Kevin M.P. Ryan

Polynomial Symmetry in Butterworth Filter Synthesis

This book presents a rigorous method for designing analog electronic filters, specifically Butterworth filters, which are used to control how electrical signals pass through circuits. The author has developed a systematic algebraic approach that exploits the inherent symmetry of normalized Butterworth polynomials to formulate and solve algebraic equations directly for inductor and capacitor values at a specified cutoff frequency. Unlike traditional approaches that rely on approximations, lookup tables, or software defaults, this book demonstrates how to calculate exact component values - capacitors, inductors, and resistors - to achieve precise filtering. The book also extends the methodology to low-pass to high-pass transformations that preserve polynomial symmetry. The findings demonstrate that explicit symmetry considerations can lead to exact, scalable component solutions, providing a transparent framework that advances the understanding of polynomial monotonicity in filter synthesis. The book includes fundamentals such as symmetry and cutoff frequency and progresses step-by-step through first- to sixth-order network synthesis. Advanced observations and series expansions also provide deeper insight for precision design. Readers will learn how to design circuits that perform predictably even when source and load resistances are unequal, bridging the gap between theory and real-world application.