Test procedures for antennas-Measurement of power gain and directivity
Some standard content:
Standard of the Ministry of Electronic Industry of the People's Republic of China SJ 2534.10-86
Antenna Test Method
Measurement of Power Gain and Directivity
Published on January 24, 1986
Implemented on October 1, 1986
Ministry of Electronic Industry of the People's Republic of China
Ministry of Electronic Industry of the People's Republic of China Standard Antenna Test Method
Measurement of Power Gain and Directivity
This standard applies to the measurement of antenna power gain and directivity. 1 Overview
1.1 Definition
1.1.1 Power Gain
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The 4-fold ratio of the radiation intensity of an antenna in a certain direction (the power radiated by the antenna per unit solid angle) to the net power obtained by the antenna from its signal source is called the power gain of the antenna in that direction. The power gain characterizes the inherent properties of the antenna, excluding the system loss caused by impedance or polarization mismatch. The input impedance of the antenna and the polarization of the antenna are measured and considered when determining the power transfer of the entire system. 1.1.2 Directivity
The 4-fold ratio of the radiation intensity of the antenna in a certain direction to the total power radiated by the antenna is called the directivity of the antenna in that direction. This term is different from power gain because it does not include the dissipative losses of the antenna. 1.1.3 Radiation efficiency
The ratio of power gain to directivity in the same direction is called the radiation efficiency of the antenna. 1.1.4 Peak power gain (or peak directivity) The maximum value of power gain (or directivity) is called peak power gain (or peak directivity). The power gain (or directivity) measurements referred to in this standard are all peak power gain (or peak directivity) measurements. Knowing the radiation pattern can determine the gain (or directivity) in any other direction. 1.1.5 Sidelobe level expression method
For pencil beam antennas, it is particularly important to determine the sidelobe level. There are two reference bases for sidelobe level: 3, the peak power gain of the antenna;
b. The gain of a lossless, isotropic radiator. In both cases, the power level is expressed in decibels. Since the values of these two results are often used to approximately represent the same given power level, the gain reference should be appropriately specified to avoid confusion. 1.2 Overview of measurement methods
1.2.1 Classification of power gain measurement methods
Power gain measurement methods can be divided into two categories: absolute gain measurement and gain transfer measurement. 1.2.1.1 Absolute gain measurement
Absolute gain measurement does not require prior knowledge of the gain of any antenna used in the measurement. This method is usually used for calibration of gain standard antennas. Except for laboratories specializing in standard calibration, other laboratories rarely use this method. 1.2.1.2 Gain transfer method
The gain transfer method is also known as the gain comparison method. It is the most commonly used method for gain measurement. When measuring with this method, the gain of the antenna under test needs to be compared with the gain of the gain standard antenna. Issued by the Ministry of Electronics Industry on January 24, 1986
Implemented on October 1, 1986
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1.2.2 Techniques used to determine antenna power gain The techniques used to determine antenna power gain vary depending on the operating frequency of the antenna. 1.2.2.1 Frequencies above 1 GHz
At frequencies above 1 GHz, power gain measurements are usually made using a free space test field. For these frequencies, microwave techniques can be used, for example, waveguide components such as electromagnetic horns can be used. 1.2.2.2 Frequencies between 0.1 and 1 GHz
For frequencies between 0.1 and 1 GHz, measurements are usually made using a ground reflection test field. Antennas operating in this frequency range are usually mounted on structures such as aircraft, which can affect the performance of the antenna. In this case, scale model techniques can be used (see SJ2534.5-85 "Special Measurement Methods"). Note that gain measurements cannot be made with scale models because it is not possible to simulate the finite conductivity and loss factors of the materials that make up the antenna and aircraft. However, if the scale model antenna is properly made, its directivity will be the same as that of the prototype antenna, so the directivity of the scale model antenna can be measured and the efficiency of the prototype antenna can be measured by other methods to obtain the power gain. The directivity measurements can be confirmed by flying an aircraft equipped with the prototype antenna on a prescribed route relative to an appropriate ground station. The system performance can be measured with the prototype antenna under test and compared with the scale model measurements. 1.2.2.3 Frequencies below 0.1 GHz
