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A transponder is a device for receiving and rebroadcasting a signal. Transponder on a television satellite receives a television signal beamed from large satellite uplink stations on the ground, then processes, encodes, amplifies and rebroadcasts the signal over a large area of the Earth's surface. Usually, TV signal is amplified by the transponder, and can be encoded or modified in other ways. The signal is encoded to ensure that only paying subscribers are able to access the signal.
Think of the transponder as a bright light source shining down from the satellite. It isn't targetted ant any particular place on the ground but anywhere that can see the sky can see some of the light. Radio waves and light travel in almost the same way so the same principle applies to the satellite transmissions.
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