The axial ratio is the ratio of orthogonal components of an E-field. A circularly polarized field is made up of two orthogonal E-field components of equal amplitude (and 90 degrees out of phase). Because the components are equal magnitude, the axial ratio is 1 (or 0 dB).

The axial ratio for an ellipse is larger than 1 (>0 dB). The axial ratio for pure linear polarization is infinite, because the orthogonal components of the field is zero.

Axial ratios are often quoted for antennas in which the desired polarization is circular. The ideal value of the axial ratio for circularly polarized fields is 0 dB. In addition, the axial ratio tends to degrade away from the mainbeam of an antenna, so the axial ratio may be indicated in a spec sheet (data sheet) for an antenna as follows: "Axial Ratio:

There is the three antennas method when you make your antenna as the end of the receiving HF RF  transmission string considering onther transmitting transmission line with a known antenna (wich we know the caracteristics like horn, helicoidal, patch or ...). look then for the three antennas method.

To MEASURE the axial ratio, you need to measure two orthogonal polarizations normal to the propagation direction, measuring both the magnitude and phase relationship of the two signals.  For passive antenna pattern measurement, this is relatively straightforward using a vector network analyzer, since every measurement is referenced back to the phase and magnitude of the source.  If you use the same measurement antenna (e.g. a dipole or horn) and rotate it 90 degrees to capture each component, then you can generally ignore calibration related issues.  However, many antenna measurement systems use dual polarized measurement antennas to allow simultaneous measurements of both polarizations, requiring calibration of each path relative to a reference in order to get the magnitude and phase differences between the two measurement antennas.  

Once you obtain the two linearly polarized components of the field, you have to convert from linearly polarized components to elliptically polarized components.  That will give you the major and minor components of the field which can then be used to evaluate axial ratio.  For circularly polarized fields, the major and minor components are equivalent and the axial ratio is one.  For a linearly polarized field, the minor component is zero and thus the axial ratio is infinite  (I would have defined AR the other way and made it range from one to zero, but I wasn't there when it was defined!).  Elliptical polarizations then range from circular (zero) to linear (infinite) axial ratio.

Choose receiving antenna as a simple dip[ole at your frequency. Keep receiving antenna in front of radiating antenna along with power measurement set up at a distance of fronhaufer region. (1) Measure the received power keeping Rx dipole Horizontal. (2) Measure the received power keeping Rx dipole in Vertical position. 

Ratio of these two power is Axial ratio if measurement is linear or Difference is axial ratio if measurement is dB

Amir has given the proper theoretical background and Amipara gave you the simplest measurement procedure. However, usually Axial Ratio(AR) is required to check the quality of circular polarization in a CP antenna. Even if you find the AR to be 0 dB following the procedure suggested by Amipara, that does not necessarily mean that the antenna is truly CP, since this observation would have been valid even if the antenna were DP(dual polarized). A DP antenna has got two orthogonal field components equal and in phase, whereas CP requires phase quadrature along with this equality. So to check for CP, you need to measure the radiation pattern at two other cut planes, preferably at 45 and 135 degrees to horizontal and measure AR again in the same way. For good CP, these two ratios should be almost same.

Thank you for all, and for that kind example from "Amipara" that really helpfull 

A question to (Amipara): what if the difference between the power levels received in dBm became negative? Is it reasonable to take the absolute value after subtraction?

Just to clarify, I am focused on the axial ratio in dB here, not the linear.

There are a LOT of assumptions in the method described by Amipara that aren't likely to be valid.  What's described there is the measurement of V/H ratio, not AR, although it MIGHT be equivalent to AR under specific cases.  Again, AR is the ratio of max to min on an elliptical polarization.  If the major axis of the ellipse is along either V or H and you are doing the measurement in free space, then the V/H ratio and AR will be the same value to within a sign difference.  However, for any other orientation of the ellipse  you'll get the wrong answer.  For example, a linearly polarized antenna with a 45 degree tilt would give you a V/H ratio of 1 (0 dB) indicating it's circularly polarized, rather than linear.   Also, if you're not in a free space environment, reflections off of the ground or other objects will impact the measured result and throw off the calculation of AR.  

The modification to Amipara's procedure that will work with a scalar analyzer (e.g. spectrum analyzer, etc.) is to rotate the linearly polarized measurement antenna or the antenna under test about its polarization axis (the line between the two antennas) until you maximize the measured signal.  That will be the major axis of the ellipse.  Then rotate one of the antennas 90 degrees about the line between the antennas to measure the minor axis of the ellipse.  The axial ratio is then the major to minor axis.  This again assumes that there is no ground bounce interfering with the measurement.  

As far as the case of a negative ratio in dB, that means you have the axes backwards and are looking at min/max instead of max/min.

Thank you Michael Foegelle for the reasonable and detailed answer.

I am measuring an omni-directional circularly polarized antenna and it is a tough one it seems, unlike simple directional antennas such as the ceramic ones used for GPS appliactions, which you most probably only need to rotate around the axis of propagation and maximize the received power to characterize the ellipse and get the correct AR.. because the AR is usually specified along the direction of propagation. Nobody usually cares about how good or bad the AR gets when you move away from the center where you get the highest gain and AR.

