1. ANTENNA FACTOR CALIBRATION TECHNIQUES
Prof. N. K. Agarwal
KIIT College of Engineering
Gurgaon

2. 1. Introduction
Electromagnetic radiations are natural byproducts of modern electronic equipment.
Such emissions can cause interference to other users of electromagnetic spectrum
Hence various regulatory and advisory agencies have established limits on emissions
Limits are expressed as field strength in terms of volts per meter (or dB μv/m )
Emissions are measured using calibrated antennas and a receiver

3. 1. Introduction (cont.)
If E is the field strength, AF is antenna factor and V is receiver input voltage then Or
EdB μv/m = AFdB + VdB μv (2)
So to obtain radiated field as EdB μv/m one has to measure antenna terminal voltage with a calibrated receiver in VdB μv and add the antenna factor in dB
Thus antenna factor permits computation of electric field intensity (E) by measuring the voltage at the output terminal of the antenna loaded by an impedance matched receiver
𝐸=𝐴𝐹∗𝑉              1

4. 2. Formula for Antenna Factor
Power received by antenna
Where E = Electric field intensity
G = Receiving antenna gain
= Wave length
If V is the voltage at the input of the impedance matched receiver then power received is
𝑃 𝑟 = 𝐸 ∗ 𝐺 𝜆 2 4𝜋        3

5. 2. Formula for Antenna Factor (cont.)
Where Z is the receiver input impedance. Equating the two values of in (3) and (4)
𝑃 𝑟 = 𝑉 2 𝑍         4

6. 2. Formula for Antenna Factor (cont.)
For 50 ohms system
Hence the antenna factor of an antenna in free space and in far zone for a 50-ohm system is
Thus if gain of an antenna is measured its antenna factor can be computed at the frequency of measurement.
𝐴𝐹=  𝐸 𝑉 = 9.73 𝜆 𝐺       7

7. 3. Antenna Factor Calibration Techniques
The antenna calibration can be accomplished by four independent methods:
Insertion loss method
Standard antenna method
Standard field method
Standard test site method

8. 3.1 Insertion Loss Method The antenna can be calibrated by using
Two identical antennas
Three unknown antennas
This is the most common and the simplest method of antenna gain measurement

9. 3.1.1 Two Identical Antennas Method
Based on Friis’s transmission equation
Described in ARP-958 of March 1968 and Mil-Std-461
Power received by an antenna is given by
𝑃 𝑟 = 𝑃 𝑡 𝐺 𝑡 𝐺 𝑟 𝜆 4𝜋𝑅 2       8 𝑊ℎ𝑒𝑟𝑒    𝑃 𝑡 =Transmitter power                   𝐺 𝑡 = Trannsmitting Antenna Gain                   𝐺 𝑟 =Receiving Antenna Gain                  𝑅   = Distance 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑎𝑛𝑡𝑒𝑛𝑛𝑎𝑠

10. 3.1.1 Two Antenna Method (cont.)
If the transmitting and receiving antennas are identical and assuming Gr = Gt = G then OR
If measuring system has an impedance of Z (normally 50 ohms) and Vt and Vr are the transmitting and receiving voltages respectively then
𝑃 𝑟 = 𝑃 𝑡 𝐺 2 𝜆 4𝜋𝑅 2       9
𝐺= 4𝜋𝑅 𝜆 𝑃 𝑟 𝑃 𝑡               10
𝐺= 4𝜋𝑅 𝜆 ∗ 𝑉 𝑟 𝑉 𝑡                  11

11. 3.1.1 Two Antenna Method (cont.)
Hence by measuring Vr and Vt antenna gain or antenna factor or both can be determined
The test set up for measuring Vr and Vt is shown in Fig.1
Fig.1 Test Set Up

12. 3.1.1 Two Antenna method (cont.)
The test area in which the test set up is situated should be clear of any obstruction in order to achieve free space conditions as nearly as possible
At each designated test frequency the receiver is used as a reference device.
Step by step test procedure, as given in Mil-Std-461 and SAE ARP-958, is used to determine the ratio Vr / Vt

13. 3.1.1 Two Antenna Method (cont.)
Measurements should be repeated at every 10 MHz from 20 MHz to 1 GHz and every 1 GHz above 1 GHz
If R = 1m and fMHz is the frequency in MHz corresponding to wavelength λ then
Since So
𝐴𝐹= 9.76 𝜆 𝐺                        13
𝐴 𝐹 𝑑𝐵 =10log 𝑓 𝑀𝐻𝑧 +10log 𝑉 𝑡 𝑉 𝑟 −16 𝑑𝐵       14

14. 3.1.2 Three Antenna Method
Identical antennas may actually differ in gain by an appreciable amount. So gain measured will be equal to geometric mean of the individual gains.
Where G01 and G02 are gains of antenna #1 and antenna #2 respectively
So measurement is supplemented with a 3rd reference antenna whose gain need not to be known.
Also, if 2 identical antennas are not available, the 3- antenna method for gain determination may be used.
3 simultaneous equations for gain products can be written by using combination of 2 antennas at a time. Then from the equations (11) and (15)

