# Technical Papers

This site has many original technical articles written on a wide range of topics from * phase-locked loops* and

*to methods of computing*

**frequency synthesizers***and*

**square-roots***as found on this page. The papers are grouped by tab / subject matter below:*

**elliptic integrals**#### Communication Systems

“Multimode RF Transceiver Advances WEDGE Radio System,” J.A. Crawford, rf design, January 2007.

“Phase Noise Effects on Square QAM Symbol Error Rate,” J.A. Crawford.

Mathematical means for computing symbol error rate of QAM signal constellations with phase noise present.

“Translation Loop: Passing GMSK Modulation,” J.A. Crawford.

“Satellite Doppler with Type-3 PLL Tracking,” J.A. Crawford.

“Substantiation of Water-Filling Concept Using Lagrange Multipliers,” J.A. Crawford.

#### Digital Signal Processing

“Approximation for Root( I^{2} + Q^{2}),” J.A. Crawford.

“Computation of Square Roots,” J.A. Crawford .

“Optimum Eigenfilter Design Methodology,” J.A. Crawford.

“Computing Data Windows Recursively,” J.A. Crawford.

Discusses simple numerical means suitable for DSP implementation for computing Gaussian and Blackman data windows. Method can be easily extended to many other window types.

#### Frequency Synthesizer Design

Chapter 5 Excerpt from *Advanced Phase-Lock Applications- Frequency Synthesis*, J.A. Crawford.

“Charge-Pump Noise Models for PLLs,” J.A. Crawford.

“Extending Sampling to Type-2 Phase-Locked Loops- Part II,” J.A. Crawford, Microwaves, Sept. 1984 .

“The Misunderstood Phase/Frequency Detector,” rf design, J.A. Crawford, Feb. 1985.

“The Phase-Locked Loop Concept for Frequency Synthesis,” J.A. Crawford, 1987.

“Phase-Locked Loop Concept for Synthesis- Time Domain ,” J.A. Crawford, 1987.

“Effects of Small Contaminating Signals in Nonlinear Elements Used in Frequency Synthesis and Conversion,” W.F. Egan, July 1981 (Reprinted in Frequency Stability: Fundamentals and Measurement, 1983, IEEE Press.

“A GSM Modulator Using a Delta-Sigma Frequency Discriminator Based Synthesizer,” W.T. Bax.

“Phase-Locked Loop Phase Noise Assessment,” J.A. Crawford.

“PLL Basics- Loop Filter Design,” Fujitsu.

“Derivation of the Fractional-N Phase Noise Formula,” J.A. Crawford

#### Miscellaneous

“Potato Cannon with Arduino-Based Chronograph- Part II (Wrap-Up)”, J.A. Crawford.

“Potato Cannon With Arduino-Based Chronograph- Part I,” J.A. Crawford.

“Moveable 4×10 Workbench with Pneumatic Lift,” J.A. Crawford.

“Dreaded Interview Questions- Part I,” J.A. Crawford.

“Start-Up Company: Opportunity or Just a Job?”, J.A. Crawford, Dec. 2003.

“Pendulums and Elliptic Integrals,” J.A. Crawford. Derivation of the formula involved with pendulum motion with specific attention to the calculation of elliptic integrals and accurate time domain simulation using numerical methods.

“Random Variable Sums and the Central Limit Theorem,” J.A. Crawford, Feb. 2005.

“Current Flow in a Conductive Sheet,” J.A. Crawford, May. 2008.

#### Orthogonal Frequency Division Multiplex (OFDM)

#### Oscillators

“A Low Noise Oscillator,” Masters Thesis, June 1967, E. Janning.

“VCOs for Mobile Communications,” H. Yabuki, M. Sagawa, M. Makimoto.

“Low Noise Oscillator Design,” R. Muat, A. Upham, Hewlett Packard (circa 1981).

“A Simple Analytic Method for Transistor Oscillator Design,” A. Grebennikov.

“Fundamentals of Quartz Oscillators,” Application Note 200-2, Hewlett-Packard.

Chapter 9 of Advanced Phase-Lock Techniques is devoted entirely to oscillators.

#### Phase-Locked Loops

“PLL Terminology,” J.A. Crawford, Jan. 2008.

“Digital Redesign of Continuous-Time Phase-Locked Loops,” J.A. Crawford, April 2005.

PLL Tutorial: “Phase-Locked Loops- A Broad Perspective” J.A. Crawford.

A broad mathematical perspective on PLLs for frequency synthesis, carrier tracking, bit symbol timing recovery, and estimation theory.

“Introduction to Phase-Locked Loop System Modeling,” Wen Li, Jason Meiners

“Phase-Locked Loop Design Fundamentals,” Motorola, AN535 (Classic)

“GMSK Translation Phase-Locked Loop,” J.A. Crawford

Appendix 6C from 2008 text *Advanced Phase-Lock Techniques*

Appendix 6D from 2008 text *Advanced Phase-Lock Techniques*

Appendix 7A from 2008 text *Advanced Phase-Lock Techniques*

“Introduction To Phase-Lock Loop System Modeling,” Wen Li

#### Phase Noise

“Extending the Range and Accuracy of Phase Noise Measurements,” F.L. Walls, et al., NIST.

“The Art of Phase Noise Measurement,” D. Scherer, May 1983.

“PLL Phase Noise Performance Assessment (Example),”,J.A. Crawford.

“Low Noise Frequency Synthesis,” F.L. Walls, C.M. Felton, NIST.

“Design Principles and Test Methods for Low Phase Noise RF and Microwave Sources,” D. Scherer, 1980.

“Generation of Low Phase Noise Microwave Signals,” Dieter Scherer, Sept. 1981.

Phase Noise Measurement Seminar, Hewlett-Packard Spokane Division, 1983.

“Specifying Local Oscillator Phase Noise Performance- How Good is Good Enough?”, R. Gilmore.

“Some Aspects of the Theory and Measurement of Frequency Fluctuation in Frequency Standards,” L.S. Cutler, C.L. Searle, 1966 (Classic, reprinted in Frequency Stability: Fundamentals and Measurement, IEEE Press, 1983).

“Phase Noise Measurement,” Lance, A., Seal, W., TRW.

#### Transceiver Design

Excerpts from U.S. Air Force SBIR 1992 “Advanced Manpack Satellite Terminal.” J.A. Crawford Principal Investigator

“CMOS Frequency-Hopped Transceiver,” Behbahani, et al.

“Receiver Architectures,” Renfors, M.

#### RF Design

“Tunable Bandpass Filters- Part I,” J.A. Crawford

“Tunable Bandpass Filters- Part II,” J.A. Crawford

“Tunable Bandpass Filters- Part III,” J.A. Crawford

On-Line Filter Article at Microwaves & RF, J.A. Crawford

“Coaxial Line and 50 Ohms,” J.A. Crawford

“Bartlett’s Bisection Theorem for Electrical Filters,” J.A. Crawford

LPF Designer Documentation, J.A. Crawford