Understanding RF Experiment 8

Experiment 8: The Colpitts Oscillator
Purpose and Discussion
The purpose of this simulation is to demonstrate the characteristics and operation of a
Colpitts oscillator. As is the case with other LC oscillators, the Colpitts oscillator is
used for higher frequencies, typically between 1 and 500 MHz. It is characterized by
the capacitive voltage divider made up of C 1 and C 2. This feedback voltage is used for
the oscillations. Colpitts oscillators can be designed using BJTs, FETs or JFETs. In
the design illustrated in Figure 8-1, the loading effect is greatly reduced as compared
to a BJT design due to the high input impedance at the gate.
As with other LC oscillators, the Barkhausen criteria must be met in order for
oscillation to take place. Specifically the gain from input to output must be one and
the net phase around the loop must be zero. In the design illustrated in Figure 8-1, the
JFET must exhibit an absolute value of open circuit voltage gain greater than or equal
to the ratio C 1 /C 2 in order to sustain oscillations. In other words, the gain of the JFET
must make up for the attenuation created by the feedback fraction:
B C 2
C Since AvB then Av 1 C1
= . = 1,
= =
1
B C2
In order to vary the frequency of oscillation, L 1 should be varied. If C 1 or C 2 were
chosen instead, the feedback fraction B would be affected.
Parts
DC 12 V Supply
Transistor: Ideal N JFET
Resistors: 1 kΩ, 120 kΩ
Inductor: virtual 60 µH, 5.1 mH
Capacitor: virtual 22 pF, 180 pF
Test Equipment
• Oscilloscope
• Spectrum Analyzer
Formulae
Frequency of Oscillation
fc =
2π
1
LCC
C + C
1 1 2
1 2
Equation 8-1
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38 Understanding RF Circuits with Multisim
Gain
Av = -g m r d
Equation 8-2
Condition for Oscillation
Av ≥
C
C
2
1
Equation 8-3
Procedure
Figure 8-1
1. Connect the circuit components illustrated in Figure 8-1.
2. Double-click the oscilloscope to view its display. Set the time base to 200 ns/Div
and Channel A to 10V/Div. Select Auto triggering and DC coupling.
3. Select Simulate/Interactive Simulation Settings, and select Set to Zero for Initial
Conditions.
4. Start the simulation. When the oscillator has stabilized, measure the frequency of
oscillation.

The Colpitts Oscillator 39
5. Compare with theoretical calculations:
f c = measured = calculated
6. Stop the simulation and place a Spectrum Analyzer on the workspace.
7. Connect the output lead of the oscillator to the input of the Spectrum Analyzer.
8. Double-click to open the Spectrum Analyzer window.
9. Press Set Span. Set Start = 10 kHz, End = 10 MHz, Amplitude = Lin and Range =
2V/DIV. Press Enter.
10. Restart the simulation. When the oscillation has stabilized, drag the red marker to
the position of the spectrum line observed. Note the frequency in the lower left
corner of the Spectrum Analyzer window:
f c =
11. Calculate L 1 necessary to achieve a frequency of oscillation of 8 MHz. Replace L 1
by double-clicking on it and selecting Replace. Run the simulation to verify your
calculation.
12. Given that g m = 1.6 ms and r d = 12 kΩ, determine whether oscillations will be
sustained.
Expected Outcome
Figure 8-2 Oscilloscope Display of Initial Colpitts Oscillator Oscillations
Additional Challenge
Re-design the circuit of Figure 8-1 choosing values of C 1 and C 2 so that Avβ = 10 and
the frequency of oscillation is approximately 3 MHz. Replace existing simulated
component values by double-clicking on the component of interest. Run the
simulation and compare the output data with expected theoretical values.

40 Understanding RF Circuits with Multisim