Maxima Detection: Solving a 750MHz Wave Question with Two Radio Antennas

[zhen]

the question is:
Two radio antennas are separatedf by 2.0m. Both broadcast indentical 750MHz waves. If you walk around the antennas in a circle of radius 10m, how many maxima will you detect?

I am stucked in the question, and have very little idea to approch it...
the distance between two maximum is not uniform along the circular path...so how can i get the number of it...



can you give me some hint for approching this question? I know the answer is 20...but no idea how to get it...please help...

 

[berkeman]

Hint -- make a scale drawing of the system as seen from above (assuming vertical antennas). Draw a set of concentric circles around the left antenna spot, with each circle spaced at n times the wavelength, with n=1,2,...,something. Then draw a set of concentric circles around the right antenna spot in the same way. Now draw one circle with a radius of 10m, centered on the spot directly between the two antennas.

So call the concentric circles around each antenna an instantaneous snapshot of the vertical E-field strength. Look around the 10m circle to see how many times you go through a cycle of seeing the two sets of E-field circles line up and then do the opposite of line up (where one circle line is between two other circle lines from the other antenna).

Now think about what happens when the concentric circles are actually moving away from their respective antennas with equal velocity...do you see how the patterns move through each other? Do you start to get a feel for how the concentric circles' alignment in the drawing tells you something about where the maxima and minima of the pattern will be?

 

[zhen]

thanks very much, but i wonder what kind formula will be apporiated for this kind question?

 

[berkeman]

What is it that causes a maxima in the radiated EM pattern from this cophase antenna arrangement?

Try a different pair of drawings. Draw x and y axes on some graph paper or engineering paper. Put a single antenna seen from the top at the origin. Now write an equation for the amplitude of the electric field radiated from that antenna as a function of time and distance. You can use either rectangular or polar coordinates (or better yet, write it both ways). In polar form, your equation will have an E field z-axis amplitude that varies with time and distance r, but not with the polar angle. The radiation pattern from a single vertical dipole antenna is symmetric when seen from the top.

Now make a new drawing, with the two antennas again seen from the top (to scale on the graph paper), with the antennas placed symmetrically at +/-1m on the horizontal x axis. Write the equation for each of the antennas' radiated emission, and add the two. Now in polar coordinates, look to see what the maximum amplitude does as you swing around from zero to 2*Pi around your drawing. Once you get out of the near field for the antenna array, the number of maxima and minima will be constant as you swing around through 2*Pi in phase.

BTW, I googled antenna array pattern, and got lots of helpful hits. Check out this one to start visualizing how the antenna pattern is changed by having multiple elements at various spacings (like the two antennas in your problem which are spaced a few wavelengths apart...)

http://www.ee.surrey.ac.uk/Personal/D.Jefferies/antarray.html

 

[zhen]

thanks again.