15. 3.1.2 Three Antenna Method (cont.)
Thus the gain of three antennas is obtained without previous knowledge of the gain of any one of them
Two or three antenna method provides maximum accuracy but is very time consuming
𝐺 01 𝐺 02  = 4𝜋𝑅 𝜆 ∗ 𝑉 𝑟1 𝑉 𝑡2                  𝐺 02 𝐺 03  = 4𝜋𝑅 𝜆 ∗ 𝑉 𝑟2 𝑉 𝑡3                  𝐺 03 𝐺 01  = 4𝜋𝑅 𝜆 ∗ 𝑉 𝑟𝟑 𝑉 𝑡𝟏                  18

16. 3.2 Standard Antenna Method
This method consists of generating an unknown field and measuring it with a calculable receiving antenna
Voltage induced in a standard (dipole) antenna is measured
Field strength is calculated in terms of induced voltage and dimensions of the receiving antenna
Measurements are performed in an open, large (typically 30x60 m) ground screen site
Plane wave, far zone field generated by a suitable antenna
Voltage is measured across centre gap of the dipole which is horizontal and parallel to E-vector

17. 3.2 STANDARD ANTENNA METHOD (Cont)
Electric field is determined from open circuit voltage (Voc) induced in the standard half wave resonant antenna
Then
(19)
Where
Einc = Field strength of locally generated field in
V/m
Voc = Open circuit RF voltage induced in the
standard dipole (V)
Leff = Effective length of the dipole (m)

18. Fig. 2 Voc Measurement set up
3.2.1 Measurement of Voc
RF voltage is measured in terms of the dc voltage detected by a high impedance Schottkey diode
Output filtered and measured by a high impedance calibrated dc voltmeter
Impedance of resonant dipole is negligible compared to that of voltmeter (100 M Ohm)
Fig. 2 Voc Measurement set up

19. 3.2.2 Determining Leff 𝐿 𝑒𝑓𝑓 = 𝜆 𝜋 ≈0.32𝜆 21
Effective length of receiving dipole is a measure of the e-field intercept
Effective length of a dipole is the length to which a homogenous current is applied to generate the same field strength in the main direction of radiation as that by the actual antenna fed with actual current
Assuming sinusoidal current distribution effective length of a thin dipole in free space is
Also
𝐿 𝑒𝑓𝑓 = 𝜆 𝜋 ≈0.32𝜆              21

20. 3.2.3 Determination of Antenna Factor
Antenna factor of the antenna under test is determined by placing it in the same field and measuring antenna terminal voltage
Fig. 3 Measurement set up

21. 3.2.3 Determination of Antenna Factor
Antenna factor is measured at a specified height usually 3 m
Different height over ground having different constants cause an error for height less than one wave length because antenna impedance depends on height above ground
Error generally less than 10 percent for heights greater than λ/2
𝐴𝐹= 𝐸 𝑖𝑛𝑐 𝑉 50𝛺                    22

22. 3.2.3 Determination of Antenna Factor (cont.)
The transmitting and receiving antennas should be separated by at least 3λ
Separation of 30m for MHz and 12m for MHz for an accuracy of ± 1 dB
Advantages of this method are:
- Measurement of Einc is not appreciably affected by the presence of
ground plane
- Output is high enough to take care of uncertainty caused by
ambient fields and temperature changes of the diode detector

23. 3.2.4 Limitations of standard antenna method
Since standard dipole is not frequency dependent, strong interfering fields affect measurements
Response is independent of frequency up to 500 MHz, beyond which a small error is introduced because of series resonance of diode mount
Measurements have to be performed separately for each frequency
Results are valid for free space, far zone conditions only
Close proximity of the ground plane changes results by several dBs

24. 3.3 Standard Field Method
This approach consists of generating a field and calculating its strength in terms of the type and dimensions of a standard transmitting antenna, net power delivered, distance from the transmitting antenna to the field point, and effect of ground or other reflection
Ideally, measurements are to be performed in an anechoic chamber under plane wave, far zone field conditions but the cost is prohibitive
Alternatively, field intensity in the near zone of standard gain antennas within a small anechoic chamber is calculated
Rectangular open end guides (OEG) are used for MHz and rectangular pyramidal horns for ,000 MHz frequency range

25. 3.3 Standard Field Method (cont.)
On-axis field intensity is calculated in terms of power delivered to the transmitting antenna, measured distance from the aperture, and calibrated near zone gain of the antenna
where
E = Radiated field intensity, V/m
P = net power delivered to antenna, w
G = calibrated gain of antenna including
near zone correction
R = distance between antenna aperture
and calibrating field points
𝐸= 30𝑃𝐺 𝑅          23

26. 3.3.1 Open End Guide (200 – 450 MHz)
For an open end guide having a width to height aspect ratio of 2:1
G = 21.6 fGHzW (24)
Where
fGHz is the frequency in GHz and W is width (larger side) in meters
Accuracy is better than ±0.5 dB if distance (R) is much greater than the width

