University of Central Florida STARS Retrospective Theses and Dissertations 1986 Phase-Locked Loop Based Oscillator Phase Noise Measurement Technique Luis M. Jimenez University of Central Florida Part of the Engineering Commons Find similar works at: https://stars.library.ucf.edu/rtd University of Central Florida Libraries http://library.ucf.edu This Masters Thesis (Open Access) is brought to you for free and open access by STARS. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of STARS. For more information, please contact [email protected]. STARS Citation Jimenez, Luis M., "Phase-Locked Loop Based Oscillator Phase Noise Measurement Technique" (1986). Retrospective Theses and Dissertations. 4980. https://stars.library.ucf.edu/rtd/4980 PHASE-LOCKED LOOP BASED OSCILLATOR PHASE NOISE MEASUREMENT TECHNIQUE BY LUIS MIGUEL JIMENEZ B.S.E., University of Central Florida, 1984 THESIS Submitted in partial fulfillment of the requirements for the degree of Master of Science in the Graduate Studies Program of the College of Engineering University of Central Florida Orlando, Florida Summer Term 1986 ABSTRACT Oscillators play an important role in the performance of various radio frequency (RF) systems. The generation of stable carrier and clock frequencies is necessary at both the transmitter and receiver ends of a communication system. Phase noise is the parameter used to characterize an oscillator frequency stability. This thesis introduces a phase noise measurement technique using a phase-locked loop. A 100 MHz Colpitt's oscillator, for the phase noise source, was designed and built. The output of the oscillator was mixed down to 10 MHz, before a phase-locked loop extracted the phase noise information. Measurements were taken and compared to measurements taken at RF frequencies using an HP spectrum analyzer. Finally, a fee~back phase noise model was derived, such that oscillators can be designed with phase noise being a design parameter. ACKNOWLEDGEMENTS I would like to acknowledge and thank the people who have contributed to the thesis. Frist, I would like to dedicate it to my parents for their love and support through the years. I would like to express my appreciation to the members of my committee for their corrections and time spent evaluating the thesis. Special thanks to my advisor, Dr. M. Belkerdid, whose help and suggestions were crucial to the development of the thesis. I would also like to express my gratitude to Carl Bishop, Jeff Abbott, and Gary Morrissette for their contributions. Finally, a special thank you to my wife, Charlotte, for her patience and understanding. iii TABLE OF CONTENTS LIST OF FIGURES . vi Chapter I. INTRODUCTION 1 II. NOISE IN AN OSCILLATING SIGNAL . 3 An ideal oscillating signal . 3 Real oscillating signals . 4 Components of frequency stability . 6 Definitions . 7 III. REPRESENTATIONS OF PHASE NOISE IN THE FREQUENCY DOMAIN: SPECTRAL DENSITIES . 9 Phase and power spectral densities . 9 Fractional frequency fluctuations . 10 Spectral density of frequency fluctuations 12 Spectral density of fractional frequency fluctuations . 12· £(f) spectral density . 12 Relation between £(f) and s . 13 0 IV. PHASE NOISE MEASUREMENTS . 16 Importance of phase noise measurements . 16 Random noise corrections . 18 Measurement techniques . 20 V. 100 MHz OSCILLATOR DESIGN 23 Oscillator Analysis 23 Oscillator design . 29 Results . .. 33 VI. PLL MEASUREMENT TECHNIQUE DESIGN AND IMPLEMENTATION . 37 System design . 37 Mathematical analysis 42 Calibration . 45 Measurements and results . 48 iv VII. A FEEDBACK MODEL FOR OSCILLATOR PHASE NOISE 53 Noise in amplifiers . 53 Feedback model of phase noise . 57 Phase noise design considerations 59 VIII. CONCLUSION 62 Appendices A. OSCILLATOR DESIGN FORMULAS . 64 B. PROGRAMS LISTINGS 67 C. AUTOMATED PHASE NOISE SYSTEMS 70 REFERENCES . 74 v LIST OF FIGURES 1. Ideal oscillating signal . 4 2. Components of frequency 5 3. £(f ) definition . 13 m 4. Effect of high level sidebands . 17 5. Phase noise effect on a QPSK system 17 6. Frequency discriminator system . 22 7. Phase quadrature system 22 8. Colpitt•s oscillator . 24 9. Equivalent transistor model 25 10. Equivalent oscillator model 25 11. Colpitt•s tank circuit . 28 12. Colpitt's ideal transformer equivalent . 28 13. Oscillator equivalent output circuit . 30 14. Oscillator DC circuit 32 15. Colpitt•s final circuit configuration 34 16. Time domain output . 35 17. Frequency domain output 36 18. Phase noise measurement system . 37 19. Normalized third-order Butterworth . 38 vi 20. LPF magnitude response . 39 21. PLL circuit schematic 40 22. Local oscillator spectrum 43 23. Oscillator spectrum 44 24. Calibration system . 46 25. RF phase noise spectrum result . 50 26. Audio spectrum of demodulated output . 51 27. PLL measurement result . 52 28. Amplifier noise spectrum 54 29. Model for a noise free amplifier . 55 30. Phase deviation at f + fm 55 0 31. Amplifier phase noise model 56 32. Phase noise feedback model . 