9 PRINCETON UNIVERSITY PHYSICS 104 LAB Physics Department

9 princeton university physics 104 lab -------------------------------------- physics department week #12 experiment xi buil

9
PRINCETON UNIVERSITY PHYSICS 104 LAB
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Physics Department Week #12
EXPERIMENT XI
BUILD AND SIGNAL-TRACE AN AM RADIO CIRCUIT
If you have a set of headphones with a 1/8” stereo plug (the most
common type), please bring it with you to Lab to listen to your AM
radio.
Introduction.
Like the transistor amplifier lab (Lab 10), this Lab goes beyond the
material that you learn in lecture and class. You will use your
knowledge of electronic circuits to construct an AM radio and
understand how it works.
The term “radio” includes both the broadcast and reception of an audio
signal, whose frequencies are between about 100 and 10,000 Hz. An
immediate difficulty is that direct broadcasting of electromagnetic
waves of these relatively low frequencies is not very practical, in
large part because antennas must be roughly one wavelength long to be
efficient. What is the wavelength of a 100 Hz electromagnetic wave?
Usable broadcasting of electromagnetic waves involves frequencies of
0.5 MHz or higher. The challenge is to superimpose an audio-frequency
signal on a “carrier” frequency MHz. One way of accomplishing
this is via amplitude modulation, the principle of AM radio
broadcasting. In its simplest form, the audio frequency signal is
multiplied by the carrier wave, . For the case when the signal
is a pure audio tone of angular frequency , the product of the
two frequencies can be written as

using a trig identity. Because the carrier frequency is much larger
than the audio frequency , the result of the multiplication is
a combination of two high-frequency signals. If we passed this
waveform through a low-pass filter, say with characteristic angular
frequency , nothing would emerge since the waveform contains
only high frequencies. It is not sufficient for the radio receiver to
amplify the signal – you cannot hear the high frequencies that it
contains. Rather, the radio receiver must demodulate the AM signal,
revealing the audio-frequency information that has been shifted to
high frequency by the modulation.
Demodulation cannot be performed by linear circuit elements alone (i.e.,
by resistors, capacitors, inductors in which oscillatory voltages and
currents are related by a generalized Ohm’s law, , or even by
linear amplifiers in which is independent of frequency). These
devices do not change the frequency of a signal, whereas an AM radio
receiver must transform the high-frequency modulated signal in a
low-frequency audio signal. A radio receiver must contain at least one
nonlinear device. The simplest nonlinear circuit element is a diode,
which you have studied in Lab 10. And indeed, a basic AM radio can be
made using a diode, although the way in which the diode demodulates
the AM signal is quite sophisticated.
The lefthand side of the figure below shows a modulated signal, which
has the form of eq. . The diode rectifies this waveform, meaning
that it transmits only the positive portion of the wave, as shown on
the right of the diode in the figure.

The rectified signal now has low-frequency content, as can be verified
by passing it through a low-pass filter. A hint that the waveform on
the right in the figure above has low-frequency content, while the
waveform on the left does not, is that the average of the waveform on
the right is nonzero there is a zero-frequency component.
However, the period of the rectified signal is one half the period of
the period of the audio signal, and so the rectified signal has twice
the desired frequency. If the signal were the voice of a person, the
effect would be humorous at best.
To be able to extract an audio signal of the proper frequency from the
modulated wave, the modulation is performed by first adding an offset
to the audio signal, and then multiplying it by the carrier wave. For
the example of an audio signal of angular frequency , an
appropriately modulated waveform is

This waveform and its diode rectification are shown in the figure
below. Now the period of the rectified signal is the same as that of
the audio signal, as desired.

An AM radio transmitter implements the scheme of eq. , as shown in
the figure below. Since the modulation circuit results in a change of
frequencies, it cannot be built using only linear circuit elements,
but we do not pursue this further here.