At frequencies below 0.1 GHz, the effect of the ground on the antenna characteristics becomes very significant, making the measurement of power gain more difficult. In this frequency range, the size of directional antennas is quite large and measurements must be made in the field. It is usually satisfactory to calculate the gain of the antenna and estimate the effect of the ground. Alternatively, a scale model can be used, but because the ground has a serious effect on the antenna characteristics, the electrical characteristics of the ground should also be simulated to scale. 1.2.2.4 Frequencies below 1 MHz
For frequencies below 1 MHz, the power gain of the antenna is usually not measured, but the field strength of the ground wave radiated by the antenna is measured. 1.2.3 Directivity measurement
The directivity of the antenna under test can be obtained by integrating the measured far-field radiation pattern of the antenna on a closed sphere. If the antenna loss can be determined by other methods, the power gain of the antenna can be determined according to the measured directivity. 2 Gain standard antenna
2.1 Characteristics of gain standard antenna
The closed line used as a gain standard should have the following characteristics: a. The gain of the closed line should be accurately known, b. The antenna has a high degree of dimensional stability: c. The antenna must have high polarization purity (linear polarization or circular polarization). 2.2 Types of gain standard antennas
Although any antenna that meets the requirements of 2.1 can be used as a gain standard antenna, the two most commonly used types of antennas are dipoles and pyramidal horns. The gain of these two types of antennas can be calculated very accurately and their mechanical structure is simple, so the repeatability of their manufacture is very high. Both types of antennas are nominally linearly polarized. Another type is a specially designed gain standard antenna. It should be emphasized that if high accuracy is required, the gain standard antenna should be specially calibrated for the standard test line calibration of the gain standard. 2.2.1 Dipole Antenna
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A properly excited thin dipole antenna has a gain of approximately 2.15dB when its length is adjusted to half-wavelength resonance (calibration involves adjusting the length of the dipole to obtain resonance). The dipole antenna itself has a high polarization purity. However, due to its wide radiation pattern, its characteristics are affected by the surrounding environment, especially its transmission line. For this reason, it is difficult to determine the limits of its polarization purity.
2.2.2 Horn Antenna
2.2.2.1 Conical Horn Antenna
In the microwave frequency band (0.3590GHz), the conical horn antenna is widely used as the gain standard antenna. The horn antenna used as the gain standard antenna should be accompanied by a calculated calibration curve (provided by the relevant department). The calibration curve has a smooth characteristic, while the measured gain shows an undulating characteristic with the change of frequency. This is caused by multiple reflections between the horn mouth and the transition connecting the waveguide and the horn. For frequencies above 2.6GHz, the calculated calibration curve can be considered accurate to 0.25dB, and for frequencies below 2.6GHz, it is accurate to ±0.5dB. If higher accuracy is required, the conical horn antenna should be calibrated by a suitable standard laboratory. This antenna has a high gain, so it is less affected by its surrounding environment when used for gain measurement. The axial ratio of its polarization circle is above 40dB in the axial direction. 2.2.2.2 Corrugated Conical Horn
The corrugated conical horn antenna has extremely low side effects and is therefore an ideal gain standard antenna. Whether using theoretical calculations or experimental calibration, its gain can reach an accuracy of 0.1dB. The corrugated conical horn is particularly suitable for precise gain measurements. 2.2.3 Specially designed gain standard antennas
Sometimes it is necessary to design a gain standard antenna with special properties. For example, a dipole antenna has an omnidirectional radiation pattern in its plane, so its radiation pattern will change greatly due to the influence of the surrounding environment. For this reason, it is necessary to design a directional antenna, such as a dipole array with a reflector, a corner reflector antenna, or a log-periodic antenna, and calibrate its gain. 2.3 Calibration of gain standard antennas in a free space test field 2.3.1 Friis transmission formula
Absolute gain measurement is based on Friis transmission formula. For the two-antenna system shown in Figure 1, Friis transmission formula is:
Pr=PoGAGB
Where: Pr-the power received by the matching load connected to the receiving antenna Po-the input power of the transmitting antenna;
GA is the power gain of the transmitting antenna;
Gu is the power gain of the receiving antenna.
This formula implies the following assumptions: that the antennas are impedance matched and polarization matched in their specified orientations, and the distance between the antennas meets the far-field condition.
