ECE 401L COMMUNICATIONS LABORATORY
LAB 4: Crystal Oscillator and Frequency Multiplier
1. Objective
Oscillators are an essential part of most communication systems. In this lab, students will build
and test an oscillator circuit using both an LC feedback path and a crystal. Students will design
the oscillator for a specific frequency of oscillation. Students will also construct and test a
frequency multiplier circuit and design it for a specific output center frequency. A frequency
multiplier can be used to change the frequency of a fixed oscillator and to convert a narrowband
FM signal into a wideband FM signal (effectively increasing its modulation index or frequency
deviation).
2. Background
2.1 Noise Driven Oscillator
An oscillator can be made by starting with an amplifier. If we add positive feedback, oscillation
is possible. Consider the example of holding a microphone next to a public address (PA) system
speaker. The PA provides the amplifier and the speaker to microphone path provides the positive
feedback. The system will oscillate at the frequency where the fed-back signal as it enters the
amplifier is in phase with the output signal. Thus, the feedback path system controls this. Noise
or some initial signal with energy at this frequency as all that is needed to get oscillations started.
Consider the circuit shown in Fig. 1. This is a class A single-stage transistor amplifier that you
should be familiar with from Electronics, plus a positive feedback path. The feedback path
consists of an L, C, and the input resistance of the amplifier and parasitic (stray) resistance and
capacitance (possibly stray inductance, but not much). So basically it is a series RLC circuit.
Based on simple phasor analysis, the output of the RLC will be in phase with the input when the
impedance of the feedback path is real (no phase). The feedback path impedance is given by
Z = R + jω L +
1
= R+
jω C
This is real when
ω=
1 

j ω L −
.
wC 

1
.
LC
(1)
(2)
White noise (containing all frequencies) from natural and man-made sources initially picked up at
the amplifier input is enough to start the oscillations. How do you think R affects the oscillator
performance? If you think of the feedback path as a BPF, what is the Q value? Note that here
phase is more important than gain (although the feedback gain + amplifier gain must be > 1).
However the “small” phase region of our frequency response corresponds to the pass-band
region. So a small pass-band generally means a narrow small-phase window.
A crystal can be put into the feedback loop in lieu of the RLC. A crystal can be modeled as a
type of RLC circuit. What is nice about a crystal is that the Q is very high (e.g. 80,000). This
means the circuit will only oscillate in a VERY narrow window of frequencies. That is, there is
R. C. Hardie, Department of Electrical and Computer Engineering,
University of Dayton, Fall 2003
1
only a small window of frequency where the output of the crystal will be close to the phase of the
input and have sufficient amplitude to maintain oscillation.
2.1 Frequency Multiplier
In some cases, it is helpful to be able to multiply the frequency of a signal. A typical frequency
multiplier outputs a sinusoidal signal at an integer multiple of the input signal fundamental
frequency. This can be used, for example, to increase the modulation index of an FM signal. By
outputting a frequency multiplied FM signal, the frequency deviation is increased
correspondingly. Thus, a narrow band FM signal can be converted into a wideband FM signal.
The frequency multiplier we will construct is shown in Fig. 2. This circuit generates an output
signal near the resonant frequency of the LC circuit ( nω0 = 1/ LC ) when the input is near a
frequency of ω0 . Harmonics of the input signal are generated by the transistor amplifier portion
of the circuit (operating somewhat in its nonlinear region). The harmonic near the resonant
frequency of the LC circuit dominates at the output due to the LC circuit. The output of the
frequency multiplier goes through a DC blocking capacitor and into a band-pass limiter. The
band-pass limiter is designed to “clean up” the frequency-multiplied signal.
3. Prelab Assignment
•
Based on the characteristic curves attached for a generic 2N2222 BJT (hFE=130.5), design
the biasing circuitry for the Class A amplifier in Fig. 1 (assuming no feedback). Use
VCC=12V, VCE= 6V, Ic = 4mA and Ib = 31uA as the quiescent (Q) point. See
Appendices A and B to help you complete your design.
•
Design the feedback path in the circuit in Fig. 1 so that the circuit oscillates at
approximately 130kHz. Select values available in the lab (see website or Lab 3). Don’t
forget about the DC blocking capacitor (you may let C2 = .1 µ F).
•
Design the circuit in Fig. 2 to pass a frequency multiplied output of 130kHz. Select
values available in the lab (see web site or Lab 3).
4. Procedure
4.1 Oscillator
If the curve tracer is available in laboratory, plot and record the characteristic curve for your BJT.
If it is significantly different from the generic curve used in the prelab, you will need to redesign
your biasing circuitry for an appropriate Q-point. Once you are satisfied with your biasing
circuitry design, construct the oscillator in Fig. 1.
1. Observe the oscillation at the output (after the DC blocking capacitor) on the
oscilloscope, in both the time and frequency domains. Using a high impedance probe
so that we do not change the operation of the oscillator by changing the impedance of
the feedback path too much.
2. Explain in your own words why the circuit oscillates in your write-up.
R. C. Hardie, Department of Electrical and Computer Engineering,
University of Dayton, Fall 2003
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3. Record the frequency of oscillation. Is it what you expected?
4. If the oscillation frequency is not what you expected, calculate the effective stray
capacitance (taken to be in series with C in the circuit above), assuming that the
inductance L is unchanged from your design value. What do you think is the source
of the stray capacitance?
