If the frequency of the signal is 1 MHz, the minimum height of the transmitting antenna should be:
75 m
Frequency and Antenna Height Calculation
Understanding the relationship between the frequency of a signal and the required height of a transmitting antenna is crucial in radio communication. For efficient transmission of radio waves, the dimensions of the antenna are often related to the wavelength of the signal being transmitted.
Wavelength Calculation for a Given Frequency
The first step in determining the minimum height of a transmitting antenna is to calculate the wavelength of the signal. Wavelength (\(\lambda\)) is the distance over which a wave's shape repeats. It is inversely proportional to the frequency (f) and directly proportional to the speed of light (c).
- The speed of light (c) in a vacuum is approximately \(3 \times 10^8\) meters per second (m/s).
- The given frequency (f) of the signal is 1 MHz. We need to convert this to Hertz (Hz):
\(1 \text{ MHz} = 1 \times 10^6 \text{ Hz}\)
The formula to calculate the wavelength is:
\( \lambda = \frac{c}{f} \)
Let's substitute the given values into the formula:
\( \lambda = \frac{3 \times 10^8 \text{ m/s}}{1 \times 10^6 \text{ Hz}} \)
\( \lambda = 300 \text{ m} \)
So, the wavelength of the 1 MHz signal is 300 meters.
Minimum Transmitting Antenna Height
For effective transmission of radio waves, especially for simple dipole antennas or quarter-wave monopoles which are common for ground wave propagation, the minimum effective height of a transmitting antenna is often designed to be a fraction of the wavelength. A commonly used and efficient height for a ground-mounted vertical antenna (quarter-wave monopole) or one arm of a dipole is one-quarter of the wavelength.
The minimum height (h) of the transmitting antenna can be calculated as:
\( h = \frac{\lambda}{4} \)
Now, let's use the calculated wavelength to find the minimum antenna height:
\( h = \frac{300 \text{ m}}{4} \)
\( h = 75 \text{ m} \)
Therefore, the minimum height of the transmitting antenna required for a 1 MHz signal is 75 meters.
| Parameter | Value |
|---|---|
| Frequency (f) | 1 MHz (\(1 \times 10^6\) Hz) |
| Speed of Light (c) | \(3 \times 10^8\) m/s |
| Calculated Wavelength (\(\lambda\)) | 300 m |
| Minimum Antenna Height (h = \(\lambda\)/4) | 75 m |
This calculation shows that for a 1 MHz signal, a transmitting antenna height of 75 meters is ideal for efficient signal radiation based on the quarter-wave principle.
Important Questions from Basics of Antenna
The antenna which provides circularly polarized waves is
A dipole carries RMS current of about 300 A across the radiation resistance 2 Ω. What would be the power radiated by an antenna?
A Yagi antenna is a directional antenna consisting of parasitic elements-
Arrange the following antennas in ascending order of their radiation resistance.
A. Short dipole (L = \(\frac{\lambda}{10}\) )(I av = l o)
B. Short dipole (L= \(\frac{\lambda}{10}\) )( I av = l o/2)
C. Linear \(\frac{\lambda}{2}\) dipole (sinusoidal current distribution)
D. Small Loop (square loop) single turn of(L = \(\frac{\lambda}{10}\) )
Choose the correct answer from the options given below
Which of the following is NOT true with respect to antennas?
