APPENDIX A Excerpts from FINAL REPORT POST ENVIRONMENTAL NEAR-FIELD MEASUREMENTS OF THE MAGELLAN HGA/MGA 4.0 ANTENNA GAIN Antenna gain, as measured at the NFML is a calibration of the peak received signal relative to that of an isentropic lossless antenna. Using the standard definition of gain, all losses due to mismatch at the antenna port to the transmitter were compensated out of the measurement of absolute gain of the antenna to provide mathematical maximum power transfer from the transmitter to the antenna. Also, peak power includes cross-pol contribution although in all cases it was a small term, less than .07 dB for circularly polarized X-Band Telecom and less than .005 dB for the linearly polarized S-Band systems. In this section, we will explain the technique of near- field gain measurement, both physically and mathematically. This section also covers the special case of defining gain for the LGA, both with the HGA reflector, and as it was initially calibrated in the far-field range. An accuracy estimate will be given for the S-Band, X-Band and LGA antennas separately. The accuracy estimate reflects the best accuracy currently achievable at the NFML and is based on known errors, all of which have gaussian distributions, and have been experimentally evaluated by the NFML. 4.1 Gain Measurement Gain measurement at the NFML requires obtaining two measurements directly from the system as configured in Figures 25 and 26 (Archivist's note: these are HGA_APF1.EPS and HGA_APF2.EPS, or HGA_APF1.PS and HGA_APF2.PS, on the PDS archival volume). Both of these measurements have to be extremely accurate and repeatable. The first measurement, that of the near-field of the antenna, is used to calculate a peak far-field signal relative to the near-field. This measurement alone is sufficient to give the far-field radiation pattern of the antenna and its directivity (neglecting any backlobe power). However, to go from the relative measurement of directivity to the absolute measurement of gain requires a system response normalization. The second figure shows how this measurement is performed using the system circuit while substituting a precision attenuator for the test antenna and near- field probe. This measurement is used to calibrate the antenna far-field power to the antenna input power, which then is used to determine gain. 4.2 Gain Equation and Error Estimate In order to calculate gain, some other terms need to be measured beyond the two mentioned above. However, these terms are independent of the current system configuration and have been measured separately. The terms include the reflection coefficients of the various ports used in measuring the antenna, the attenuation value of attenuator used in the system calibration and the gain of the near-field probe. When all these terms are known, they are used in equation 4.1 to calculate absolute gain of the test antenna. 2 2 2 2 4 (4*pi) (FFTmax) |1-Rta*Rt| |S21a| Dxy Ga = ------------------------------------------------------ 4 2 2 2 2 2 Lo (1-|Rta| ) |1-Rt*S11a| |1-Rr*S22a| |S21ad| |a| Gpeff Ga = absolute gain of the test antenna Lo = wavelength at the test frequency (in inches) pi = 3.141592654... Gpeff = measured gain of the near-field probe including probe mismatch terms Rta = reflection coefficient of the antenna port Rt = reflection coefficient of the transmitter port Rr, = reflection coefficient of the test port S21ad = transmission loss of the interface adapter to the antenna Dxy = sample spacing in the near-field (in inches) a = received voltage in Figure 26 FFTmax = peak calculated far-field voltage S11a, S22a, S21a = parameters of the precision attenuator Table 5 lists the errors in the gain measurement resulting from each of the above parameters, and estimates total system error. The total error is given as a RSS estimate because all of the parameter errors are gaussian in distribution and uncorrelated. Therefore, the system error bound is defined as 3 standard deviations, with the true value of antenna gain having a 0.3% probability of occurring outside the error bound, thus the quoted error bound of Table 5 is not absolute but statistical. Table 5 Absolute Gain Error Estimate Error Term S-Band (dB) X-Band (dB) LGA (dB) ---------- ----------- ----------- -------- Lo <0.0001 <0.0001 <0.0001 Dxy <0.001 <0.004 <0.001 S21a <0.10 <0.10 <0.11 S21ad, Rta, Rt and Rr <0.02 <0.02 <0.02 Gpeff <0.10 <0.10 <0.10 FFTmax <0.15 <0.20 <0.30* a <0.02 <0.04 <0.02 ----- ----- ----- Total Error Ga <0.21 <0.25 <0.34 * The higher uncertainty on the LGA arises from trying to define antenna gain in the presence of a 3 dB ripple caused by the reflector backscatter. Table 6 lists the gains measured for the various antennas using the near-field gain equation. Gains are given for the pre- environmental and post-environmental testing with the same error bounds applying to both data sets. Table 6 Antenna Measured Gain Antenna Port Frequency Pre- Post- Environmental Environmental (GHz) Gain(dBi) Gain(dB) ------------ --------- ------------- ------------- 2.116 7.38 7.72 S-Band Telecom 2.116 34.82 34.92 2.298 35.92 35.92 Radar 2.385 35.88 35.82 X-Band Telecom RHCP 7.171 46.65 46.76 8.425 48.27 48.49 X-Band Telecom LHCP 8.425 48.18 48.13 None of the S-Band gains listed in Table 6 are referenced to the spacecraft interface. To obtain those numbers requires the adding of the insertion loss of the cables to the measured gains of Table 6. Also, all measurements were made under standard laboratory conditions of 70F and 30% humidity. Obviously, additional information is required to determine the performance in flight from these laboratory condition results. 4.3 The Special Case of Defining Gain of the LGA The HGA/LGA system is configured with the LGA mounted approximately 12" above the focus of the HGA. Since the LGA has a significant backlobe, it also illuminates the HGA reflector. The characteristic response of the HGA reflector generates a highly directive pattern near boresight when illuminated along its focal axis. When this pattern is superimposed with the direct radiation pattern of the LGA, it generates a ripple in the resulting pattern over a region of approximately 20 degrees off-boresight. Near boresight, this ripple exceeds 3 dB peak-to-peak. While defining peak gain is still simple, it no longer correlates with the gain of the LGA alone. Therefore, to generate the gain listed in Table 6, some additional processing was done to determine the gain of the LGA in an isentropic environment. In addition, this peak gain can be referenced directly to the gain measured on the LGA alone in a far-field range. All the patterns of the LGA, to clarify this gain characteristic, are plotted in this report on an isentropic scale. 5.0 PATTERN DATA The pattern data in this report was generated using planar near- field measurement techniques. This measurement technique yields accurate data over the front hemisphere with an extremely broad dynamic range. It also completely characterizes the antenna pattern over this region to whatever detail desired by the user. This section will explain how this measurement is performed, how patterns are calculated and what errors are generated by this method of measurement. It will also tabulate the beamwidth and the electrical boresight observed in each of the antennas measured. 5.1 Near-Field Measurement Theory The equations of near-field theory are an application of transform theory. The specific method used in planar near-field theory is to measure the radiated fields of an antenna near their origin over a plane. Once this information is collected, it is used in a two-dimensional Fourier transform to generate a function set of planewaves that completely define the forward radiation characteristics of the antenna. The relationship used in the planewave calculation is stated in equation 5.1. --- --- \ \ A(K) = (|kz|/ko) > > E(xm,ym,zo)*exp{-jK*(xm*X + ym*Y)} (5.1) / / --- --- m n A(K) = far-field pattern K = wavenumber vector (determines direction of propagation) E(xm,ym,zo) = electric field (vector) measured above the aperture at plane z = zo kz = z-component of K ko = magnitude of k in free space X,Y = unit vectors in x,y directions To generate the true far-field pattern from experimental measurement requires additional compensation, especially when the angle of radiation is large relative to the scanner boresight (greater than 30 degrees), to compensate for using a non-ideal probe. These decoupling relationships are explained in detail by Newell (1). Compensating for the near-field probe is not critical near boresight since it has almost pure linear polarization (axial ratio exceeds 40 dB). However, when