The earliest form of radio transmission did not use amplitude
modulation. Rather, the carrier wave was turned on and off at
intervals corresponding to the “dashes” and “dots” of Morse Code; no
voice signals were transmitted. AM radio came into use only around
1920, following the development of the diode vacuum tube. The
commercial AM radio band is between 500 and 1600 kHz. Only 10 kHz is
allotted to each radio station. Since the modulation requires use of
frequencies both higher and lower than the carrier frequency, the
maximum allowed audio frequency is only 5 kHz, which is too
restrictive for high-quality sound reproduction. To overcome this
limitation, new radio bands were created at higher frequencies and
with larger bandwidth. And to provide better sound quality, another
type of modulation, FM = frequency modulation, was developed for use
with these new radio bands.
The rest of this Lab focuses on understanding of an AM radio receiver.
The job of such a receiver is to
1.
Receive the high frequency signal (often called the RF or radio
frequency signal) with an antenna.
2.
Select the desired carrier frequency (“tune” to the desired radio
station).
3.
Detect the signal using a diode to restore low-frequencies to the
modulated RF signal.
4.
Amplify the diode-rectified signal.
5.
Filter out the audio frequency part of the rectified signal with a
low-pass filter for clearer sound. (Steps 4 and 5 could be
reversed.)
In previous Labs this semester you have built circuits that perform
each of these functions separately. In this Lab you combine them to
build a working AM radio. Besides listening to your radio, you will
use an oscilloscope to examine the signal at each stage.
This Lab differs somewhat from previous Labs in that the emphasis is
on making a device work, rather than on a program of measurements.
This Lab is therefore the most representative of how experiments
actually proceed, since in most cases much more effort is spent in
making a new apparatus work than in taking data with that apparatus.
1. I Can’t Believe That This is a Radio.
On your lab bench is a small Radio Shack amplifier/speaker with two
wire leads. Connect these leads to the leads of the antenna (whose
wires extend outside the lab). Turn on the amplifier via the
thumbwheel, and you should hear a faint mixture of signals from
several radio stations.
How can this be? The Radio Shack device is labeled “amplifier” not
“radio”.
Indeed, if the Radio Shack amplifier were a high-quality linear
amplifier it would not act like a radio. But this low-cost amplifier
is rather nonlinear in its behavior, and a nonlinear circuit element
is essential for a radio receiver. Hence, a poor amplifier can act as
a radio receiver, and part of the “noise” of such an amplifier is
pickup from radio stations.
2. Antenna + Diode
Connect the antenna leads to a circuit that contains a 1N34A germanium
diode (with diode drop of only 0.2 V), as shown in the figure below.
Build the circuit on a “breadboard”.

Is this a better of worse radio than that of part 1? Does the
direction of the diode make any difference to the performance of this
receiver?
3. Add a Tuner
To isolate the signal from a single radio station, your receiver
should include a kind of “bandpass” filter that can be tuned to any
desired central frequency. Among the basic circuits that you have
studied, an LC resonant circuit is best suited for this task. Recall
that the resonant angular frequency of an LC loop is where L is
the inductance and C is the capacitance of the circuit elements. We
desire that Hz to tune on AM radio stations.

Build a parallel-plate capacitor out of two brass bars, separated by a
piece of index card. By sliding the upper bar with respect to the
lower bar, you can vary the capacitance of your capacitor, which will
provide the tuning of your receiver.
Use the solenoid with turns of fine wires as the inductor
for your resonant circuit.
The problem now is how to couple the antenna to the resonant LC
circuit. An elegant way to do this is to attach the antenna to the
second inductor coil, which has turns and which slides over the
first inductor to form a transformer. Then, you obtain an
amplification of the voltage of the antenna signal according to the
law of an ideal transformer (p. 6 of Lab 7),

when inductor i has turns. Furthermore, a limited amount of
tuning can be obtained by sliding one inductor with respect to the
other. Try it.
However, the primary tuner for your AM receiver is the capacitor. How
many different radio stations can you detect by sliding one bar of the
capacitor relative to the other?
To tune on one radio station while rejecting the signal from an
adjacent channel would require a resonant circuit whose resonance
curve has a full width at half maximum of only 10 kHz. The quality of
the tuning circuit is a major factor in the overall quality of a
radio.
4. Add Your Own Amplifier
Tune the radio of part 3 to the strongest station you can find, and
replace the Radio Shack amplifier/speaker with your headphones, using
the headphone jack with two leads. Probably you won’t hear anything.
The signal is too weak.
To be able to hear the radio signal on your headphones, build the
version of a 2N2222 transistor voltage amplifier shown below, which
attaches to the load resistor that is placed across the diode.

