Co-phasing Antennas


Array definitions.

An array of antenna elements is a spatially extended collection of N similar radiators or elements, where N is a countable number bigger than 1, and the term "similar radiators" means that all the elements have the same polar radiation patterns, orientated in the same direction in 3-d space. The elements don't have to be spaced on a regular grid, neither do they have to have the same terminal voltages, but it is assumed that they are all fed with the same frequency and that one can define a fixed amplitude and phase angle for the drive voltage of each element.

        That means that an array (at least for our purposes) is an antenna system where two or more elements are driven by the same transmitter and that the drive to one antenna  need not be of the same phase or amplitude as the other antennas.
 

        For the most part this discussion concerns the operation of two mobile CB antennas operated in FREE SPACE (pattern distortion will result for each vehicle type).  Although the discussion is based around mobile antennas the theory is the same for base station antennas, just not as widely put into use.   To start the discussion lets consider that CB antenna systems are designed around a 50 ohm feed point impedance, and so is the most common types of coax, and so is the output of the radio.  This is all great until we try to operate two antennas in an electrical "parallel" relationship which results in a total impedance of 25 ohms (that's a 2:1 mismatch to the radio).   It would be easier to match if the antennas in question had a 100 ohm feed point impedance.  So to accomplish the task of matching we most commonly use an interesting property of 1/4 wave transmission lines.  By taking the input and output impedance's of a 1/4 wave coaxial line multiplied by each other then take the square root of the product, we get the impedance of the coax required to be used in the 1/4 wave transformer.  In our case the 50 Ohms impedance of the antenna we would like to transform to 100 Ohms so that when put in parallel with another 100 Ohm antenna we get a 50 Ohm match to the radio.  Soooo,  that's the square root of (50x100) = 70.71 Ohms.  OR.. let the computer do the math for you.  This tells us that using approximately 71 Ohm coaxial cable at 1/4 wave multiples will produce an output of 100 Ohms and when paralleled together will match a 50 ohm Radio.  Simply put...using RG-59 coaxial cable at lengths of 18 ft to each antenna with sufficient spacing between the antennas will result in a good match.
    (for the Techno CBers out there,  if you have an RF noise bridge or similar equipment capable of measuring the true 1/2 or 1/4 wave length of the coax you have on hand you will derive even better results.  For instance the last 3 shipments of RG-59 here have shown 1/4 wave measurements of 6.7 feet instead of the typical 6 foot theoretical, thus using a 20 foot leg resulted in a better match.)

        I hope I have not been too confusing, I am not a very good writer.  So the final question is :  "why do I want to do this?"  The answer is PATTERN and GAIN.  The resulting pattern in such a system is directional and provides a small amount of signal gain in 2 directions (sometimes one).  Some truckers feel that in front and back is all they need to talk to.  Some users want to have more gain for "shoot-out" purposes.
 

Here is an example of a power polar radiation pattern for two Antennas spaced 1/4 wavelength apart ( about 9 feet) along the x axis (horizontally on your screen or paper) and fed with equal amplitudes and phases .....-->

FIG (1)  TWO ANTENNAS 1/4 WAVELENGTH APART FED IN PHASE


If we increase the spacing to 1/2 wavelength, but still keep the excitation in phase and equal amplitudes, we see deep nulls developing .......-->

FIG (2)  TWO ANTENNAS 1/2 WAVELENGTH APART FED IN PHASE


If we restore the original 1/4 wavelength spacing and feed the antennas in phase quadrature (that is, one antenna is fed with 1/4 wave coaxial feed and other with 1/2 wave resulting in a 90 deg. phase shift), we see a single lobe develop.

(To make the lobe face the other direction we would have to reverse the relative phase, and feed the second antenna at -Pi/2 phase angle.)

FIG (3)  TWO ANTENNAS 1/4 WAVELENGTH APART 90 DEGREES PHASE SHIFT


Returning now to feeding the two antennas in phase, as we increase the spacing we see more sub-lobes or side lobes develop. Here is a picture for spacing of a whole wavelength (36 feet, you would need a BUS)....-->

FIG (4)  TWO ANTENNAS 1 WAVELENGTH APART, IN PHASE


If we now take two antennas spaced by a half a wavelength and feed the elements in anti phase (180 deg. phase shift).  This is the same as FIG (2) accept the pattern is in line with the antennas rather than perpendicular to the line of antennas.
 

 

TWO ANTENNAS 1/2 WAVELENGTH APART ANTI PHASE (END FIRE ARRAY)
 

 

    I have been discussing 1/4 wave spacing and lengths allot and didn't explain how to derive these numbers.  Let me Explain.