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# The physical sizes of the transmitter and receiver antenna in a communication system are?A. Proportional to carrier frequency.B. Inversely proportional to modulation frequency.C. Inversely proportional to carrier frequency.D. Independent of both carrier frequency and modulation frequency.

Last updated date: 13th Jun 2024
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Hint: Communication is the phenomenon to send and receive any message through a medium(transmission channel).For the proper communication to be happen we need one transmitter antenna(from which the message will be sent) and one receiver antenna(from which the message will be received).In this context the sizes of transmitter and receiver antennas play a very important role. These will determine the strength of the signal which is to be transmitted and the strength of signal is also dependent on its frequency (carrier and modulation frequency). So the physical sizes of antennas and frequencies will be dependent on each other.

Here we will consider only carrier frequency not modulation frequency because originally when we transmit the signal we have carrier frequency not modulation frequency and receiver also gets the carrier frequency not modulation frequency, so carrier frequency will decide the physical sizes not modulation frequency.
The most fundamental concept in this discussion is the relation between the frequency and wavelength, which is they are inversely proportional to each other by the following relation by keeping the speed of wave constant,
$\lambda \upsilon {\text{ = c}}$
Where,
$\lambda {\text{ = }}$wavelength,
$\upsilon =$frequency
C=speed of wave
And we know that the physical size of antenna is directly proportional to the wavelength (we know that the length of antenna usually be kept $\dfrac{\lambda }{4}$) and wavelength and frequency are inversely proportional to each other.
Hence from the above discussion we conclude that higher the frequency smaller the antenna size (for both transmitter and receiver).

So, the correct answer is “Option C”.

Note:
For the proper communication we have to choose the proper sizes of antennas keeping in mind the frequency and wavelength which we have to deal with. Higher the frequency, the elements in the antennas need to be smaller so the more elements can be fit for a given physical height. More elements will allow more directivity in the given direction.