STEP3: Model combining direct and reflected waves. Antenna measurements Nordic VHF Meeting, Íland 970606

(Feb 16 1998)

Why all these details ??

Since the method of measuring antenna performance by comparision of far field amplitudes and phases is not commonly used and since it leads to a considerable amount of data processing it is described in great detail here.

All data and software needed is presented in full detail in such a way that the evaluation process can be repeated by anyone interested. It is possible to investigate how sensitive different parameters in the computer model are to changes. For example it is possible to move the center of rotation along the boom or perpendicular to see if the change that occurs can be compensated by changing other parameters.

This site serves as a back up for software and general information about this method for later use at better sites than the one used at the Nordic VHF Meeting on Íland 1997.

Description of the data

The model calculates the expected complex voltage that would be observed when the AUT is rotated at a fixed frequency. These model patterns are all normalised so the average power from all directions is 1 for each frequency.

The experimental patterns are normalised in the same way, and the phase of all points is shifted by a fixed angle to make the phase zero in the forward direction.

The amplitude and phase change with frequency not only because of the AUT - the fixed antenna also adds a contribution. The attenuation and phase shift caused by mismatch has a large influence on the change with frequency of phase and amplitude. It is not meaningful to build a model that includes the absolute phase and absolute amplitude without accurate measurements of feedpoint impedances, cable lengths and geometric data. The VSWR changes with frequency and NEC2 does not model it well for folded dipoles.

The model produces 51 radiation patterns at 51 different frequencies for each antenna. For 17M2 an additional series of measurements was made at different heights, but with the elevation angle = 0 at all heights. In this way 17M2 was measured twice at 10 meters and 0 degrees. The height series was scaled in amplitude and phase to be similar to the angle series for the common geometry (10 metres and 0 degrees) because unfortunately the network analyser was recalibrated between these two series.

K1FO 51 frequencies in 32 directions
VARG13 51 frequencies in 25 directions
17M2 51 frequencies in 31 directions
17M2 51 frequencie at 8 heights, direction=0
BSZ9 51 frequencies in 29 directions
VARG9 51 frequencies in 22 directions

Running the STEP3.EXE program with the files supplied with it produces .DAT files containing amplitudes and phases for the measured data and for the model. These files also give separately the different waves that sum up to the model.

Global parameters

Some parameters are common for all measurement series. These parameters are contained in the file GLOBAL.TXT which is one of the input files to step3.

-----------------------------------------------------------
FIXTOWER     0   0  7.0
In the final parameter fitting process this parameter is kept fixed at 7.0. It is the height above ground in meters for the fixed antenna. Allowing this parameter to adjust freely does not improve the parameter fit, it just degrades convergency by introducing linear dependances. The model does not improve when the height of the fixed antenna is allowed to deviate from the measured value 7 metres. The height of the fixed antenna is used to calculate the direction from which the direct wave and the the ground reflection come. It does not affect the phase of the direct wave, but it does affect the phase of the ground reflection.

-----------------------------------------------------------
TOWDISTANCE  0   0 63.140541   0.00005
The distance between the two towers. Used together with the fixed tower height for angles and phase of ground reflection.


-----------------------------------------------------------
RFLAMPL144   0   1  0.705472   0.00005
RFLAMPL432   0   1  0.826093   0.00005
RFLDISTANCE  0   1  1000.
RFLHEIGHT    0   1  0.
RFLPHASE144  0   1  3.609131   0.00002
RFLPHASE432  0   1  5.024800   0.00002
These are the remaining parameters for the first reflection, the one from the ground between the towers. The 1 in the third column tells that these parameters belong to the first reflection. The values are in the fourth column and RFLDISTANCE = 1000 means that FIXTOWER and TOWDISTANCE are to be used to get the geometry for a reflection from the ground between the two towers.

RFLAMPL gives the amplitudes as a fraction of the amplitude of the direct wave and RFLPHASE gives a phase shift that is added to the phase shift due to the path length being longer than the direct wave path.


-----------------------------------------------------------
RFLAMPL144   0   2  0.012967   0.00002
RFLAMPL432   0   2  0.014963   0.00002
RFLDISTANCE  0   2 -92.441969  0.0002
RFLHEIGHT    0   2  6.0
RFLPHASE144  0   2  0.721643   0.00002
RFLPHASE432  0   2  5.290989   0.00002
These parameters describe reflections from a building about 100 meters behind the AUT. (92.44 m from parameter fitting)


-----------------------------------------------------------
RFLAMPL144   0   3  0.008875   0.00002
RFLAMPL432   0   3  0.028954   0.00002
RFLDISTANCE  0   3 -78.945276  0.0002
RFLHEIGHT    0   3  0.5
RFLPHASE144  0   3  5.072266   0.00002
RFLPHASE432  0   3  4.428474   0.00002
These parameters describe a stone wall and perhaps some parked cars in front of the building. It is clearly seen from the data that there are two different (or maybe more) reflections from behind. It is not possible with the limited number of angles around 180 degrees to determine the different heights, so the heights were fixed at reasonable values. Allowing the heights to find optimum values gives unrealistic positions for the reflection points but it does not change the sum of the two reflected waves significantly.


