Physics 241 Lab – RLC Radios

Physics 241 Lab – RLC Radios
http://bohr.physics.arizona.edu/~leone/ua/ua_spring_2010/phys241lab.html
Name:____________________________
Section 1:
1. Begin today by reviewing the experimental procedure for finding C, L and resonance . This may
help you to do well on your lab practical. (Be sure to sign up for your lab practical time slot today.)
1.1. Reminder of how to measure an unknown capacitance C with an RC circuit:
The component voltage amplitudes of an RC circuit driven sinusoidally with angular frequency
drive are given by
V C,amplitude
C
Z V source,amplitude and V R,amplitude R Z V source,amplitude .
These component voltage amplitudes are equal when C
R. Substituting R C
1
drive
C and
solving for C gives
1
C
.
R 2 f drive
Remember this is only true when the voltage amplitude across the resistor is equal to the voltage
amplitude across the capacitor. Therefore, to find an unknown capacitance C, measure R and find the
driving frequency where V C,amplitude
V R,amplitude
. (No question.)
1.2. Reminder of how to measure an unknown inductance L with an RL circuit:
In an RL circuit driven sinusoidally with angular frequency drive ,
V L,amplitude
L
Z V and V R source,amplitude R,amplitude
Z V .
source,amplitude
These component voltage amplitudes are equal when L
R. Substituting R L
drive
L and
solving for L gives
R
L .
2 f drive
Remember this is only true when the voltage amplitude across the resistor is equal to the voltage
amplitude across the inductor. Therefore, to find an unknown inductance L, measure R and find the
driving frequency where V L,amplitude
V R,amplitude
. (No question.)
1.3. Reminder of how to measure the resonant frequency resonance of an RLC circuit:
In a sinusoidally driven RLC circuit, there is a driving frequency at which the current in the
resistor is maximized (i.e. absorbing the most power from the oscillating source). This happens when
the total circuit impedance Z R 2 L
C 2 is minimized. This occurs when L
C 2 0.
The driving frequency at which L
C
0 occurs is called the resonant frequency. This can
1
be found by setting C equal to L so that
drive
C L. Solving gives 1
drive drive
resonance L C . (No
question.)

1.4. A plot of current vs. driving frequency in an RLC circuit has a maximum at the resonant
frequency. This is useful because an RLC circuit can be tuned to a specific resonant frequency by
adjusting its C or L. If you lower the resistance of an RLC circuit and retake your measurements, the
resonant frequency won’t change (since L and C don’t change), but you will measure a higher quality
factor:
The smaller the resistance, the sharper this peak gets. This is useful because an RLC circuit
with low resistance only “reacts to” frequencies very near resonance while ignoring other driving
frequencies. A radio can be made using a low-resistance RLC circuit that responds only to a specific
radio frequency electromagnetic wave. How could you make the peak as sharp as possible in an RLC
circuit for use in a radio? Take the resistor out so that only the tiny resistance of metal wires is present.
(No question.)
1.5. Reminder of how to observe f resonance using an oscilloscope:
The most accurate way to find f resonance is to utilize the fact that at resonance, V R (t) and V source (t)
are exactly in phase with each other with equal amplitudes. You should place each of these voltages
on your oscilloscope channels and examine an XY formatted display. The resonance frequency is
easily found because you will see an ellipse when V R (t) and V source (t) are out of phase and a diagonal
line when they are in phase. You see a straight line when they are in phase because both voltages must
reach zero simultaneously.
(No question.)
Section 2: Modulating High Frequency Waves
with Low Frequency Waves
2.1. Imagine that you want to transmit the following
sound wave from one solenoid (the transmitter) to
another solenoid (the receiver). The two solenoids are
not connected in any way so that the oscillating
magnetic field inside one solenoid must be made to
oscillate within the other solenoid to utilize Faraday’s
Law.

