A Generalized Order-Reduction Method for Transfer Function and Pole–Zero Analysis of Linear Analog Circuits
Year: 2026
Type: article
Abstract: Accurate pole–zero determination is essential for predicting the frequency response, stability, and bandwidth of analog circuits. Conventional transfer function derivations based on nodal or mesh analysis, however, often produce lengthy symbolic expressions and provide limited physical insight, particularly for high-order networks. This paper presents a generalized order-reduction method for deriving the transfer functions of linear time-invariant analog circuits with constant coefficients. The proposed approach decomposes a higher-order network into lower-order configurations and determines the coefficients of its characteristic and zero polynomials by selectively suppressing or isolating energy storage elements. First-order time constants are obtained from the equivalent resistance or conductance associated with each capacitor or inductor. Higher-order coefficients are then evaluated by systematically considering combinations of energy storage elements and successively reducing the network order. The relationship between driving-point impedance and admittance is also employed to establish a unified procedure for determining poles and zeros. The method is applicable to passive and active RLC circuits, including networks containing dependent sources and transistor small-signal models. Several representative examples, ranging from elementary RC networks to higher-order active circuits, are analyzed to demonstrate the derivation procedure and its ability to retain explicit dependence on circuit parameters. Compared with direct symbolic expansion, the proposed framework reduces algebraic manipulation while preserving the physical interpretation of the resulting coefficients. The method therefore provides a systematic and design-oriented tool for transfer function characterization and pole–zero analysis of linear analog circuits.
Source: Chips
DOI: 10.3390/chips5040036
Language: English
Subfield: Biomedical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,207
OpenAlex ID: W7221324136