The Size of the Transmitting Antenna: One Fourth the Wavelength of an EM Wave, What Should Be the Length of the Receiving Antenna?

In antenna theory, the relationship between the length of an antenna and the wavelength of the electromagnetic (EM) wave it is designed to transmit or receive is crucial for optimal performance. When the transmitting antenna is constructed to be one-fourth the wavelength ((lambda)) of the EM wave, the calculation of its length is straightforward.

Calculating the Transmitting Antenna Length

The length of the transmitting antenna can be calculated using the formula:

[ text{Length of transmitting antenna} frac{lambda}{4} ]

This formula provides a basic understanding of how the size of the transmitting antenna is determined to efficiently transmit the EM wave.

Receiving Antenna Length: Resonance and Effective Reception

For a receiving antenna, optimal performance is often achieved by designing it to resonate at the same frequency as the transmitting antenna. This typically means the receiving antenna should also be approximately one-fourth the wavelength of the EM wave. Thus, to ensure effective coupling and resonance, the length of the receiving antenna should be similarly calculated:

[ text{Length of receiving antenna} frac{lambda}{4} ]

Flexibility in Antenna Length

It is important to note that the receiving antenna can be any length that is in a 1/8, 1/4, 1/2, or even a harmonic division of the wavelength. However, structural limitations may necessitate a smaller size. For instance, a 1/4 wave antenna effectively uses the earth or a ground plane as a reflection to achieve a 1/2 wave effect.

Practical Considerations

In practical scenarios, the ideal length of the receiving antenna is primarily dependent on capturing the most amount of the desired signal. This does not necessarily have to adhere to the size of the transmitting antenna unless both the transmitting and receiving antennas are being used simultaneously. In such cases, the antenna sizes are more determined by the operating frequency than by each other’s size.

Example of Real-World Applications

For instance, I operate an antenna that is 5/8 of the wavelength with my transceiver. I communicate with people who use antennas ranging from 3/4, 5/8, 1/2, 1/4 wavelength, and even handhelds with antennas of various lengths. A friend often experiments with homemade antennas, which can range from 3/8 wave to full wave.

Despite the diverse lengths of these antennas, they have often worked effectively with both my 5/8 wave base station and my mobile device's 1/4 wave antenna. It is clear that unless you are transmitting, the focus should be on what captures the best signal.

If you are also transmitting, the physical and/or electrical size of the antenna should be a division of the operating frequency, more often a half or a quarter.

The main function of the transmitting antenna is to convert AC electrical current into an EM wave, while the receiving antenna only needs to capture the signal. This broadens the range of acceptable sizes for the receiving antenna, making it more flexible in design and application.

Conclusion

The relationship between the length of the transmitting and receiving antennas and the wavelength of the EM wave is critical for optimizing communication performance. By carefully considering the frequency and the practical constraints, engineers and hobbyists can design antennas that suit their specific needs effectively.