27. 3.3.2 Pyramidal Horn (450 –10000 MHz)
Field at frequencies above 450 MHz is produced by standard gain pyramidal horns
Spherical rather than plane wave front across horn aperture reduces the effective gain in the near region
Further reduction due to distance between various elements in the radiating aperture and the on-axis field points

28. 3.3.2 Pyramidal Horn (450 –10000 MHz)
The theoretical gain of pyramidal horn is given by
Where RH and RE are near zone gain reduction factors (in dB) as given below
Where
a, b, lH and lE are horn dimensions
𝐺 𝑑𝐵 =10log 𝑎𝑏 +20log 𝑓 𝐺𝐻𝑧 − 𝑅 𝐻 − 𝑅 𝐸       25
𝑅 𝐻 = 0.01𝛼 𝛼+0.51 𝛼 2 −0.097 𝛼 3        26
𝑅 𝐸 = 0.1 𝛽 𝛽        27
𝛼= 𝑎 2 𝑓 𝐺𝐻𝑧 0.3 ∗ 1 𝑙 𝐻 + 1 𝑅    &     𝛽= 𝑏 2 𝑓 𝐺𝐻𝑧 𝑙 𝐸 + 1 𝑅 (28)

29. Pyramidal Horn Antenna
Fig. 4 Horn Antenna Dimensions

30. Determining Antenna Factor
Place the unknown antenna in the known field
Measure the antenna output voltage by standard method
Antenna factor can be computed as the ratio of the known field strength to the output of the test antenna

31. 3.4 Standard Site Method Antenna is calibrated as per ANSI C63.5
Standard site method does not require standard antenna nor the generation of standard field
The method is based on measuring site attenuation of a near ideal open field site
Accuracy depends on the quality of the site
Needs a stable signal source and a calibrated receiver
Test set up is shown in figure 5

32. 3.4 Standard Site Method (Cont.)
Fig. 5 Test Set Up

33. 3.4 Standard Site Method (cont.)
For a standard or ideal site the measured site attenuation is given by
where
= Calculated maximum (height scan) electric field
strength at the receiving antenna from a half wave
dipole with 1 pw radiated power
A= 𝑉 𝑇 𝑉 𝑅 = 279.1​𝐴 𝐹 𝑇 + 𝐴 𝐹 𝑅 𝑓 𝑀𝐻𝑧 𝐸 𝐷 max        29

34. 3.4 Standard Site Method (cont.)
Even though true for any polarization, as a practical matter only horizontal polarization is used
Reflection coefficient of earth as a function of incident angle varies rapidly for vertically polarized waves
The method needs measurement of site attenuation using three antennas under identical conditions

35. 3.4 Standard Site Method (cont.)
𝐴 𝐹 1 ∗𝐴 𝐹 2 = 𝑓 𝑀𝐻𝑧 𝐸 𝐷 max 𝐴 1           𝐴 𝐹 1 ∗𝐴 𝐹 3 = 𝑓 𝑀𝐻𝑧 𝐸 𝐷 max 𝐴 2           31 𝐴 𝐹 2 ∗𝐴 𝐹 3 = 𝑓 𝑀𝐻𝑧 𝐸 𝐷 max 𝐴 3           32

36. 3.4 Standard Site Method (cont.)
Solving the above equations and expressing in dB
𝐴 𝐹 1 =− 𝐸 𝐷𝑑𝐵𝜇 𝑣 𝑚 max + 𝐴 1𝑑𝐵 + 𝐴 2𝑑𝐵 − 𝐴 3𝑑𝐵     33 𝐴 𝐹 2 =− 𝐸 𝐷𝑑𝐵𝜇 𝑣 𝑚 max + 𝐴 1𝑑𝐵 + 𝐴 3𝑑𝐵 − 𝐴 2𝑑𝐵     34 𝐴 𝐹 3 =− 𝐸 𝐷𝑑𝐵𝜇 𝑣 𝑚 max + 𝐴 2𝑑𝐵 + 𝐴 3𝑑𝐵 − 𝐴 1𝑑𝐵     35

37. 3.4 Standard Site Method (cont.)
The accuracy of measurement depends on the quality of measuring site and the accuracy with which site attenuation can be measured.
This method is suitable for measurements above 50 MHz
Minimum size of obstruction free site with maximum surface roughness, minimum size and location of the reflecting surface are defined in ANSI C63.5
Calculated value of E Dmax for some measurement geometry are given in
“Calculation of Site Attenuation from Antenna Factors” A. A. Smith & J. B. Pati; IEEE EMC-24, August 1982

38. 3.4 Standard Site Method (cont.)
The main precautions to be observed are:
- Antenna separation should be large enough to avoid near field and
antenna-to-antenna coupling effects
- The heights h1 and h2 should be large enough to minimize antenna
to ground mutual impedance and contribution from surface wave
component
- Scanning of receiving antenna height is a must to avoid large errors in the region of nulls

39. 4. Conclusion
The choice of calibration method depends on factors such as type of the antenna, frequency range and actual application
The user of the antenna must make sure that it has been calibrated under the conditions which are most appropriate for its use.