor.
The level of the volume is controllable by a potentiometer, making the
system user friendly. The output of the
IF amplifier is over 7 volts peak-to-peak; this indicates incredible reception
and amplification. All parts of the
system worked as expected and very closely to their designed behavior. The system has met the specifications that
were set forth at the beginning of the project, providing a fully functional
superheterodyne receiver.
One of the critical
components to this design was that operating points of amplifier circuits
should be designed for maximum signal swing.
This is critical because message information is lost any time saturation
or cutoff occurs within the path of the message, causing distortion in the
audio output. For a cascode amplifier,
the best approach is to allow 3 volts at the emitter of the transistor that is
connected to ground through a resistor, minimizing the effects of a change in
base-emitter voltage on the operating point while maximizing the output that
can be produced without distortion.
A couple of recommendations
exist for improving the design. The
first is that the design of the buffer amplifier that serves as the second
stage of the IF amplifier be modified to provide 12 volts at the emitter
instead of 3 volts. This is because
this circuit is connected in the common collector configuration, and placing a
larger operating point at the emitter of the circuit could allow for a larger
signal swing. However, the fact that
the amplifier was designed for 3 volts at the emitter was not a detriment to
the success of the project. The second
suggestion for improvement would be to design a higher resistance at the
voltage divider network of the IF amplifier, providing a larger load resistance
to the mixer output and creating a larger conversion gain. Once again, however, the load resistance of
approximately 1 kilo-ohm that was used did not seem to be detrimental to the
project’s success.
The superheterodyne AM
receiver is a milestone in the world of communications theory; it is a concrete
example of how communications theory can be implemented and effectively used to
produce clear wireless communications.
IX. REFERENCES
Carlson, A. Bruce, Crilly, Paul B., and
Rutledge, Janet C. Communication
Systems: An Introduction to Signals and
Noise in Electrical Communications, Fourth Edition. New York:
McGraw-Hill, 2002.
World Wide Web Location: http://www.digikey.com
World Wide Web Location: http://www.econowire.com
World Wide Web Location: http://www.oselectronics.com
World Wide Web Location: http://www.radioshack.com
Krauss, Herbert L., Bostian, Charles W.,
and Raab, Frederick H. Solid State
Radio Enginering. New York: John Wiley and Sons, 1980.
Sedra, Adel S. and Smith, Kenneth C. Microelectronic Circuits, Fourth
Edition. New York: Oxford University Press, 1998.
X. APPENDIX A – COMPLETE CIRCUIT DIAGRAM
XI. APPENDIX B – SIMULATION RESULTS
RF Amplifier Simulation – AC
Analysis
Local Oscillator Simulation
(Transient Analysis)
Mixer
Simulation (FFT Function after Transient Analysis)
IF Amplifier Simulation (AC Analysis)