Do NOT connect the antenna to the ground of your amplifier circuit.
Use the transformer!
This is the same circuit that you built in Lab 10, with only minor
variations. The bias voltages for the transistor Base still involve a
10:1 voltage divider, but the resistor values have been multiplied by
10, which helps the diode to perform more like an ideal diode. Also,
the resistor connected to the Emitter now has a
capacitor in parallel, which improves the performance of the amplifier
at high frequencies. If you have time, compare the performance of the
circuit without the capacitor and with the Base bias resistors
having values and .
If you have constructed your amplifier correctly, you should be able
to hear, somewhat faintly, the radio signal in your headphones now. If
not, there may be a problem with the circuit, and you may wish to jump
ahead to part 6 = circuit diagnostics with scope and wave generator.
5. Add a Low-Pass Filter
The performance of your circuit can be improved slightly by adding a
simple RC low-pass filter, as shown in the figure below.

6. Circuit Diagnosis with a Wave Generator and Oscilloscope
It is almost impossible to build a circuit as complicated as the one
above such that it works correctly on the first try. Rather, it is
helpful to have a step-by-step set of checkout procedures to verify
that one part of the circuit is working before constructing the next.
Here we sketch a possibly useful set of tests of pieces of the
circuit, which also may teach you a bit more about how those
subcircuits work.
Your breadboard has the flexibility to accommodate most of these tests
with minimal disruption to the wiring of the rest of the circuit.
6a. The Diode
Connect the output of the Wavetek generator to test points a and b
shown on the lower figure on p.6, and use “tee” to send a copy of the
output to Ch 1 of your oscilloscope. Set the output frequency to about
1 MHz to simulate a radio carrier wave, and set the amplitude to about
1 V so that you will have no trouble seeing the effect of the signal.
Connect the 10X scope probe to Ch 2 of the scope, connect the probe
tip to test point c, and connect the probe ground to test point b
(where the probe ground should remain for all subsequent tests). The
scope display of Ch 2 should be a clipped off version of the input
signal on Ch 1. If not, there is trouble with your diode. The clipped
signal from a working diode may be less perfect than textbook
illustrations! This is a nonlinear device.
You may wish to reverse the diode in the circuit to see what happens.
The Wavetek generator has an additional feature that is very useful in
simulating an AM radio signal. Near the center of the control panel is
a push button labeled amplitude modulation ON/OFF. Press this button
to ON. The scope display on Ch 1 should now look something like the
lefthand side of the lower figure on p. 2. You can adjust the
modulation depth with the knob just to the left of the ON/OFF button.
The modulated signal is still a high-frequency signal, as described by
eq. , which contains information about a low frequency that the rest
of your circuit should be able to detect, when it is working.
For subsequent tests, you can switch back and forth between the pure
sine wave and the modulated sine wave as you find useful.
6b. The Transistor Base
The rectified waveform at testpoint c extends from ground to some
maximum (or minimum) voltage. But testpoint d will have a DC level of
about 1.5 V if the 15 V power supply is turned on. So when checking
out testpoint d, you should use Ch 2 of the scope on both AC and DC to
verify that the signal is as expected. Of course, the AC signal at
testpoint d should be the same as that at testpoint c.
6c. The Transistor Emitter
The DC level at testpoint e, the transistor Emitter, should be about
0.8V. The AC signal at this testpoint should be very similar to that
at testpoints c and d.
6d, The Transistor Collector
The DC level at testpoint f, the transistor Collector, should be about
10 V. The AC signal at this point should be about 10X that at
testpoints c, d and e if the amplifier is working properly.
6e. The Circuit Output
Turn on the amplitude modulation of the Wavetek generator for these
