Circuit Analysis of a Colpitts OscillatorPresented by:, Ryan Jolly, Santana Padilla, Kadeja Salem, and Audrey Whitesell

PHY 212 002, Spring 2020

Background

Voltage controlled oscillators were commonly found in radios before the 1990s, when

digital systems became more popular. While voltage controlled oscillators are not

widely-used in radios today, they still apply a key aspect of Physics II material, circuits,

to the real world.

Idea and Purpose

The idea of this project was to build and test a Colpitts voltage controlled oscillator

(VCO) frequency modulated (FM) radio and conduct circuit analysis on the VCO. The

purpose was to understand circuits better while expanding past the circuit analysis

studied in the classroom. Data collected was primarily related to frequency to

demonstrate the influence of individual components and how frequency plays a role in

circuits.

Build and Design

Due to the availability of parts, the design had to be modified to only include the

Colpitts VCO and not include the other radio components. Since there are slight

variations in the Colpitts design, two circuit diagrams were referenced before the final

design could be built. With limited components, the final design (far right) allowed for

frequencies that could be measured in testing. The frequency generating circuit, ‘tank’

circuit, consists of L1, C2, and C3.

Two inductors were wound by hand using 22 AWG copper wire for the initial

design that allowed for variation in inductance for the final design. One main

breadboard (far right, middle) was used to hold all components that would not vary

and the capacitors that would vary (C2 and C3), one inductor breadboard was used

to quickly vary inductance (far right; top), and one resistance breadboard was used

to vary R3 (far right; bottom).

Testing and Theoretical Calculations

Theoretical calculations were calculate en masse using a Google Docs spreadsheet equipped with the two rightmost equations, as well as those for percent error.

Testing involved cycling through every combination of two inductor values, five R3 values, and six values for C2 and C3 (collectively). Certain combinations involving R3=542 and R3=9820 generated unmeasurable frequencies; the lower inductance also did not always generate measurable frequencies.

R3 VE VB VC

47 2.97 3.64 6.60

67 3.57 4.23 6.84

86 3.93 4.60 7.03

542 5.44 6.08 7.66

9820 5.87 6.44 7.84

Testing showed that the value of R3 had significant impact on the test point voltages, which means that the value of R3 can greatly influence the effectiveness of the BJT PNP. It should be noted the excessive voltage at VE of R3=542 and R3= 9820.

Initial design Final design

Testing Images

Circuit Diagrams

Data

For Experimental Frequency (Hz) vs. Total Capacitance, notice the overall downward trend as capacitance increases. Here, a third dimension is introduced by allowing the red data points to represent the lower inductance and the black the higher inductance.

For Percent Error vs. R3, there is a narrowing downward trend, preference for higher R3. Note that for some combinations, the highest two values for R3 did not generate measurable frequencies. A log base ten scale is used for the horizontal axis..

Analysis and Conclusion

Even though limited facilities and materials were available for testing, a key trend was able to be identified. As the value of R3 was increased and the percent error calculated, a strong inverse correlation was found. As noted in the voltage test point table, when R3 increased, so did the voltage going out of VE and the voltage going into VB. Without further investigation, it is expected that this causes the BJT PNP to effectively regulate current flow, allowing for the tank frequency module (L1, C2, and C3) to generate the expected frequencies.

Future teams could isolate the BJT PNP for exclusive testing that might explain a correlation between R3 and the voltage going into VB which allows for current to enter the tank circuit.

Bibliography

No Author. “The Colpitts Oscillator.” Electronics Tutorial. Web. Retrieved from: No Author. “Experimenting with Colpitts Oscillators.” MakeRF. Web. Retrieved https://www.electronics-tutorials.ws/oscillator/colpitts.html from: https://makerf.com/posts/experimenting_with_colpitts_oscillators“Activity: The Colpitts Oscillator.” Web. Retrieved from: No Author. “Voltage-Controlled Oscillator.” OpAmps Second Edition. 1996. Web. https://wiki.analog.com/university/courses/electronics/comms-lab-colpitts-osc Retrieved from: “Colpitts Oscillator Practical Project.” Web. Retrieved from: https://www.sciencedirect.com/topics/engineering/voltage-controlled-oscillator https://learnabout-electronics.org/Oscillators/osc24.php Dutton. “Using Oscillators to Generate FM Signals.” Stanford University. Web. Nicholas Jon Stave. “Analysis of BJT Colpitts Oscillators - Empirical and Retrieved from: https://web.stanford.edu/class/ee133/handouts/labs/lab2osc.pdf Mathematical Methods for Predicting Behavior.” Marquette University. Web. Jojo. “Colpitts Oscillator.” Circuits Today. 2018. Web. Retrieved from: Retrieved from: http://www.circuitstoday.com/colpitts-oscillator https://epublications.marquette.edu/cgi/viewcontent.cgi?article=1556&context “VOLTAGE-CONTROLLED OSCILLATOR FOR FM BROADCAST RADIO RECEIVER”Retrieved =theses_open from:https://www.eit.lth.se/fileadmin/eit/courses/eti041/VT2011/04a.pdf