5. Is the oscillation a clean sinusoid? What harmonics can be seen in the frequency
domain? What are their relative power levels?
6. Move your hand near and/or touch the LC circuit. What happens to the oscillation
frequency? (Remember: your body has capacitance and this is a low Q circuit.)
7. Replace the LC combination with a crystal. From your handouts you will recall that
crystals are equivalent LC circuits with Q’s of nearly 80,000. With this in mind,
repeat questions 1-6 and explain the differences in the crystal oscillator and the LC
oscillator schemes.
Document all your results in your report for this section and provide printouts of all important
time domain signals and frequency domain spectra.
Figure 1: Basic class A amplifier with positive feedback forming a noise-driven oscillator.
R. C. Hardie, Department of Electrical and Computer Engineering,
University of Dayton, Fall 2003
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Figure 2: Frequency multiplier circuit.
4.2 Frequency Multiplier Circuit
Construct the frequency multiplier circuit shown in Fig. 2 using your design values. Use a choke,
rather than regular inductor in the frequency multiplier circuit. For safety, you will also need to
power the frequency multiplier portion of your circuit your circuit with a 9V battery, due to the
high current possible with this circuit at resonance. Now apply a simple sinusoidal input to the
multiplier circuit and answer/perform the following questions and exercises:
1. What happens if your input frequency is greater than the final output frequency you
have designed your circuit for?
2. While monitoring your output signal on an oscilloscope, you will notice as you
reduce your input frequency that periodically the signal strength will increase in
voltage level. At these frequencies, the output is an integer multiple (i.e., harmonic)
of the input. Try to see how low you can choose your input frequency and still see an
appreciable output.
3. Does the output frequency ever change?
4. Compare the signals at the input and output of the band-pass limiter.
5. Provide interesting time and frequency domain plots in your lab report for all parts
above.
R. C. Hardie, Department of Electrical and Computer Engineering,
University of Dayton, Fall 2003
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You are now to use your frequency multiplication circuit with a tone modulated FM input signal.
For such FM modulation, the bandwidth of the modulated signal can be given by Carson’s rule
which states that BW = 2fm(1+ β ), where BW is the bandwidth of the tone modulated FM signal,
fm is the frequency of the modulating tone and β is the modulation index. With this in mind,
answer/perform the following questions and exercises:
NOTE: Since we are using only a single pole BPF in the band-pass limiter circuit, above, for FM
modulation the benefit of using the limiter circuit is lost, due to amplitude distortion. This is
because we must have an absolutely flat frequency response over the bandwidth of the FM
modulated carrier at the output of the frequency multiplier circuit. With β =3 (see below) this
will require a flat response over a bandwith of about 20kHz, which is impossible using a single
pole filter. For the following questions, then, disconnect the band-pass limiter and use the output
directly from the frequency multiplier circuit.
1. Choose a carrier frequency such that the output of your multiplier is the third
harmonic of the input. Set the modulation frequency to any convenient value; I used
fm = 3 kHz.
2. Determine how many side-lobes one would expect if the tone modulated FM
modulation index were one?
3. Using your signal generator, establish an FM signal with a modulation index of 1 and
provide a frequency domain plot of your result. Now apply this to your frequency
multiplier circuit and observe the output. Make a frequency domain plot of your
output and demonstrate that the modulation index and carrier frequency have both
been multiplied by three. How does the measured bandwidth of your multiplied
output and that expected from Carson’s Rule with β =3 compare.
5. Lab Write-up
Create a Word document organized according the numbered procedure sections. Provide screen
captures with detailed descriptions and answers to the questions posed in the lab next to the
appropriate procedure section.
Bonus Question: Who invented the first transistor and how did it work? Hint: check out
http://www.pbs.org/transistor/
R. C. Hardie, Department of Electrical and Computer Engineering,
University of Dayton, Fall 2003
5
APPENDIX A: Generic 2N2222 Characteristic Curve
R. C. Hardie, Department of Electrical and Computer Engineering,
University of Dayton, Fall 2003
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APPENDIX B: Biasing a BJT Amplifier
Below is the most widely used biasing scheme in general electronics. For a single stage amplifier
this circuit offers the best resilience against changes in temperature and device characteristics.
Here R1 and R2 form a potential divider, which will fix the base potential of the transistor. The
current through this bias chain is usually set at 10 times greater than the base current required by
the transistor. The base emitter voltage drop of the transistor is approximated as 0.6 volts. There
will also be a voltage drop across the emitter resistor, Re, this is generally set to about 10% of the
supply voltage. The inclusion of this resistor also helps to stabilize the bias: If the temperature
increases, then extra collector current will flow. If Ic increases, then so will Ie as Ie = Ib + Ic.
The extra current flow through Re increases the voltage drop across this resistor reducing the
effective base emitter voltage and therefore stabilizing the collector current.
Ve = 0.1 * Vcc (rule of thumb)
Vc = Ve+Vce (Vce from Q-point)
Rc = (Vcc-Vc) / Ic (Ic from Q-point)
Ie = Ib + Ic as Ic >> Ib then Ie ~ Ic
Re= Ve / Ie
Vb = Ve + 0.6
R2 = Vb / (10 * Ib) (Ib comes from Q-point, or from Ic/hFE)
R1 = (Vcc-Vb) / (10 * Ib)
R. C. Hardie, Department of Electrical and Computer Engineering,
University of Dayton, Fall 2003
7