Two-antenna system illustrating the Friis transmission formula Py
2.3.2 Two-antenna method
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The Friis transmission formula expressed in decibels can be written as: (GA)dB+(Gn)aB=201g(
-101g(
If the two antennas are the same, it can be inferred that their gains are equal, so the power gain of the antenna can be obtained as: (Ga)an=(Gan)n[201g(4R)-101g(P)] The steps to determine the antenna power gain are to measure R, Two identical antennas are used, 101g and 101g, so this method is called the two-antenna method. 2.3.3 Three-antenna method
(3)
, and then calculate (GA)aB. Because
is required in the three-antenna method, three sets of measurements must be completed using all combinations of three antennas, and the result is the following simultaneous equations: (G)an+(Gp)an\=201g(4R)-101g(P9)(G)an+(Ge)an=201g(R）-101g(P)(Gn)an+(Ge)ai=201g(R-)-101g (P) The gains of all three antennas can be determined from this simultaneous equation. 2.3.4 Typical block diagram of test equipment
2.3.4.1 Typical block diagram of point frequency test equipment Calibration network
Equalizer
Bai I Xi device
Conversion connector
1Bei Liu sensor integration
Ke period adapter
Ai Shooting Test Point
East Source
One teaching device
Tide adapter
|Conversion
Test object
Receiving test point
Figure 2 Typical test equipment for two-antenna method and three-antenna method for power gain measurement (4)
For point frequency measurement, the block diagram of the two-antenna method or three-antenna method test equipment is shown in Figure 2. The test equipment should be highly stable, and the signal source generates a single frequency sine wave. Referring to Figure 2, the measurement steps are: a. Accurately align and orient the two antennas; b. Align the signal source and the transmitting antenna A Calibrate the coupling network between the two antennas to accurately find the relationship between the power measured at the transmitting test point and the power entering the A antenna:
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C. Use the adapter to make all the components of the system achieve impedance matching; d. Adjust the attenuator of the coupling network to make the power level at the transmitting test point the same as the power level at the receiving test point; e. Determine the relative power level Po/P based on the calibration value of the coupling network. 2.3.4.2 Block diagram of swept frequency test equipment
The gain of broadband antennas is usually measured by swept frequency technology. The measurement method can be two-antenna or three-antenna method. The block diagram of a typical swept frequency test equipment is shown in Figure 3. Note that it is impossible to match all components in the entire frequency band, so the impedance or reflection coefficient of all components must be measured by the swept frequency method. 2.4 Calibration of gain standard antennas on the ground reflection test field For frequencies below 1GHz, some antennas used as gain standard antennas must have medium-width beams. For these antennas, if their gain needs to be accurately determined, a ground reflection test field is usually used. As long as certain restrictions and corrections are made, the two-antenna or three-antenna gain measurement method can also be used on the ground reflection test field. Correction signal
Property
Signal source
Transmitting antenna Receiving antenna
Precision variable
Attenuator
Transmitting signal Test, receiving signal
XY record group
Receiving system
Figure 3 Typical test equipment for the swept frequency two-antenna and three-antenna methods for power gain measurement 2.4.1 Requirements for the test field
The criteria for the ground reflection test field described in SJ2534.2-85 "Design of antenna test field" should be met. The site geometry of the ground reflection test field for gain measurement is shown in Figure 4. The desired test field length R. 》2hr, hr is the height of the receiving line.
Connecting antenna
Transmitting antenna
Test items
H-transmitting antenna image
Geometry of ground reflection test field
2.4.2 Calculation formula
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Adjust the height of the transmitting antenna so that the field at the receiving antenna is at the first maximum value closest to the ground. At this time, the equation for the sum of the gains of the two-antenna method or the three-antenna method can be corrected to: (C,)b+(C)a=201()-101g()-201[(D,D)*+]..·5）
Where D. and Dz are the directivities along R, relative to the peak directivities of antennas A and B, respectively. D. and D= are obtained from the amplitude radiation patterns of the two antennas, which should be tested before the gain measurement. The values RD, R?, A and the ratio Po/Pr are directly measured quantities. What needs to be determined is the factor which is a function of the electrical and geometrical properties of the antenna test site, the radiation pattern of the antenna and the operating frequency. Once this is determined, the gain can be calculated. 2.4.31 Determination of the value of
To obtain 1, the measurements of 2.4.2 are repeated. However, this time the measurement is made with the height of the transmitting antenna adjusted to minimize the field at the receiving antenna. The value is calculated as: CRRRR
[(P/DDDD.)R (.)
