--- title: "Parabolic reflector operation and Cassegrain feed" subject: "Propagation and Antenna" chapter: 3 key: "semester_6/propagation_and_antenna:parabolic-reflector-cassegrain" source: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/parabolic-reflector-cassegrain site: BCT Engineering --- # Parabolic reflector operation and Cassegrain feed Propagation and Antenna · Chapter 3: Antenna Classification - Asked in: 2079 Chaitra, 5+3 marks - Video: [Feeding Methods of Reflector Antenna (Center Feed, Offset Feed & Cassegrain Feed) Explained](https://www.youtube.com/watch?v=XLcXpZTUcv4) — Engineering Funda - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/parabolic-reflector-cassegrain - Whole chapter: https://www.bctengineer.com/md/semester_6/propagation_and_antenna/chapter-3 ## Question Explain in detail about the operation of parabolic reflector. What is Cassegrain feed system? ## Short answer Parabolic reflector: feed at focus, equal path-length property yields in-phase aperture, producing a narrow high-gain beam; gain = η(πD/λ)², HPBW ≈ 70λ/D. Cassegrain feed: a horn at the vertex illuminates a hyperboloidal subreflector near the focus, reflecting waves onto the main dish; advantages: short waveguide, low noise, easy maintenance. ## Answer #### Operation of parabolic reflector A **parabolic reflector antenna** is a large conducting surface shaped as a paraboloid of revolution, with a small primary antenna (feed) placed at its **focus**. It converts the spherical wave of the feed into a plane wave and so produces a very narrow, high-gain pencil beam. **Geometry**: a parabola is the locus of points equidistant from the focus F and a fixed line (directrix). The distance from vertex to focus is the focal length f; the opening (aperture) has diameter D; f/D is usually 0.25–0.5. ```text )| ) |----> ray ) |----> all paths F o-->-) |----> F→P→Q equal feed ) |----> (plane wave) ) |----> )| <-f-> aperture plane, diameter D ``` **Working** 1. **Equal path (phase) property**: for every point P on the surface, FP + PQ = constant, where Q is on the aperture plane. Hence all rays from F arrive at the aperture in phase. 2. **Parallel ray property**: the tangent at P makes equal angles with FP and the axis, so every reflected ray is parallel to the axis. 3. The aperture therefore has a uniform phase distribution and radiates a plane wave: a narrow beam along the axis. 4. By reciprocity, an incoming plane wave along the axis is focused at F, where the receiving feed is placed. 5. The feed must radiate mostly towards the dish; energy spilling past the rim (**spillover**) and the shadow of the feed (**aperture blocking**) reduce efficiency. **Performance** ```text Gain G = η (πD/λ)² η ≈ 0.55-0.7 HPBW ≈ 70 λ/D degrees FNBW ≈ 140 λ/D degrees ``` E.g. D = 3 m at 6 GHz (λ = 5 cm): HPBW ≈ 1.17°, gain ≈ 43 dBi (η = 0.6). Uses: satellite communication, radar, microwave links, radio astronomy. #### Cassegrain feed system The **Cassegrain feed** is a dual-reflector feed: a horn located at the **vertex** of the main paraboloid illuminates a small **hyperboloidal subreflector** placed near the focus, which reflects the waves back onto the main reflector. ```text main paraboloid ) ) hyperboloid ) subreflector ) <------- ( [horn]o --------> ( F (focus of paraboloid at F' ) <------- ( = near focus of hyperbola) ) ) ) horn at F' = far focus of hyperbola, near the vertex ``` - One focus of the hyperboloid coincides with the focus F of the paraboloid; the feed is at the other focus F′. Waves reflected from the subreflector appear to come from F, so the main dish produces a plane wave. - **Advantages**: feed and receiver behind the dish (short waveguide, low loss, low noise), long effective focal length, easy maintenance. - **Disadvantage**: subreflector blocks part of the aperture, so it is used with large dishes such as satellite earth stations. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What does the equal-path property of a paraboloid ensure? A. FP + PQ is constant, so rays from the focus reach the aperture in phase B. Rays from the focus spread out in all directions C. The dish has a spherical aperture phase D. Only the vertex reflects Answer: A. For every surface point P, FP + PQ is constant, giving a uniform phase across the aperture (plane wave). (Key point: Equal path property) 2. Which gives the gain and HPBW of a parabolic dish? A. G = eta(lambda/piD)^2, HPBW ~ 70 D/lambda B. G = eta(piD/lambda)^2, HPBW ~ 70 lambda/D C. G = 4 pi D, HPBW ~ D/lambda D. G independent of D Answer: B. Gain grows with (D/lambda)^2 and beamwidth shrinks with D/lambda. (Key point: Gain and beamwidth) 3. Which two effects reduce dish efficiency mentioned in the answer? A. Polarization and Faraday rotation B. Skin effect and ground wave C. Spillover and aperture blocking D. Reciprocity and image theory Answer: C. Energy spilling past the rim and the feed's shadow reduce efficiency. (Key point: Efficiency losses) 4. In a Cassegrain feed, where are the horn and subreflector? A. Horn at the rim, no subreflector B. Horn at the focus, flat reflector behind C. Horn outside the beam, ellipsoidal subreflector beyond focus D. Horn at the vertex, hyperboloidal subreflector near the focus Answer: D. The horn at the vertex illuminates a hyperboloid subreflector whose one focus coincides with the dish focus. 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