-----------------------------------------------------------
The second column is 0 if a parameter should not be changed. If the second column is made = 1 for a parameter, the STEP3 program will try to find a better value for that parameter.

The last column gives the step size used by the optimisation algorithm when calculating derivatives.

Antenna specific parameters

For each antenna there is a file ANTPAR.TXT in respective subdirectory. These files are used by all three evaluation steps. The file for 17M2 is used as an example:

-----------------------------------------------------------
PATHLEN       0 250.

This parameter is manually set to a reasonable value as described in STEP1.
250 meters is the free space distance that is required to compensate
for the total delay through cables and the air between the towers
for the 17M2 antenna.


-----------------------------------------------------------
HEIGHT       10 10.

The second column gives the step size in decimeters for search of
files xxxxHyyyM.DAT files.
If the second column is 0 only files xxxx.DAT are looked for.
The third column is the height of the center of rotation for the AUT.

The height parameter is just the measurement data. It is not meaningful to try to fit better values - it would only introduce linear dependances.


-----------------------------------------------------------
ELCORR        0 -5.2

This parameter is used by STEP2 as an input to the NEC2 simulation
of the radiation pattern.
If the second column is changed from 0 to 1 the optimisation
procedure will suggest a new value for the boom correction in the
last iteration.
When ELCORR is changed STEP2 has to be rerun.


-----------------------------------------------------------
RZNOM         0 200.
The nominal feed impedance. It is used to calculate the phase shift due to the mismatch at the feed point by use of the NEC2 impedance values. For 17M2 the nominal impedance is 200 ohms because a 4:1 balun is used.

This parameter has no effect at all on the final result. It just makes the phase vs frequency function more flat, allowing it to be ommitted in the early parameter fitting process.


-----------------------------------------------------------
BOOMPOS       0 4.265814  0.00001
The distance from the reflector to the center of rotation. The NEC2 simulation assumes the antenna is rotated around the reflector which is placed at the origin. This parameter is used to calculate how the path lengths for the direct wave and for the reflected waves are changed at different elevation angles.

If the 0 in the second column is changed to 1 STEP3 will try to find a better value for this parameter. The last column is the step size in the optimisation process.


-----------------------------------------------------------
BOOMOFFSET    0-0.153713  0.00001
The distance from the plane of the elements to the center of rotation. This parameter is used to calculate how the path lengths for the direct wave and for the reflected waves are changed at different elevation angles.

If the 0 in the second column is changed to 1 STEP3 will try to find a better value for this parameter. The last column is the step size in the optimisation process.


-----------------------------------------------------------
FIXPHASE      0 0.283605  0.00001
A constant phase shift, equal for all frequencies and elevation angles but particular for the current antenna, cable length... (17M2)

If the 0 in the second column is changed to 1 STEP3 will try to find a better value for this parameter. The last column is the step size in the optimisation process.


-----------------------------------------------------------
PHSINCOS   9910 0.00001
A flexible function for the phase vs frequency for this particular antenna. This function will absorb errors in the NEC2 impedance and phase shifts due to the fixed antenna.

If the number (9910) in the second column is larger than 25 (no of frequencies/2) the parameter values from the file PHSINCOS are used and no attempt is made to find better values.

If a negative value is put in the second column, a new phase function of the corresponding size is given the initial values 0 and optimisation is started.

If the second column is given a value below 25 (e.g.10) a flexible function of that order (e.g. 10 lowest sine and cosine functions) is optimised.

The last column is the step size in the optimisation process.

STEP3 will overwrite the PHSINCOS.TXT file after the last iteration if the value in the second column is below 25. The PHSINCOS.TXT file typically looks like this (first 12 lines):

   1  0.624393 -6.133963
   2 10.105142 -2.851466
   3  5.650404  9.744010
   4 -6.440431  6.575216
   5 -5.545404 -2.853227
   6  0.630104 -3.589655
   7  1.738404 -0.125290
   8  0.168252  0.593389
   9 -0.130768  0.065073
  10 -0.008689 -0.014077
  11  0.000000  0.000000
  12  0.000000  0.000000
This is the phase vs frequency function expressed as a fourier series of 10 sine and cosine terms.


-----------------------------------------------------------
ANGCORR       0 0.00001
The angle and height measurements contain errors. The second column allows the optimisation of errors that improve the total agreement between model and measurements. If the second column is made -1, the errors are initiated to zero and optimised. The last column is the step size used by the parametrisation process.

The angle/height errors are stored in MTANGFIX.TXT. The errors in MTANGFIX.TXT are used as they are without optimisation if the second column is 0 and they are taken as initial values for optimisation if the second column is 1.

