--- title: "Compensation theorem for antennas" subject: "Propagation and Antenna" chapter: 1 key: "semester_6/propagation_and_antenna:compensation-theorem" source: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/compensation-theorem site: BCT Engineering --- # Compensation theorem for antennas Propagation and Antenna · Chapter 1: Radiation and Antenna Fundamentals - Asked in: 2081 Chaitra, 3 marks; 2080 Chaitra, 3 marks; 2078 Chaitra, 2 marks; 2075 Bhadra, 2 marks; 2074 Bhadra, 2 marks; 2073 Magh, 2 marks (asked 6 times) - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/compensation-theorem - Whole chapter: https://www.bctengineer.com/md/semester_6/propagation_and_antenna/chapter-1 ## Question State the compensation theorem for an antenna system. ## Short answer If branch impedance Z carrying current I changes by ΔZ, the resulting current changes equal those produced by a series voltage source −IΔZ, with other sources replaced by internal impedances. New current is I'=I+ΔI. It is used for nearby objects, parasitic elements, or load changes in antenna systems. ## Answer **Compensation theorem:** If the impedance Z of a branch carrying current I is changed by ΔZ, the changes in currents everywhere in the network are the same as those produced by a voltage source of value **−I·ΔZ** (opposing the original current) placed in series with the changed branch, with all other sources replaced by their internal impedances. ```text Original Changed Compensation network --[ Z ]-- I --[Z+ΔZ]-- I' --[Z+ΔZ]--(−I·ΔZ)-- gives ΔI = I' − I ``` So the new current is I' = I + ΔI, where ΔI is found from the compensation source alone. Use in antenna systems: - To find the change in antenna current and input impedance when a **nearby object, parasitic element or ground** changes the impedance of a branch. - To find the effect of changing a **load or tuning impedance** at the antenna terminals without solving the whole system again. - In arrays, to study how changing one element's impedance alters currents in the other (mutually coupled) elements. The theorem holds for linear, bilateral networks, so it applies to antennas in a linear medium. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. If the impedance of a branch carrying current I is changed by ΔZ, what source replaces the change? A. A voltage source +I·ΔZ aiding the current B. A voltage source -I·ΔZ opposing the original current, in series with the branch C. A current source I/ΔZ in parallel D. A voltage source I/ΔZ in series Answer: B. The change in currents equals that of a source of -I·ΔZ placed in series with the changed branch. (Key point: Compensation source value) 2. In the compensation network, what is done with all the other sources? A. They are doubled B. They are kept at their original values C. They are replaced by their internal impedances D. They are open-circuited regardless of type Answer: C. Only the compensation source acts; the other sources are replaced by their internal impedances to give the change ΔI. (Key point: Other sources) 3. How is the new current obtained using the theorem? A. I' = I - ΔI, where ΔI is from the original sources B. I' = I·ΔZ C. I' = I + ΔI, where ΔI is found from the compensation source alone D. I' = ΔI only Answer: C. I' = I + ΔI and ΔI is calculated from the -I·ΔZ source, avoiding a full re-solution. (Key point: Finding the new current) 4. What is a typical antenna use of the compensation theorem? A. Finding how a changed load, parasitic element or nearby object alters antenna current without re-solving everything B. Measuring the radiation pattern C. Computing the far-field phase D. Finding the antenna's physical length Answer: A. It gives the effect of an impedance change on currents and input impedance directly. 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