Unfortunately, this wave is alternating much too slowly to induce a large voltage in the
receiving solenoid. Remember the equation for mutual inductance, V induced
dI circuit 1
M 1 to 2
, where
in circuit 2 dt
M is a constant that describes how much the solenoids overlap. If the current doesn’t oscillate rapidly
enough, then V induced
in circuit 2
is very small.
“Gee, I wish this wave oscillated more quickly to cause a bigger induced voltage in the
receiving solenoid,” you might say. But then it wouldn’t be the same sound pitch that you wanted to
hear in the first place! Still, it sounds like something you would say. (No question.)
2.2. Next examine a wave that oscillates quickly, radio or slightly sub-radio frequency for example.
This isn’t the frequency you want to hear (you are not able to!), but it does oscillate so quickly
as to create a large induced voltage in the receiving solenoid. I.e., it oscillates quickly enough to be
transmitted into the receiving circuit through the mutual inductance of the “transformer” (overlapping
solenoids).
2.3. The solution is to combine the two waves by multiplying them together. This modulated wave
has the properties of both waves: it carries information about the audio frequency component and it
oscillates quickly enough to generate a highly induced voltage in the receiver circuit.

The modulating wave (or envelope wave) is the low frequency oscillation while the high
frequency oscillation is often called the carrier wave.
2.4. Why are we interested in using a low frequency envelope wave in today’s lab?
Your answer:
2.5. Why do we need to use a rapidly oscillating carrier wave in today’s lab?
Your answer:
2.6. In today’s lab, we would like to transmit a modulated sound wave transmitted by one solenoid
into another “receiving” solenoid. We will use a capacitor in the second “receiving” circuit to make an
RLC “receiving” circuit. By changing the capacitor of the “receiving” circuit, we can adjust its
resonant frequency. Therefore, we will be able to “tune” our “receiver” to a particular radio frequency.
Now you would like to listen to your transmitted wave. But there is a huge problem.
Whenever the wave is positive, it causes an upward force on the speaker, and whenever it is negative it
causes a downward force on the speaker. The modulated wave is oscillating up and down with the
rapid radio frequency, much too fast for the speaker to respond to. It just sits there quivering.
The trick is to add a diode to the output. Remember that a diode is a quantum mechanical
component that only allows current to flow in one direction once a turn-on voltage has been reached
(determined by the semiconductor band gap energy). This will allow only positive voltage to reach the
speaker.
The speaker now gets pushed out a maximum distance at the maximum amplitude of the pulse and
relaxes at the minimum.
2.7. Would you be able to hear the speaker if the direction of the diode in the circuit was reversed?
Explain your answer? Your answer and explanation:

Section 3: Now you will experimentally use a sound wave to modulate a radio frequency wave.
Never insert the speaker directly into your ear without first verifying that the sound level is safe.
The basic set-up provided consists of two solenoids wound together (to be perfectly
overlapping) and a diode-speaker connector:
Clean your ear-speaker with alcohol. Set your function generator to 3,600 Hz. Connect your
function generator to the speaker/diode connection of your double-solenoid board as shown below
(PVC pipe with wound red wire, only looks like one solenoid but is really two wound together).
3.1. Slowly increase the output voltage until you can hear the signal. Ask for help if you have any
doubts about the proper operation of these devices. Find the upper end of the frequency range of
your hearing. It may be significantly less than your classmates if you are older or have suffered
hearing loss due to loud noises. Also note any intermediate ranges of hearing loss. Do these
frequencies correspond to the kinds of music you listen to (too loudly)? Record your measured
range(s) of hearing:
f max,sound = ___________________Hz
3.2. What frequency makes the speaker diaphragm vibrations resonate, i.e. what is the resonant
frequency that makes the speaker the loudest? There may be more than one resonant frequency for
your speaker since it is a complex mechanical system.
Your observed speaker resonant frequency(s):
f resonance,speaker = ___________________Hz

3.3. Now input an audio-frequency signal of 1,000 Hz from your function generator into your RF
modulator. Use a carrier radio-frequency wave of 500,000 Hz to create a modulated output wave of
1,000 Hz envelope waves surrounding a 500 kHz high frequency wave. What are the periods for these
two kinds of oscillations in the output modulated wave? Your answer:
T audio = ________________ s
T RF = ________________ s
Examine the output of this signal on your oscilloscope at two time ranges so that you can see
the audio-frequency signal and the radio-frequency signal separately. To do this, choose a seconds per
division setting for the time axis that is appropriate for the time scale of the wave you wish to examine
(i.e., use the wave’s period). You may need to press the “run-stop” button to view the wave packets if
they appear smeared out on the oscilloscope.
Sketch the appearance of the modulated wave at the audio frequency scale and then the radio
frequency scale, and record the time scales used to observe the waves. Notice that the RF generator
does not necessarily produce a clean RF output as was discussed earlier in this handout. Be sure you
can hear the envelope waves of the modulated signal.
Make sketches of the modulated wave and record the time-scale used:
Radio Frequency
Audio Frequency