59 33. Power-law processes of oscillator phase noise. 60 vii CHAPTER ONE INTRODUCTION The increasing use of the electromagnetic spectrum requires the need for very accurate and stable frequencies. Phase noise is the term used to describe frequency stability. It is because of this phase noise that many microwave and RF systems offer a limited performance. Poor resolution in radar, interference in communications, and bit error rate degradation in phase modulated systems are some of the results of high levels of phase noise. Nevertheless, phase noise is a term sometimes misunderstood due to the light coverage of the subject in most engineering books. For information on the phase noise concept one must resort to the specialized literature such as Hewlett-Packard application notes, National Bureau of Standards technical notes, and IEEE publications. Phase noise will be introduced in this paper by starting with the basic concepts of an oscillator signal, such as the phase-frequency relationship, by characterizing the components of stability, and by its definition. Since phase noise is represented in the frequency domain as a 2 spectral density, four different but related spectral densities will then be developed. Random noise measurements require some corrections that are not necessary for deterministic signals; these corrections will be explained. Next, the three most common phase noise measurement techniques will be introduced. These techniques are: Direct RF Spectrum measurement, Frequency Discriminator, and Phase Quadrature Detection. Before measurements can be made a source of phase noise, an oscillator, is needed. For this purpose a 100 MHz Colpitt's oscillator will be designed in a step-by-step, detailed manner. This oscillator output will be mixed down in frequency so that a phase-locked loop extracts the phase noise information. This new phase noise measuring method will be introduced in this thesis along with the required calibration of the system used. The results will be compared to measurements taken using the direct RF technique. A key element in the design of clean oscillators is the Q factor of the resonator circuit. A feedback phase noise model will be derived from which a relationship for Q will be obtained. This will give the designer a phase noise parameter to be used in the design of oscillators. CHAPTER TWO NOISE IN AN OSCILLATING SIGNAL An Ideal Oscillating Signal An ideal oscillating signal can be represented by the sine wave shown in Figure l. The period "T" is the time it takes to complete one oscillation cycle. The frequency "f" is the reciprocal of the period, or the number of cycles per second. The phase "<I>" is the angle within a cyle corresponding to a time "t," and it is given in radians by t <I>= 2n­ T which can be written as <I>= 2nft 4> = wt ( 2. l) The voltage "V" is given by V(t) = v sin2nft ( 2. 2) p From Figure l, and equation (2.l) = w that is, for a given ~<I> and ~t there is a sine wave with an unique frequency "w" (in radians per second). 3 4 In the limit as At-+ O def> = w. (2.3) dt 1. This relationship defines the instantaneous frequency as the time derivative of the phase. 2n T-----~ Figure 1. Ideal oscillating signal. Real Oscillating Signals An ideal oscillator produces a pure sine wave carrier having a fixed frequency, constant phase, and constant amplitude. Oscillators used in practice, however, are non ideal and contain frequency instabilities and phase and amplitude noise. The instantaneous frequency of an oscillator can be considered to have three basic components: a constant or designed value (w ), a randomly varying frequency (wr(t)), 0 5 and a slowly varying drift component (at) . These components are shown on Figure 2. All these frequency deviations from the nominal or designed frequency are undesirable and are considered noise. To account for the noise components, equation (2.2) will have to be modified V(t) = [v +e(t)]sin[2nf t+0(t)] (2.4) 0 0 where v = nominal peak amplitude 0 e(t) = amplitude noise f 0 = nominal frequency 0(t) = phase noise t Figure 2. Components of frequency. 6 Components of Freguency Stability From the previous section, and working towards a definition of phase noise, it is clear that it would be advantageous to characterize three components of stability. The first component includes those frequency shifts due to changes in the environment such as temperature, pressure, and gravity. The second component includes those slow changes in frequency, such as those due to aging. This is called long-term stability, and it is expressed in parts per million of frequency change per hour, day, month, or year. These two components are important in certain applications, but with proper design, such as a feedback loop to correct for the slow drift in frequency, or the use of compensating capacitors for the temperature changes, most of these effects can be eliminated or minimized.