Equation Section 1

CORRECTING DUAL PORT PROBE'S PORT-TO-PORT CALIBRATION USING NEAR-FIELD MEASUREMENTS

Jeff Way TRW Space and Electronics Group One Space Park Redondo Beach CA 90278

**Abstract**

When a dual port probe is used for near-field measurements, the amplitude
and phase difference between the two ports must be measured and applied to
the probe correction files so that the measurements and calculations will
have the same reference. For dual port linear probes, the measurement of
this "Port-to-Port" ratio is usually accomplished during the gain or pattern
measurements by using a rotating linear source antenna.^{ [1]}

When a dual port linear probe is used to measure a circularly polarized
antenna, the uncertainty in this Port-to-Port ratio can have a significant
effect on the determination of the cross-polarized pattern. Uncertainties
of tenths of a dB in amplitude or 1-3 degrees phase can cause changes in
the cross polarized pattern of 5-10 dB.^{ [2] [3]} The paper will
present a method for measuring the Port-to-Port ratio on the near-field range
using a circularly polarized antenna as the AUT (Antenna Under Test). The
AUT does not need to be perfectly polarized nor do we need to know its correct
polarization. The measurements consist of two separate near-field scans.
In the first measurement the probe is in its normal position and in the second
it is rotated about the Z-axis by 90 degrees. A script then calculates the
Port-to-Port ratio by comparing the cross-polarization results from the two
measurements. Uncertainties in the Port-to-Port ratio can be reduced to hundredths
of a dB in amplitude and tenths of a degree in phase. Measurements were taken
at TRW's Large Horizontal Near-field Antenna Test Range.

**Keywords:** Antenna measurements; Circular polarization;
Planar near-field; Probe Correction;

Figure 1 Schematic of near-field measurement with dual port probe

- Probe Correction Equations for Dual Port Probes

A typical planar near-field measurement using a dual port probe is shown schematically in Figure 1. The probe is moved over a planar area that is usually very close to the AUT and at equally spaced points on a rectangular grid the receiver measures the amplitude and phase of the signal received by both ports of the probe. A switch is used to change from the X-polarized port to the Y-polarized port of the probe. This is done very fast so the measurements are made at essentially the same point. The port-to-port ratio is due to the difference in the electrical properties of the two paths from the space side of the probe to the common output connector on the switch. This ratio must be known so the measured data from the two ports will have a common amplitude and phase reference. The port-to-port ratio includes the electrical properties of the probe, the polarizer, connectors and cables, impedance mismatch between components and the switch.

The main and cross-component patterns of both the AUT and the probe have some effect on every measured data point in the near-field, and that effect is correctly accounted for in the two Equations describing the near-field measurements.

(1)

(2)

In the above equations, BThe first step in the data processing is the calculation of the spectrum of the measured data using the Fourier transform.

(3)

(4)

Once the spectrum has been obtained, the transmitting spectra for the AUT are obtained by applying the probe correction.

(5) (6)

Where the probe polarization ratios are,

(7)

Equations (5) and (6) are the full probe correction equations that are generally implemented in the software. For well-polarized probes with axial ratios on the order of 40 dB, the equations can be simplified, and for the following derivation we will neglect the cross-polarized terms in the probe correction. They will have a second order effect on the derived result. The term involving the ratio of polarization ratios in the denominators of (5) and (6) is extremely small compared to one and can be neglected. The second terms in the numerator of Equations (5) and (6) are due to the cross component coupling of the probe and will also be neglected.