finals tests.
Testpoint g should show the same AC signal as at testpoint e, but with
no DC level. The AC signal here should still show the 1 MHz
oscillations within the halfwave form due to the rectification of the
diode.
The waveform at testpoint h is a low-pass filtered version of the
waveform at testpoint g, and hence the high-frequency oscillations
should be gone now.
If all these tests are successful, remove the input from the Wavetek
generator, and you should be able to hear (perhaps rather faintly) the
radio signal in your headphones, when they are connected to testpoints
h and b. If the tests were successful but the headphones still sound
quiet, substitute the Radio Shack amplifier/speaker for the
headphones. You may need to tune your capacitor (and also the pair of
inductors) to maximize the signal.
Connect your headphones to testpoint g to hear the unfiltered signal.
Do not connect your headphones to testpoints d, e or f, as the DC
levels there could damage your phones.
6f. OPTONAL: The Effect of Overmodulation
This test is optional because it requires borrowing a 2nd Wavetek
generator from another lab station.
The goal is to verify that the conceptually simpler modulation scheme
described by eq. , and shown in the figure at the top of p. 2, is
undesirable.
To study this you need to generate a waveform like that on the
lefthand side of the figure at the top of p. 2. Borrow a 2nd Wavetek
generator and set its output frequency to about 1 kHz. Connect the
output of this generator to the AM Sweep input of the first generator.
Press the EXT button that is just to the left of the AM ON/OFF button.
The waveform from the 2nd generator now modulates the waveform of the
first (which latter should be set to about 1 MHz frequency).
While listening to the output of your amplifier on your headphones, or
with the Radio Shack amplifier/speaker, vary the amplitude of the
output of the 2nd Wavetek generator. You can view the effect of the
modulation on Ch 1 of the oscilloscope (which should still be
connected to the output of the first Wavetek generator via a “tee”).
“Overmodulation” begins when the “envelope” of the modulated signal
reaches all the way to the middle height of the signal, and even goes
beyond to create a waveform with a double peak structure.
The quality of the Wavetek generators is not sufficient to produce an
overmodulated signal exactly like that shown on the top of p. 2; the
modulations become somewhat “squarish” in the case of severe
overmodulation.
However, if you have a good ear, you can hear that the audio tone
becomes less pure as soon as any overmodulation is present, and that
the form of the impurity is the presence of the first overtone of the
audio signal (plus even higher overtones in the case of “squarish”
overmodulation). If the Wavetek generators were of higher quality, you
would hear the fundamental tone completely disappear in the case of
full overmodulation, and all you would hear is the first overtone.
The value of this Lab is in the process of making your radio work, so
record the details of this process in your Lab notebook. Verify with
your Lab partner that both of you can explain the process of amplitude
modulation and demodulation that are the bases of AM radio.
PRINCETON UNIVERSITY PHYSICS 104 LAB
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Physics Department Week #12
Name:_____________________________ Date/Time of Lab:_____________
EXPERIMENT XI PRELAB PROBLEM SET
1. The inductor consists of 100 turns of 37 mm diameter with a
total length of 58 mm. What is the inductance? You may consider to
inductor to be a long solenoid.
2. The variable capacitor is made from two brass bars of length 120 mm
and width 37 mm. They are to be separated by an index card whose
dielectric constant is unity, and whose thickness is such that 125
cards form a stack 1” high. What is the maximum capacitance C?
3. What is the lowest resonant frequency, in Hertz, of the tuning loop
that contains the inductor and the variable capacitor C?
4. What is the characteristic frequency, in Hertz, of the low-pass
filter shown on p. 6? Will the carrier wave of frequency MHz
pass this filter? Will a middle C tone (262 Hz) pass?