The error parameters should only be used in a final optimisation step, to make them all zero STEP3 can be run once with column 1=-1 and column 3 = 0.0

The STEP3 program updates MTANGFIX.TXT after the last iteration. MTANGFIX.TXT typically looks like this (17M2):

   1 -0.089569
   2 -0.142826
   3 -0.052437
   4  0.070051
   5 -0.020195
   6  0.027081
   7 -0.008145
   8 -0.019665
   9 -0.067518
  10 -0.049239
  11 -0.017488
  12  0.021288
  13  0.037849
  14 -0.020631
  15  0.030455
  16  0.033081
  17  0.024513
  18  0.055751
  19  0.032891
  20  0.040328
  21  0.038341
  22  0.018537
  23  0.015333
  24 -0.002747
  25 -0.025470
  26 -0.031196
  27 -0.034792
  28 -0.040578
  29 -0.185917
  30  0.061891
  31 -0.040877
  32  0.464845
  33 -0.035564
  34 -0.031201
  35 -0.244949
  36 -0.090103
  37  0.017230
  38 -0.059835
  39 -0.014126
The first 31 values are errors in angle in degrees while values 32 to 39 are height errors in meters. It is not surprising that a large error is observed for the measurement at a height of 3 meters. This measurement should have been excluded since the antenna was only 2 meters above a metal fence in front of the antenna. All other error parameters take very low values, well within the estimated accuracy of measurement for 17M2. For the VARG13 one angle has a large error, 0.46 at 322 degrees. All other errors are small for the measurements included in the parametrisation of the model.

How to run STEP3.EXE with optimum(?) parameters

First follow the instructions for STEP1 and for STEP2 DownloadSTEP3.ZIP containing the source code and .EXE file for STEP3 into the main directory and unpack. DOS4GW is still needed.

If you have a FORTRAN compiler, you may recompile the source code that is supplied with the .EXE file. Note that some of the .FOR and .INC files contained in STEP1.ZIP and in STEP2.ZIP are also needed.

Once you have STEP3.EXE in the main directory, start it by typing DOS4GW STEP2.

The STEP3 program uses the file ANTLIST.TXT which is one of the files in STEP2.ZIP. The ANTLIST.TXT file has to contain the names of the subdirectories for the antennas to process.

When STEP3.EXE is run, with GLOBAL.TXT and CONTROL.TXT as supplied with STEP3.EXE and with ANTPAR.TXT, PHSINCOS.TXT and MTANGFIX.TXT as supplied with the measurement data for the respective antennas, .DAT files are written to the main directory with data for measurement, model and the different waves summing up to the model.

There is a primitive graphic package that allows comparision between the model and the experiment as the last part of the STEP3 program.

As an example, these are a few lines of the 17M2.DAT file:


            17M2.DAT
 FREQ,ANGLE,CORR.ANGLE,H,CORR.H,EXP,TEO,DIR,(REFL(N=  3)
 NFREQ  51    IAZ  39
  138.00    0.00   -0.09  10.0   9.9  17.51898035   0.00000000
                                      15.76606973   2.37782670
                                      28.44451984  -6.30352282
                                     -12.67113677   8.59936082
                                      -0.02940860   0.04878664
                                       0.02209526   0.03320206
  138.00   23.50   23.36  10.0   9.9   9.48307946   8.12605642
                                       8.45351209   8.71592520
                                       6.55343685  12.29657050
                                       1.88786353  -3.67255268
                                      -0.01401265   0.05836163
                                       0.02622436   0.03354575
  138.00   27.80   27.75  10.0   9.9   2.52218927   5.84970814
                                       1.70898396   6.18798079
                                      -0.69885775   8.67478798
                                       2.37871858  -2.56815193
                                      -0.00049556   0.05289295
                                       0.02961869   0.02845180
At 138MHz the forward measured signal is ( 17.52 , 0 ). The model gives ( 15.77 , 2.38 ) and that signal is composed of a direct wave of ( 28.44 , -6.30 ) that is partly canceled by a reflected signal of (-12.67 , 8.60 ) and some very small contributions from the reflections behind.

Optimisation of parameters

The STEP3.EXE program is controlled by the CONTROL.TXT file. To change the contents of CONTROL.TXT while STEP3 is executing some other memory resident program is needed like SideKick (Borland).

If the first line of CONTROL.TXT is blank, the parametrisation continues until convergency is obtained.

If the first line in CONTROL.TXT contains the word STOP, the iterations are stopped and the current parameter values are written to PAR.TXT in the main directory and the PHSINCOS.TXT and MTANGFIX.TXT files are updated for all the antennas contained in ANTLIST.TXT. The ELCORR parameter is not changed (rerunning STEP2 is slow) It is up to the user to copy values from PAR.TXT to GLOBAL.TXT and the ANTPAR.TXT files.

If the first line in CONTROL.TXT contains the word ELCORR, One more iteration is made in which the boom corrections are allowed to change. Then the iterations are stopped and the parameter values written to PAR.TXT in the main directory and the PHSINCOS.TXT and MTANGFIX.TXT files are updated for all the antennas contained in ANTLIST.TXT.