The simplified probe correction equations are then,

(8)

For a circularly polarized antenna the linear components are combined to give the right and left hand circular components. For receivers and numerical calculations that use for the time dependence of periodic variables, the right and left hand components are,

(9) (10)

and the ratio of left to right components for the case where the main component is right hand circular is

(11)

The axial ratio and tilt angle are given in terms of the ratio by the equations

(12)

For a right hand circularly polarized AUT,

(13)

and if the ratio ofis
incorrect due to errors in the port-to-port ratio, there may be large errors
in the polarization parameters of the AUT. To represent the effect of such
errors, we use Equation (8) to substitute for D_{X }and D_{Y} in
Equation (11). (14)
where the bold symbols represent the AUT and probe parameters without any
error due to the port-to-port measurement. The measured data and the calculated
spectra D_{X} and D_{Y} are defined by the true AUT and probe
parameters not by any errors in the measured probe parameters. The probe
errors only affect the results when the probe correction is applied. We also
use the inverses of Equations (9) and (10) to represent the ratio of linear
components in terms of the circular components also for the AUT parameters
without probe errors.

(15)

Using the fact that the magnitude of the ratio of the circular components is small and the phase is equal to twice the tilt angle,

.(16)

a is the amplitude of the CP polarization ratio, is proportional to the
axial ratio in dB, and or a perfectly polarized RHCP AUT,a =0.

Using Equations (14) and (16), Equation (11) for the circular polarization
ratio calculated using the measured probe parameters becomes

(17)

The terms in the first brackets represent the influence of the AUT properties on the measured and calculated results and the terms in the second bracket represent the influence of the probe Port-to-Port ratio uncertainties on the results since they are the ratios of the true to the measured parameters. The probe ratio error will in general have both an amplitude and phase contribution and these can be represented by the term e and d.

(18) e

and d represent the errors in the measured
port-to-port ratios and these are the parameters that we need to determine.
Combining Equations (17) and (18) and retaining first order terms gives for
the ratio of Left to Right components for the measurement with the X-Probe
aligned with the X-axis

of the measurement system, (19)

If the probe is now rotated about its axis by 90 degrees so the X-probe is now oriented along the Y-axis of the measurement system. Then the new near-field data is measured and processed, the probe parameters are still the same, and the amplitude of the circular components of the AUT will also be unchanged. The tilt angle of the AUT will change by 90 degrees since the reference for the tilt angle is the location of the major axis of the X-polarized probe. The complex polarization ratio for this situation is then

(20)

Adding the complex polarization ratios from the measurements at 0 and 90 degrees gives the desired result, an expression for the probe Port-to-Port errors,

(21)

The real part of the sum is equal to the amplitude error and the imaginary part is equal to the phase error. The error may be calculated at each point of the far-field pattern, but the calculations will only be reliable in the regions where the assumptions used in deriving the final equation are valid. The two major assumptions are that the Left circular component is much smaller than the Right and that the probe errors are small. The first assumption is valid over most of the main beam, and so the equation should only be applied in this region. The final results will be improved by averaging all of the values calculated over the main beam. A weighted average is used where the weight is the ratio of main to cross component amplitude.

**Figure 2 Main and Cross component far-field patterns before
correction of Port-to Port**

- Measurement Example

Figure 2 shows the far-field main and cross component patterns that were obtained from a measurement with the probe at Pol = 0 orientation along with the cross component pattern from the Pol = 90 degree data. The nearly 10 dB difference between the two cross component patterns is an indication of the error in the probe Port-to-Port ratio. The circular polarization ratios were calculated using the two near-field data files and the amplitude and phase corrections were calculated for each point in the far-field pattern over the 4 X 4 degree region of the far-field using Equation (21). The resulting errors for the H-cut are shown in Figures 3 and

**Figure 3 Amplitude error determined from using Equation
(21) and near-field data at Pol = 0 and 90 **

**Figure 4 Phase error determined from using Equation (18)
and near-field data at Pol = 0 and 90.**

The weighted average was computed using all of the far-field data points and in this case gave a correction of 0.16 dB and 1.66 degrees. When these corrections were applied to the X-port of the probe and the far-field patterns recalculated the resulting patterns for the same data files are shown in Figure 5. The cross component patterns now agree to within one dB or less over the full pattern.

