Yagi antenna radiating with respect to original signal

[SleepDeprived]

I have a question regarding how a Yagi type antenna radiating its energy with respect to faithfully replicating the original signal. So let's say you have a FM modulating signal, F(x(t)) whereas x(t) is the data, and F(t) is the carrier, so basically x(t) would FM modulate the carrier F(x). The Yagi antenna (or any type antenna) needs to faithfully radiate the original signal F(x(t)) as much as possible. I include a pic of a Yagi below for reference.
The reason I have a question on the Yagi because it has a rather unique way of radiating. As you can see in the pic, the signal is fed to the 2nd element, the main element (where the wire is connected), whereas the first element is used to reflect the main signal which will combine with the main element to form an incident wave front. How the signal reflected by the first element depends on how far way it is from the main element in term of the carrier wave length. The rest of the elements are used further to direct the radiating pattern depends on the application.
Since the signal that is radiated by the main element (2nd element) is interfered by the reflected element (1st element), the final radiated signal is not the same as the original intended signal. For example, if you have the reflected element a quarter wave from the main element, if you send in a pure sinewave to the main element, the final signal would be the original sinewave plus the quarter wave delay of itself. So if the original signal is : F(x(t)), then the final radiating signal would be the summation: F(x(t)) + F(x(t) - q) where q is the quarter wave delay.
My guess is since the carrier frequency is much higher than the baseband data frequency, this won't be an issue in term of demodulate the signal to obtain the baseband data.
Your input is appreciated, thanks.

 

[tech99]

I have a question regarding how a Yagi type antenna radiating its energy with respect to faithfully replicating the original signal. So let's say you have a FM modulating signal, F(x(t)) whereas x(t) is the data, and F(t) is the carrier, so basically x(t) would FM modulate the carrier F(x). The Yagi antenna (or any type antenna) needs to faithfully radiate the original signal F(x(t)) as much as possible. I include a pic of a Yagi below for reference.
The reason I have a question on the Yagi because it has a rather unique way of radiating. As you can see in the pic, the signal is fed to the 2nd element, the main element (where the wire is connected), whereas the first element is used to reflect the main signal which will combine with the main element to form an incident wave front. How the signal reflected by the first element depends on how far way it is from the main element in term of the carrier wave length. The rest of the elements are used further to direct the radiating pattern depends on the application.
Since the signal that is radiated by the main element (2nd element) is interfered by the reflected element (1st element), the final radiated signal is not the same as the original intended signal. For example, if you have the reflected element a quarter wave from the main element, if you send in a pure sinewave to the main element, the final signal would be the original sinewave plus the quarter wave delay of itself. So if the original signal is : F(x(t)), then the final radiating signal would be the summation: F(x(t)) + F(x(t) - q) where q is the quarter wave delay.
My guess is since the carrier frequency is much higher than the baseband data frequency, this won't be an issue in term of demodulate the signal to obtain the baseband data.
Your input is appreciated, thanks.

Yes I agree with your conclusion. In addition, you will notice that the Yagi cannot operate over wide bandwidths because of the need to retain correct spacing/phasing between elements. In addition, the antenna relies on de-tuning elements to obtain currents in the elements having the desired phase, and these phase shifts change rapidly with frequency. As the antenna cannot operate over wide bandwidths, the base band width is naturally limited.

 

[Baluncore]

My guess is since the carrier frequency is much higher than the baseband data frequency, this won't be an issue in term of demodulate the signal to obtain the baseband data.

That is correct.

For an unmodulated carrier the radiated signal remains a sinewave. That is because the “Fourier shift theorem” takes care of the summation of all the phase shifted diverse paths.

An FM modulated signal can have a very wide bandwidth with a great number of sidebands.
See; https://en.wikipedia.org/wiki/Frequency_modulation#Bessel_functions

A limited bandwidth transmitter output stage, or the antenna tuning, will remove many outer sidebands, which luckily contained only duplicated information. The lost sidebands do not represent a loss of information as the information is still contained in the zero crossings of the band limited signal. Carson's bandwidth rule is used to determine the bandwidth needed to maximise energy transfer.
See; https://en.wikipedia.org/wiki/Carson_bandwidth_rule

 

[sophiecentaur]

I think there is a general principle that this effect will happen with any antenna that is not of zero size. There will be a difference in the phases of all frequency components of the signal when you look from any random direction at a physically large antenna system. Even for a broadside array of cophased dipoles, the phase difference of the signals from all elements will only be zero in the far field (@∞). Every antenna's bandwidth can be limited by this effect amongst several others. At least, with a Yagi, the re radiated signals from the forward parasitics are almost in phase with the net signal that's traveling in the main beam direction. (which is what makes it directive in the first place.)
For a large antenna, this dispersive effect can be very relevant and for multipath propagation, in which the local gasworks behaves as part of the antenna, the frequency response of the received signals can be seriously bad - and that's for delays less than those needed to form ghost images. (Only familiar to those of us who have watched significant analogue TV )