For my omni-directional CP antenna, I have to find out how skewed the ellipse is every few degrees along the perimeter of a full circle (360 degrees) surrounding the antenna (azimuth).. or the circle that is parallel to the ground. I will then need to plot the samples of AR I get in a polar plot (of the plane parallel to the ground) to see whether the antenna provides a decent AR at any angle around it (since it is supposed to be omni-directional even in terms of the AR). And that's not enough either, I will have to look at the AR at a few angles lower than the horizon, and again all around the antenna, to see if it still provides acceptable ARs below the horizon when mounted vertically since it is the most practical case. Ideally, I should probably look at that even above the horizon for a more complete measurement, to see the what I call as the (3 to 3 dB AR beamwidth).

This kind of measurement.. deserves a party when finished.

I hope this shared info benefits somebody here.

Hi Ali,

For what you're trying to accomplish, the easiest approach is really to do a full spherical vector antenna pattern measurement with an appropriately configured/calibrated system and software.  The software we developed here can provide AR as a function of direction from a full vector pattern.  

A quick Google search turns up a good reference that shows how to calculate the elliptical components and AR from two orthogonal linear components, but as mentioned, you also need the phase relationship between those components.  See Case 3, Equations 5.8-5.11 in the following.

http://www.ece.mcmaster.ca/faculty/nikolova/antenna_dload/current_lectures/L05_Polar.pdf

Good luck with your efforts.  

Hi Michael,

Our resources are slightly limited at the moment, and we actually are negotiating a solution from ETS iteself! But that is not going to happen in the very near future anyway.

The best solution I have now is to follow an indirect way to find out how similar the AR is to the simulation. It involves the subtraction of the two power components along the two perpendicular axes measured, just like the method Amipara had suggested (with all the assumptions it came with). But this time I have to do the same with my simulated E-field/Power pattern and then match it with the measured results. This way, I can rely on the simulation results of the AR indirectly based on the safe assumption that the AR ellipse is skewed by almost the same angle in the simulation when compared to its corresponding measured value, and that is because the subtraction of the two orthogonal power components regardless of the ellipse's skew angle lead to the same result in both the simulation and measurement.

The day we get our ETS chamber, however, would be just another day to party hard.

Have a good day, Michael, and great gratitude for your time!

From the answers I have seen, none really answer the question, but provide a direction to go. If you have measured the orthogonal components with amplitudes E1 and E2 with a phase difference of del, then one development leads to

AR = sqrt((E1^2+E2^2+sqrt(E1^4+E2^4+2*E1^2*E2^2*cos(2*del)))/

                   (E1^2+E2^2-sqrt(E1^4+E2^4+2*E1^2*E2^2*cos(2*del))))

Hope this helps.

Michael has the correct set of answers here. The others are too simplistic. If you don't have phase measurements and only have received power you could try to (carefully) rotate one of the antennas about the transmission path axis and record the received power as a function of angle of rotation. This will give you the ratio and its orientation. You may get cable issues hence the carefully. The balance of the antennas is also an issue. If you rotate your probe dipole by 180deg and get a different amplitude you have a balance problem.

The answer by Amipara Manilal D is over simplified. It assumes that the polarization ellipse axes are aligned with the vertical and horizontal directions. To use his method in concept, you would first have to orient the probe for a peak response and then rotate 90 degs for the min. response (hopefully). Taking that ratio should give you the AR (in magnitude). You can also measure in 3 independent, but known, orientations and then compute the ellipse that fits all three directions and get the AR from that system.

The simplest and most complete way today (as mentioned) is to use a vector ANA and measure the theta and phi components (or vert/horz) in magnitude and phase. Then adding Eth and j*Eph components (th and ph for theta and phi) to get the RCP part, ER, and subtraction to get the LCP, EL. The circular polarization ration is then

rhoC = ER/EL

and the AR is then

AR = (|ER|+|EL|)/(|ER|-|EL|)

This form gives a positive quantity for a RH ellipse with the dB of the magnitude typically reported as the axial ratio, and the negative form indicates a LH ellipse. For further information refer to the Antenna book by Stutman and Thiele. So the advantage of the amplitude and phase measurement is that you can also determine the sense of CP, not just the |AR|.

Please follow this paper....

They gave a procedure which is widely accepted.

They explained the way of obtaining RHCP and LHCP gain of an Circularly polarized antenna. i think it would clear all the doubts.

thanks Bharath ji

Thanks a lot sir Michael Foegelle!

You're quite welcome. Always glad to help.

The axial ratio is defined as the ratio between the minor and major axis of the polarization ellipse. Recall that if the ellipse has en equal minor and major axis it transforms into a circle, and we say that the antenna is circularly polarized. In that case the axial ratio is equal to unity (or 0 dB). The axial ratio of a linearly polarized antenna is infinitely big since one of the ellipse axis is equal to zero. For a circularly polarized antenna, the closer the axial ratio is to 0 dB, the better. This parameter is majorly used to describe the polarization nature of circularly polarized antennas.

Hope this helps

Thank you Mr Bharath Reddy Gudibandi for sharing the papers.