** Figure 5 Main Cross component patters after correcting
Port-to Port Ratio.**

Running the correction program again after the first correction was applied resulted in a change in the amplitude of -0.02 dB and the phase of 0.02 degrees and a slight improvement in the agreement between the 0 and 90 degree data. This demonstrates that the process does converge to the correct answer.

- Estimating Uncertainty of Measurement

- Amplitude and phase variation in the rotary joint used to rotate the probe.
- Multiple reflections between the probe and the AUT and room scattering that may be different for the two orientations.
- Differences in the Amplitude and phase patterns of the two ports if the probe patterns are not rotated for the second set of data.
- Leakage and crosstalk signals.
- Drift in amplitude or phase between measurements.

The primary sources of uncertainty in the measurement and calculation are:

The changes due to the rotary joint can be reduced or estimated if multiple data pairs are taken for both plus and minus 90 degrees rotations with different initial angles. A good rotary joint should have changes of less than 0.05 dB and 0.2 degrees. The multiple reflections should be very similar for the two orientations, but can be estimated and reduced by taking repeat measurements at different Z-distances.

In the current implementation of the correction program the probe pattern is not rotated for the 90 degree data set. For the small angular region of the main beam and the broad probe patterns it is assumed that the azimuth and elevation patterns are identical. Comparing the pattern principal plane cuts showed that there is a slight difference in the phase patterns and this is the reason for the slope in the calculated phase correction shown in Figure 4. The maximum error is 0.3 degree and averaging over the main beam reduces this effect to less than 0.1 degree. Rotating the probe pattern for the rotated data could reduce this error.

Receiver leakage can affect the far-field cross polarized pattern in the
on-axis region if it is large enough. Methods are available to measure and
subtract the leakage signal before processing to the far-field if necessary.^{4} In
the current measurement this was not necessary because the leakage was approximately
85 dB below the peak near-field amplitude and 65 dB below the peak far-field
amplitude.

**Figure 6 Error in CP polarization ratio due to amplitude
error in probe port-to-port ratio.**

Figures 6 and 7 show worst case curves for the error in the AUT polarization ratio amplitude as a function of the error in the port-to-port ratio amplitude and phase. The actual error will also depend on the tilt angle of the AUT and these curves have been calculated for the worst case situation for each quantity. As seen from Equation (19) the sensitivity to amplitude errors is very small when t =45 degrees and the sensitivity to phase errors is small when t=0.

A technique has been developed and tests for either measuring or checking the calibration of the port-to-port ratio for a dual port linear probe. The measurement is performed using the actual CP antenna that will be measured by the probe. This approach has the advantage of testing the complete probe and associated cables and switch at the time of use and so errors in the original calibration or changes in components can be measured and correctly adjusted. Using this calibration technique, good cross-polarized results on circular polarized antennas can be obtained while using dual port liner probes.

*The authors wish to thank Chuck Chandler, John Luzwick, Louis Wilson, On
Blanchard, Benny Yee and Gary Ponte for their management, technical and test
support. *
**
**

1) Repjar, A.G.; Newell, A.C. and Francis, M.H., Accurate determination of planar near-field correction parameters for linearly polarized probes", IEEE Transactions on Antennas and Propagation, Vol. AP-36, No.6,pp. 855-886, June 1988.

2) Scott, W. G., Wilson, R. E., "NFR cross polarized pattern errors using a linear probe to measure a circularly polarized antenna," AMTA Proceedings 2000, pp 243-247.

3) Betjes, P. N., "Error analysis of circulary-polarization components synthesized from linearly polarized measurements," AMTA Proceedings 2001, pp 49-53.

4) Rousseau, P. R., "An algorithm to reduce bias errors in planar near-field measurement data," AMTA Proceedings 1999, pp269-273.

5) Hindman, G., Slater, D., "Error suppression techniques for near-field antenna measurements," AMTA Proceedings 1989, p. 14-3