(Pr/P/r)RR+RR
where: The quantities without band withdrawal are those obtained with the height of the transmitting antenna adjusted to maximize the signal at the receiving antenna, and the quantities with band withdrawal are those obtained with the height of the transmitting antenna adjusted to minimize the signal at the receiving antenna. 2.4.4 Recommended polarization orientation
This method is limited to linearly polarized antennas that couple to other fields. When a loop antenna is used, the equation must be modified. Because the reflection characteristics of the ground for vertical and horizontal polarizations are not good, this method is not suitable for circularly polarized or circularly polarized antennas. It is recommended that the antenna be oriented in horizontal polarization, so when vertical polarization is used, the ground reflection coefficient changes rapidly with the angle of incidence, while this phenomenon does not exist for horizontal polarization. 2.4.5 Measurement accuracy
The test equipment used is basically the same as the test equipment for free space test field measurements. An accuracy of ±0.3dB can be achieved with this method.
2.5 Calibration of gain standard antennas on the extrapolation test field 2.5.1 Basic principles of extrapolation
In the conventional far-field test method, the antenna parameters are measured when the distance between the antenna under test and the source antenna is finite. The measured parameters are an approximation of the far-field parameters measured at infinite distance. In fact, this conventional approximation is the simplest form of extrapolation. In the extrapolation method, the antenna parameters are measured when the distance from the antenna varies within a certain range, and then the antenna parameters are extrapolated to infinity with the change of distance. 2.5.2 Methods for eliminating multipath effects
When measuring in the antenna test field, multipath effects and proximity effects always exist. When measuring the received signal by changing the distance between the receiving and transmitting antennas, the multipath effect is manifested as a periodic fluctuation on the mountain line of the functional relationship between the received signal and the distance. The extrapolation method includes strictly calculating and correcting the errors caused by these effects. Mathematically, the average method (graphic method, numerical method) can be used to eliminate the periodic changes of the received signal caused by the multipath effect, or adjust the time constant of the test equipment so that it cannot track the periodic changes but can record the average value. The signal level that should be measured in the far field measurement can be inferred by fitting the average data with the curve. In this way, both the proximity interference effect and the multipath effect can be eliminated. The power gain can be calculated from this result. 2.5.3 Extrapolation method combined with the generalized three-antenna method If the extrapolation method is combined with the generalized three-antenna method, not only the power gains of the three antennas can be obtained, but also their polarization states. Note that none of the three antennas should be nominally circularly polarized at this time. If one of the antennas is circularly polarized, then only the characteristics of this antenna can be fully determined. If two or three antennas are nominally circularly polarized, then this method will not work.
2.5.4 Extrapolation Test Site
The extrapolation test site is equipped with a precisely movable tower which is moved over the length of the test site so that the axis of the transmitting antenna is aligned with the axis of the receiving antenna. Measurements can be made at distances from 0.2D2/in to 2D\/^, where D is the maximum dimension of the antenna under test. The tower height should be at least 15% of the maximum distance between the antennas: 2.5.5 Measurement Accuracy
By using the extrapolation method, the calibration accuracy of the gain standard antenna can reach ±0.05 dB, while with more conventional measurements, the calibration accuracy is ±0.08 dB.
2.6 Practical Limits on the Maximum Gain of the Gain Standard Antenna The existing technology for precise calibration has a practical limit on the maximum gain of the gain standard antenna. For example, in the extrapolation test site, the tower height is required to be 15% of the maximum distance between the antennas. This requirement actually limits the maximum gain of the antenna being calibrated. The reason is obvious, because the gain of the antenna to be calibrated increases, the maximum test distance increases, and the tower height also increases, which not only makes axis alignment very difficult, but also makes the tower very expensive. At microwave frequencies, the maximum gain of the gain standard antenna is 40dB.
3 Gain transfer measurement
The measurement method that compares the unknown power gain of the antenna under test with the power gain of the gain standard antenna is called gain transfer measurement. Gain transfer measurement is also called gain comparison measurement. The measurement can be performed in free space or in a ground reflection test field.
