Transistor Frequency-Response Analysis: Recursive Shunt-Circuit Transformations

Frequency-response analysis is critical in circuit design. Frequency response encodes crucial information, like gain, accuracy, bandwidth, response time, phase shift, stability, and more. Unfortunately, existing methods are either algebraic and obscure or approximations with inaccuracies. So applying them to more complex circuits is often arduous or unreliable. This paper proposes recursive shunt-circuit transformations: a simple, rigorous, and insightful analytical method for conceptualizing and designing electronic circuits. The method asserts that (a) each equivalent capacitance shunts away its parallel resistance past its RC frequency. This (b) decreases the gain (induces a pole) and (c) changes the circuit. (d) The next dominant capacitance shunts its parallel resistance past the next pole and so on until all remaining capacitances shunt their parallel resistances past the poles they establish. The method also asserts that (e) bypass capacitances increase gain (induce zeros) and (f) cross-amp capacitances couple stages and poles. By applying this method and concepts, designers can (i) simplify an arbitrarily complex circuit into simpler coupled/decoupled stages and (ii) determine and manage poles and zeros with insight. This method was applied to design and analyze single- and multi- stage amplifier circuits and results were benchmarked against traditional methods and NGSPICE simulations, demonstrating its accuracy and broad applicability.