Infor
- Title: Null Double Injection and the Extra Element Theorem
- DOI: 10.1109/13.34149
- Author: R. D. MIDDLEBROOK
- Publication Date: 06 August 2002
- Published in: IEEE Transactions on Education (Volume: 32, Issue: 3, August 1989)
Abstract
The extra element theorem (EET) states that any transfer function of a linear system can be expressed in terms of its value when a given 'extra' element is absent, and a correction factor involving the extra element and two driving-point impedances are seen by the element.
In the present work, the EET is derived and applied to several examples in a manner that has been developed and refined in the classroom over a number of years. The concept of null double injection is introduced first, because it is the key to making easy the calculation of the two driving-point impedances needed for the EET correction factor. The EET for series and parallel elements is then considered, and attention is also given to the EET as an analysis tool, to the symmetry of the two forms of the EET, and to return ratios and sensitivity.
AI Summary (Kimi, 2025.04.09)
This article, titled "Null Double Injection and the Extra Element Theorem" by R. D. Middlebrook, was published in IEEE Transactions on Education (Vol. 32, No. 3, August 1989). It introduces the Extra Element Theorem (EET) and its application in circuit analysis, simplifying the assessment of how additional components affect transfer functions in linear systems through the concept of "null double injection."
Background
In circuit design, analyzing transfer functions (e.g., gain) is essential. Traditionally, adding an extra component requires reanalyzing the entire circuit, increasing complexity. The EET avoids this by expressing the impact of an extra element as a correction factor based on two driving-point impedances.
Methodology
The article introduces null double injection: In a linear system with two driving signals, adjusting them to nullify one output enables a simplified transfer function expression, forming the basis of EET.
The core idea of EET: Any linear system’s transfer function can be expressed as its value without the extra element, multiplied by a correction factor involving the extra element and two driving-point impedances (with/without the element).
Experiments & Case Studies
Key applications demonstrated:
- Common-Emitter (CE) Amplifier: EET simplifies analyzing how an emitter bypass capacitor (C₂) affects gain by computing reference gain (without C₂) and two impedances.
- Input Impedance Calculation: EET derives input impedance with C₂ by treating it as an extra element.
- Dependent Sources: EET extends to analyze dependent sources’ impact on system gain.
Key Conclusions
- Versatility: EET applies to gain, input/output impedance, and other transfer functions.
- Correction Factor: Directly quantifies the extra element’s influence.
- Simplification: Reduces analysis complexity by referencing a simpler circuit.
- Symmetry: Parallel/series EET forms share symmetry, enabling parameter interchange.
- Sensitivity Analysis: Evaluates transfer function sensitivity to component variations.
Technical Details
- Null Double Injection: Adjusting dual inputs to null an output simplifies impedance calculations.
- Correction Factor: Combines the extra element and two driving-point impedances.
- EET Forms: Two variants for parallel (infinite impedance) and series (zero impedance) extra elements.
Insights
The article highlights EET’s value as a powerful analytical tool, particularly for complex circuits. By decomposing analysis into simpler steps, EET enhances efficiency in circuit design. While the concept may challenge students initially, practical examples facilitate mastery.
(End of Summary)
Tuntun Yuchiha