3.1 Measurement of linearly polarized antennas
In ideal conditions, the antenna under test is illuminated by a plane wave that matches its polarization, and the received power is measured on the matched load. Under the same other conditions, replace the antenna under test with the gain standard antenna and measure the received power into its matched load again. The Friis transmission formula gives the power gain (Gr) of the antenna under test in decibels: PT
(Gr)aB=(Gs)dB+101g
where:
(G,)dB is the power gain of the gain standard antenna, Pr is the power received by the antenna under test, and
Ps is the power received by the gain standard antenna. Methods for interchange between the antenna under test and the gain standard antenna 3.1.1
·(7)
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The antenna under test and the gain standard antenna can be interchanged by mounting two antennas back to back on each side of the axis of the azimuth locator. With this configuration, the antennas are switched by rotating the locator 180°. The two antennas should be mounted with particular care so that they are in the same position when the locator is rotated. Absorbing material should usually be mounted on the back of the gain standard to reduce disturbances in the irradiated field caused by reflections from adjacent structures. 3.1.2 Frequency sweep measurement
The measurement steps are basically the same as those of frequency sweep absolute gain measurement, but the measurement is repeated with the antenna under test and the gain standard antenna. In order to correct the measured power gain, the relationship between the reflection coefficient of all components and the frequency must be measured. 3.2 Measurement of circularly polarized and elliptically polarized antennas 3.2.1 Measurement with circularly polarized gain standard antennas For the special case of circularly polarized antennas under test, orthogonal circularly polarized antennas can be designed and calibrated. This method is particularly suitable for assembly line power gain measurements. 3.2.2 Measurement with linearly polarized gain standard antennas Since the total power of the wave radiated by the antenna can be decomposed into two orthogonal linear polarization components (see 1 and 2 in SJ2534.9-85 "Polarization Measurement"), generally speaking, circularly polarized and elliptically polarized antennas under test are measured with linearly polarized gain standard antennas. That is to say, the partial power gain is measured using two orthogonal linear polarization antennas (the linear polarization gain standard antenna can be rotated 90° to obtain two orthogonal polarizations) to determine the total power gain of the antenna under test. For example, the power gain transfer measurement is first performed using the vertically polarized gain standard antenna and the source antenna, and then the measurement is repeated using the horizontally polarized gain standard antenna and the source antenna. Based on the measured partial power gain, the total power gain expressed in decibels can be calculated as follows: (G^)dB(GT)&B=10lg(CTV+GTI)... In the formula: GTV - partial power gain in the case of vertical polarization, GTH - partial power gain in the case of horizontal polarization. 3.3 Measurements in the high frequency band (3-30 MHz)... (8)
At frequencies of about 3-30 MHz, the medium- and long-distance propagation of electromagnetic waves mainly relies on sky waves reflected from the ionosphere. For circuits of 2000-4000 km, the most important are the antenna pattern and power gain at elevation angles between 5° and 30° above the horizon.
As described in SJ2534.7-85 "Field Measurement of Amplitude Pattern", the measurement of the azimuth pattern and power gain is carried out on site. An aircraft equipped with a suitable transmitting antenna flies at a fixed altitude along a circular route centered on the antenna under test. In order to measure the amplitude pattern, the amplitude of the received signal and the azimuth and pitch angles of the aircraft are recorded simultaneously. The power gain can be measured by comparing the power received by the antenna under test with the power received by the gain standard antenna located nearby.
3.3.1 Gain Standard Antenna
A horizontally polarized dipole is used as the gain standard antenna. Note that in this frequency band, the directional pattern and power gain of the dipole antenna are greatly affected by the ground. When measuring the gain, the height of the dipole antenna should be adjusted so that its main lobe points in the same direction as the main swing of the antenna under test (between 5° and 30° above the ground plane). The power gain of a dipole antenna is related to its height and elevation angle. Its power gain expressed in decibels can be calculated using the following formula: 8
(Gs)aB=2.15+101g
Wherein: Re—represents the real part:
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+R.(Rn(90°)Z.)
jKHsiny
R is the real part of the self-impedance of the dipole antenna in free space; +Rh(W)-iKHsiny
Zm is the mutual impedance between the dipole antenna and its image in an ideal conductor, K is the wave number in free space;
. —Height of the dipole from the ground;
Ping —Elevation angle of the main lobe of the vertical radiation pattern of the dipole antenna; (9)
Ru() —Complex reflection coefficient of the ground for horizontal polarization at an angle measured from the horizontal plane (complementary angle of the incident angle);
R(90°) —Complex reflection coefficient of the ground for horizontal polarization at an angle of 90° measured from the horizontal plane (complementary angle of the incident angle).