measuring patterns at angles exceeding 30 degrees off-boresight as in the case of the LGA, both the probe pattern and its cross-pol component will cause noticeable differences in the measurement data unless they are compensated out of the measurement. Once these terms have been corrected for in the data, the wide angle measurement accuracy is the same as the accuracy near-boresight. The conversion of the data from the kx,ky coordinates to theta,phi or equivalent coordinates derives from the fact that for a nonreactive field (one that propagates), its direction is exactly determined by its wavenumber. This fact is essential to extracting information such as the electrical boresight of an antenna with a degree of accuracy not possible by conventional far-field techniques. The near-field measurement method also allows extremely accurate estimates of peak sidelobes, beamwidth and null depth by virtue of its high resolution of the antenna pattern over the front hemisphere. 5.2 Pattern Error Bound and Parameter Summary Section 5.2 gives estimates of the near-field measurement accuracy, including the following parameters: beamwidth, peak first sidelobe and peak cross-pol based on experimental observation of the data statistics. For all measurements, the errors had a gaussian distribution, therefore, the 3 standard deviations error bound will be used. Because the greatest source of errors, by far, in near-field pattern measurements is system repeatability, the other known error sources such as scanner planarity and system linearity will not be itemized in the error budget. Table 7 lists the error estimates for each of the pattern parameters covered by antenna requirement specification. Table 7 Pattern Parameter Accuracy Antenna Parameter Error Bound ----------------- ----------- HGA S-Band 3 dB Beamwidth <0.020 deg HGA S-Band 10 dB Beamwidth <0.030 deg LGA 3 dB Beamwidth* <4.0 deg HGA X-Band 3 dB Beamwidth <0.009 deg HGA S-Band Peak Sidelobe <1.00 dB HGA X-Band Peak Sidelobe <0.60 dB HGA S-Band Minimum Null <1.30 dB HGA S-Band Cross-pol <0.70 dB HGA X-Band Axial Ratio <0.15 dB * 3 dB Beamwidth of the LGA in an isentropic environment. Using Table 7 as the error bound on the measurement parameter, the data covering these parameters is tabulated in Tables 8 and 9. Table 8 Main Beam Pattern Parameter Antenna Port, Frequency Beamwidth (deg) ----------------------------------------- Pre-Environmental Post-Environmental ----------------- ------------------ Minimum Maximum Minimum Maximum ----------------------- ------- ------- ------- ------- LGA, 2.116 GHz 74.1 81.7 74.1 81.7 RHCP Telecom, 7.171 GHz 0.6697 0.6840 0.6727 0.6837 RHCP Telecom, 8.425 GHz 0.5711 0.5856 0.5717 0.5829 LHCP Telecom, 8.425 GHz 0.5668 0.5860 0.5704 0.5847 E-Plane H-Plane E-Plane H-Plane ------- ------- ------- ------- Telecom, 2.116 GHz 2.415 2.866 2.416 2.877 Telecom, 2.298 GHz 2.133 2.632 2.131 2.622 Radar, 2.385 GHz (3 dB) 2.111 2.530 2.101 2.529 Radar, 2.385 GHz (10 dB) 3.597 4.444 3.575 4.439 Electrical Boresite (deg) ----------------------------------------- Pre-Environmental Post-Environmental ----------------- ------------------ LGA, 2.116 GHz 0.00 0.00 Telecom, 2.116 GHz 0.11 0.10 Telecom, 2.298 GHz 0.05 0.08 Radar, 2.385 GHz 0.05 0.04 RHCP Telecom, 7.171 GHz 0.05 0.03 RHCP Telecom, 8.425 GHz 0.04 0.03 LHCP Telecom, 8.425 GHz 0.04 0.03 Table 9 Measured Peak First Sidelobe, Cross-Pol, Axial Ratio, and Null Depth Data Antenna Port, Frequency Parameter (dB) ----------------------------------------- Pre-Environmental Post-Environmental ----------------- ------------------ Peak First Sidelobe ----------------------- ------------------- Telecom, 2.116 GHz -13.2 -13.2 Telecom, 2.298 GHz -14.9 -14.6 Radar, 2.385 GHz -16.2 -15.7 RHCP Telecom, 7.171 GHz -14.3 -14.9 RHCP Telecom, 8.425 GHz -13.1 -13.2 LHCP Telecom, 8.425 GHz -13.0 -13.3 Cross-Pol* ---------- Telecom, 2.116 GHz -21.9 -22.0 Telecom, 2.298 GHz -22.6 -22.5 Radar, 2.385 GHz -20.0 -20.7 Axial Ratio ----------- RHCP Telecom, 7.171 GHz 2.0 1.0 RHCP Telecom, 8.425 GHz 2.9 1.8 LHCP Telecom, 8.425 GHz 1.9 1.6 Minimum Null Depth ------------------ Radar 20.0 20.5 * Peak cross-pol inside 3-dB beamwidth of co-pol, per program specification. The format of the remaining data in this report is assorted far- field patterns, which will be explained in detail in the next section.