Section 4: Now you will use a sound wave to modulate a radio frequency wave, then use mutual
inductance to transmit the radio frequency wave to a separate RLC circuit, and finally listen to the
sound wave.
4.1. First determine the inductances L A and L B of your solenoids using the methods described in
part 1. In other words, for each solenoid create an RL circuit driven sinusoidally and monitor the
voltage across the resistor and inductor as you vary the driving frequency. Use the appropriate
equation to solve for the inductance L. Even with the 10 resistor, you will need to use large driving
frequencies as these inductances are very small.
Your measured inductances:
4.2. Input the audio signal at f resonance,speaker from your function generator into your RF modulator
initially set to f RF = 550,000 Hz. Use the following sketch to set up your circuit. We will refer to the
solenoid connected to the RF modulator the “transmitter” and the solenoid connected to the speaker the
“receiver”. The variable capacitor component represents the capacitance you choose to use.
4.3. Calculate the resonant frequency f resonance for your receiver solenoid in series with a 0.001 F
capacitor. Your calculated resonant frequency:
4.4. With your capacitor box set to 0.001 F, use your oscilloscope to measure the voltage signal
being received across the speaker. Adjust f RF until your transmitted signal is in resonance with the
receiving circuit and record this f RF, resonance . You will see this as maximizing the signal sent to the
speaker. Some students can perform this part of the experiment searching for RF resonance by hearing
when the transmitted signal is the loudest. This occurs when L,receiver = C,receiver in your receiving
circuit. Compare this to your result in 4.3. Your measured resonant frequency and comparison:

Section 5: Write directly onto the figure below to completely explain how this compound circuit(s)
works. You can use labels, text and arrows, and you do not need to write in complete sentences. Note
that the speaker is shown wired in parallel to the receiving RLC circuit rather than in series, but you do
not need to explain this particular feature. You will need to use equations described earlier in this lab
for full credit.

Section 6: Now you will replace the function generator used in part 4 of this lab with an antenna
attached to the outside of the building to detect radio frequency electromagnetic waves permeating the
surrounding atmosphere. Room noise must be kept to a minimum for success here.
6.1. Implement the following sketch.
6.2. Using the receiver inductance L receiver measured in part 4.1 and the three smallest capacitances
available to you, calculate the three resonant frequencies f resonant that you could detect with your
receiving RLC circuit using the smallest capacitors. Your calculated detectable radio wave
frequencies:
6.3. Change your receiver capacitance using single capacitors and series capacitors to detect AM
radio stations. The AM radio band is from 520 kHz to 1.61 MHz. Rely on the oscilloscope rather than
the ear-speaker to detect induced voltages in the receiving RLC circuit since it is unlikely you will be
able to hear the radio station. (Some students manage to barely hear the station in a very quiet room).
Record the frequency of any broadcast stations you find. Your detected radio station frequencies:
Report Guidelines: Write a separate section using the labels and instructions provided below. You
may add diagrams and equations by hand to your final printout. However, images, text or equations
plagiarized from the internet are not allowed!
Title – A catchy title worth zero points so make it fun.
Goals – Write a 3-4 sentence paragraph stating the experimental goals of the lab (the big
picture). Do NOT state the learning goals (keep it scientific). [~1-point]
Concepts & Equations – [~12-points].
Procedure & Results – Do not write this section. [~0-points]
Conclusion – Write at least three paragraphs where you analyze and interpret the results you
observed or measured based upon your previous discussion of concepts and equations. It is all
right to sound repetitive since it is important to get your scientific points across to your reader.
Write a separate paragraph analyzing and interpreting your results from your open-ended
experiment. Do NOT write personal statements or feeling about the learning process (keep it
scientific). [~7-points]
Graphs – None. [0-points]
Worksheet – thoroughly completed in class and signed by your TA. [~5-points]