This formula can be used to draw a curve of the power gain of the dipole antenna as a function of the height from the ground and the elevation angle. Note that a vertically polarized dipole cannot be used as a gain standard antenna because the power gain of this antenna is low at low elevation angles and varies dramatically with the water content of the ground. 3.3.2 Measurement method
3.3.2.1 Measurement of horizontally polarized antenna
As described in 3.3.1, the gain standard antenna is a horizontally polarized dipole antenna. Therefore, as long as the power received by the antenna under test and the gain standard antenna is measured, the power gain of the antenna under test can be calculated according to formula (7) and formula (9). 3.3.2.2 Measurement of vertically polarized antenna
For the vertically polarized antenna under test, its cross-polarized partial gain (horizontally polarized partial gain) should be compared with the horizontally polarized gain standard antenna when performing gain transfer measurement. Based on this result, the required vertical polarization partial gain can be determined.
The specific method is as follows: rotate the transmitting antenna installed on the aircraft so that the transmitting signal is alternately vertically polarized and horizontally polarized, and the signal is received by the antenna under test and the gain standard antenna. Compare the maximum power received by the gain standard antenna with the minimum power received by the antenna under test to obtain the horizontal polarization partial gain of the antenna under test. Then compare the maximum and minimum powers received by the antenna under test to obtain the required partial gain of vertical polarization. Since the gain of the source antenna changes when it rotates, it is usually necessary to calibrate the rotating antenna.
3.3.3 Measurement accuracy
The accuracy of this technique is related to the understanding of the ground characteristics and the terrain at the site where the antenna is located. If the terrain is flat and free of obstacles, and the ground constants are accurately known, the measurement inaccuracy can reach ±0.5dB or better. However, in general, the inaccuracy is expected to be no more than ±1dB. 4 Power gain measurement of large electrical antennas
4.1 Overview
4.1.1 Main problems in measuring large electrical antennas9
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The main problems encountered in measuring large electrical antennas are: a. The test distance that meets the far-field conditions is too large, so it is usually impractical to measure its power gain in the antenna test field, and in some cases it is even impossible. b. When a large steerable antenna is in motion, it is usually affected by gravity, which will cause structural deformation. Therefore, it is necessary to measure the change of gain with the elevation angle of the antenna.
4.1.2 Types of sources for measuring electrical large antennas The key to solving the main problems described in 4.1.1 is whether a suitable source can be found. Two sources suitable for electrical large antenna measurements are:
a. Radio sources outside the Earth (cosmic radio sources, planets, and the Moon); b. Satellite-borne beacons.
4.1.2.1 Cosmic radio sources
The positions and radiation flux densities of some radio sources outside the Earth are precisely known, so they can be used for power gain measurements. In addition, the frequency spectrum covered by these radio sources is very wide. Their flux density varies with frequency, but in the range of 0.1 to 10 GHz, the flux density of several radio stars has been precisely measured. Figure 5 shows the flux density spectra of several radio stars. The positions, angular diameters, spectral indices and types of radio phenomena of these radio stars are listed in Table 1. 10
Cassiopeia A
Taurus A
Orion
Tianliyou A
Mystia A
Right Ascension (h)
In the table, S (4GHz) value of -1965.1: SR - supernova remnant cloud,
- emission nebula:
RG - radio star system:
Declination (\)
S (4GHz) - flux density at 4GHz;
a - Spectral index:
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Related data of several radio sources
Declination (,)
Visible area
Northern latitude (\)
Southern latitude (°)
S(4GHz)
Visible area refers to an interval of earth latitude in which the apparent diurnal path of the radio source rises at least 20° above the horizon through the sky. The minimum value of 20° assumes that the radio source can be seen by the antenna for at least 1h and is high enough above the ground plane to be distinguished from the atmospheric noise and ground noise. The relationship between the flux density S and the frequency f is expressed by the following formula: s(f) =
Where: S(f)-flux density at a given frequency (usually listed in a table at discrete frequencies) S(f)-flux density at the frequency to be measured. 4.1.2.1.1 The strongest radio sources with small angular diameters
（10）
Cassiopeia A, Taurus A and Cygnus A are the strongest radio sources with small angular diameters. Their flux densities have been accurately measured in the frequency range of 30MHz to 16GHz. In the centimeter band, the relative accuracy of the flux density of Cassiopeia A, Taurus A and Cygnus A is ±2%, ±3% and ±3% respectively. They are the most useful sources for antenna gain measurements. It should be noted that the flux density of Cassiopeia A decreases year by year, and its annual decrease rate is: d(f)=［(0.97±0.04)-(0.30±0.04)1gfJ% Where: f-frequency, GHz.
（11)
The time variation of the flux density of Taurus A and Cygnus 4 can be basically ignored. Cygnus A has a bend in its spectrum 11
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