- #1
David lopez
- 257
- 3
if you fed a rectangular waves to a radio antenna, would it still produce radio waves? does it have to be a sine wave?
How does an antenna work with harmonics?
Click For Summary
SUMMARY
A rectangular wave can effectively produce radio waves when fed to a radio antenna, as it can be decomposed into a series of sine and cosine waves through Fourier series. While the antenna responds to each sine wave independently, the overall response is a summation of these individual responses. To improve the quality of the output signal, a loading coil can be inserted between the generator and the antenna, transforming the square wave into a more desirable sine wave. However, practical limitations exist, as most antennas are not designed to operate over a wide frequency range, typically handling only about an octave of frequencies.
PREREQUISITES- Understanding of Fourier series and wave decomposition
- Knowledge of radio frequency (RF) antenna design principles
- Familiarity with loading coils and their function in RF systems
- Basic concepts of modulation and bandwidth in signal transmission
- Explore the principles of Fourier series in signal processing
- Research the design and functionality of loading coils in antennas
- Learn about the limitations of RF amplifiers and their bandwidth capabilities
- Investigate modulation techniques used in RF signal transmission
Radio frequency engineers, antenna designers, and anyone involved in signal processing and transmission optimization will benefit from this discussion.
- #2
FactChecker
Science Advisor
Homework Helper
- 9,371
- 4,646
No, it does not have to be a sine wave. In fact, a rectangular wave can be thought of as a specific sum of sine (and cosine) waves of various frequencies. That is the basis of the Fourier series. The antenna will respond to each sine wave as though it was not part of a rectangular wave, then all the responses to the sine waves can be summed to get the total antenna response to the rectangular wave.
Shown below is a sequence of better approximations of a square wave using more terms in the Fourier series. Each line is plotted a little higher so that you can see them separately. Clearly, the more terms there are, the closer it gets to a square wave. An antenna will respond to each sine wave as though it is alone. Then the individual responses can be summed to get the total response.
Shown below is a sequence of better approximations of a square wave using more terms in the Fourier series. Each line is plotted a little higher so that you can see them separately. Clearly, the more terms there are, the closer it gets to a square wave. An antenna will respond to each sine wave as though it is alone. Then the individual responses can be summed to get the total response.
Last edited:
- #3
zoki85
- 1,198
- 230
Of course, it would produce radio waves but true broad-spectrum mess. Square wave can be simply turned into decent sine wave by inserting a loading coil between output of generator and an antenna.David lopez said:
The principle is same as in this video. This would make antenna more or less electrically short though.
- #4
FactChecker
Science Advisor
Homework Helper
- 9,371
- 4,646
A single square wave contains several sine waves of different frequencies and amplitudes. It would be possible to tune to anyone of those and tune out the others (although not completely). The amount of power lost by tuning out the other frequencies depends on the response of the filter to the other frequencies.zoki85 said:
- #5
zoki85
- 1,198
- 230
It also depends on the frequency of square wave. For example if that frequncy is 3x higher than quarter wave resonant frequency system with loading coil, than the response of the system to the 3rd harmonic is particularly strongFactChecker said:
- #6
sophiecentaur
Science Advisor
Homework Helper
- 30,298
- 7,446
Most radio antennae are not designed (it's very hard!) to operate over even a single octave of frequency range. Moreover, Transmitting amplifiers seldom handle a huge range of frequencies. About an Octave is about as much as you will ever get. A UHF Broadcast Travelling Wave Tube (a typical 'wide band' amplifier) has a wide enough bandwidth to handle a number of separate UHF channels but not over an octave frequency range. Even matching a transmitter to an antenna for a number of different channels is difficult. Most systems use a small Fractional Bandwidth.
So the question in the OP doesn't make a lot of sense in the practical world. However, RF antennae are usually capable of handling a Modulated RF signal which can carry a good looking square wave where the sharpness is limited by the Bandwidth allocated to the channel. An analogue TV transmitter can send 'good' black / white / black/white patterns that will satisfy the requirements of highish quality TV. The Sideband structure of the transmitted signal will consist of a fundamental and a number of (enough) harmonics within the channel width.
Perhaps that was what the OP really meant.
So the question in the OP doesn't make a lot of sense in the practical world. However, RF antennae are usually capable of handling a Modulated RF signal which can carry a good looking square wave where the sharpness is limited by the Bandwidth allocated to the channel. An analogue TV transmitter can send 'good' black / white / black/white patterns that will satisfy the requirements of highish quality TV. The Sideband structure of the transmitted signal will consist of a fundamental and a number of (enough) harmonics within the channel width.
Perhaps that was what the OP really meant.