What should be the length of transmitting Antenna for radiating radio waves of 900 MHz
8.3 cm
Antenna Length Calculation for 900 MHz Radio Waves
This question asks us to determine the appropriate length for a transmitting antenna designed to radiate radio waves at a frequency of 900 MHz. The length of an antenna is often related to the wavelength of the radio waves it is designed to transmit or receive.
Understanding Wavelength and Frequency
Radio waves are electromagnetic waves, and their wavelength ($\lambda$) is inversely proportional to their frequency ($f$). The relationship is given by the formula:
$$ \lambda = \frac{c}{f} $$
Where:
- $c$ is the speed of light in a vacuum, approximately $3 \times 10^8$ meters per second (m/s).
- $f$ is the frequency of the radio wave in Hertz (Hz).
Calculating the Wavelength
First, we need to convert the given frequency from Megahertz (MHz) to Hertz (Hz):
Frequency ($f$) = 900 MHz = $900 \times 10^6$ Hz = $9 \times 10^8$ Hz.
Now, we can calculate the wavelength:
$$ \lambda = \frac{3 \times 10^8 \text{ m/s}}{9 \times 10^8 \text{ Hz}} $$
$$ \lambda = \frac{1}{3} \text{ meters} $$
To make comparisons easier with the options given in centimeters (cm), let's convert the wavelength to centimeters:
$$ \lambda = \frac{1}{3} \text{ m} \times 100 \text{ cm/m} $$
$$ \lambda \approx 33.33 \text{ cm} $$
Relating Wavelength to Antenna Length
Antennas are often designed to be a specific fraction of the wavelength for efficient transmission or reception. Common lengths include:
- Half-wavelength antenna ($\lambda/2$): This is a common length for dipole antennas.
- Quarter-wavelength antenna ($\lambda/4$): This is a common length for monopole antennas.
Calculating Potential Antenna Lengths
Let's calculate these common lengths based on the wavelength we found:
- Half-wavelength ($\lambda/2$): $\frac{33.33 \text{ cm}}{2} \approx 16.67 \text{ cm}$
- Quarter-wavelength ($\lambda/4$): $\frac{33.33 \text{ cm}}{4} \approx 8.33 \text{ cm}$
Comparing with Options
Now, let's compare our calculated lengths with the options provided:
| Calculation | Approximate Length | Given Option |
|---|---|---|
| Half-wavelength ($\lambda/2$) | 16.67 cm | 16.7 cm (Option 1) |
| Quarter-wavelength ($\lambda/4$) | 8.33 cm | 8.3 cm (Option 3) |
The calculated quarter-wavelength ($\approx 8.33$ cm) closely matches Option 3 (8.3 cm). The calculated half-wavelength ($\approx 16.67$ cm) closely matches Option 1 (16.7 cm). Since the provided correct answer is 8.3 cm, it suggests the question is likely referring to a quarter-wavelength antenna.
Conclusion
For radiating radio waves of 900 MHz, a common antenna length is a quarter of the wavelength ($\lambda/4$). Based on the calculation, this length is approximately 8.33 cm, which aligns well with the option 8.3 cm.
Important Questions from Basics of Antenna
- If the height of an antenna increases, the angle of radiation _____
The angular distribution of the transmitted power around the antenna is generally known as :
An antenna is polarized in the plane of the field perpendicular to
The value of radiation resistance of a Hertzian dipole of length \(\dfrac{\lambda}{80}\) is given by
An antenna is generally a metallic object, often a wire or collection of wires, used to convert high frequency current into electromagnetic waves and vice-versa. Antenna serve either or both of the following two functions, generation or the collection of electromagnetic energy. In a transmitting system, a radio-frequency signal is developed, amplified, modulated and applied to the antenna. The R-F currents flowing through the antenna produce electromagnetic waves which radiate into the atmosphere. In a receiving system, electromagnetic waves "cutting" through the antenna induce alternating currents for use by the receiver.
Efficient operation also requires that the receiving antenna be of the same polarization as the transmitting antenna. Polarization is the direction of the electric field and is therefore, the same as the antennas physical configuration. Thus vertical antenna will transmit vertical polarized light, any antenna having a physical length that is one-half wavelength of the applied frequency is called a Hertz antenna. Hertz antenna are predominantly used with frequencies above 2 MHz. Usually, at frequencies below 2 MHz, a Marconi type of antenna is used. The Marconi antenna is usually a quarter-wave grounded antenna or any odd multiple of a quarter wavelength.
The Yagi-Uda antenna consists of a drivers element and two or more parasitic elements. Yagi-Uda has two parasitic elements, a reflector and a director. This Yagi-Uda antenna provides about 7 dB of power gain with respect to a half-wavelength dipole reference. More complex antennas may be circularly polarized both vertically and horizontally polarized waves are radiated with equal power in both. If the powers are unequal the antenna is said to be elliptically polarized.
A horn is an ideal antenna for terminating a waveguide and may be conical, rectangular or sectorial. Wide band antennas either when the transmissions are wide band or when working of narrow channels over a wide frequency range is the major application. Helical antenna, which consists of a loosely wound helix backed up by a metal ground plane. Loop antennas are often used for direction finding. Loops have many shapes and generally consists of a single turn of wire. Discone is a ground plane antenna evolved from the vertical dipole and having a very similar radiation pattern.
