ANTENNA FACTOR CALIBRATION TECHNIQUES Prof. N. K. Agarwal KIIT College of Engineering Gurgaon-122102

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

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

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 2 377 ∗ 𝐺 𝜆 2 4𝜋        3

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  

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

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

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

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

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

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

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

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

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)

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                  16 𝐺 02 𝐺 03  = 4𝜋𝑅 𝜆 ∗ 𝑉 𝑟2 𝑉 𝑡3                  17 𝐺 03 𝐺 01  = 4𝜋𝑅 𝜆 ∗ 𝑉 𝑟𝟑 𝑉 𝑡𝟏                  18

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

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)

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

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

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

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

3.2.3 Determination of Antenna Factor (cont.) The transmitting and receiving antennas should be separated by at least 3λ Separation of 30m for 30-400 MHz and 12m for 400-1000 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

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

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 200-450 MHz and rectangular pyramidal horns for 450-10,000 MHz frequency range

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

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

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

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 +20.54− 𝑅 𝐻 − 𝑅 𝐸       25 𝑅 𝐻 = 0.01𝛼 1+10.19𝛼+0.51 𝛼 2 −0.097 𝛼 3        26 𝑅 𝐸 = 0.1 𝛽 2 2.31+0.053𝛽        27 𝛼= 𝑎 2 𝑓 𝐺𝐻𝑧 0.3 ∗ 1 𝑙 𝐻 + 1 𝑅    &     𝛽= 𝑏 2 𝑓 𝐺𝐻𝑧 0.3 1 𝑙 𝐸 + 1 𝑅 (28)

Pyramidal Horn Antenna Fig. 4 Horn Antenna Dimensions

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

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

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

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

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

3.4 Standard Site Method (cont.) 𝐴 𝐹 1 ∗𝐴 𝐹 2 = 𝑓 𝑀𝐻𝑧 𝐸 𝐷 max 279.1 𝐴 1           30 𝐴 𝐹 1 ∗𝐴 𝐹 3 = 𝑓 𝑀𝐻𝑧 𝐸 𝐷 max 279.1 𝐴 2           31 𝐴 𝐹 2 ∗𝐴 𝐹 3 = 𝑓 𝑀𝐻𝑧 𝐸 𝐷 max 279.1 𝐴 3           32

3.4 Standard Site Method (cont.) Solving the above equations and expressing in dB 𝐴 𝐹 1 =−24.46+ 1 2 𝐸 𝐷𝑑𝐵𝜇 𝑣 𝑚 max + 𝐴 1𝑑𝐵 + 𝐴 2𝑑𝐵 − 𝐴 3𝑑𝐵     33 𝐴 𝐹 2 =−24.46+ 1 2 𝐸 𝐷𝑑𝐵𝜇 𝑣 𝑚 max + 𝐴 1𝑑𝐵 + 𝐴 3𝑑𝐵 − 𝐴 2𝑑𝐵     34 𝐴 𝐹 3 =−24.46+ 1 2 𝐸 𝐷𝑑𝐵𝜇 𝑣 𝑚 max + 𝐴 2𝑑𝐵 + 𝐴 3𝑑𝐵 − 𝐴 1𝑑𝐵     35

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

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

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.