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ENCYCLOPEDIA OF RADIO ELECTRONICS AND ELECTRICAL ENGINEERING To the calculation of the efficiency of antennas in computer simulation. Encyclopedia of radio electronics and electrical engineering
Encyclopedia of radio electronics and electrical engineering / Civil radio communications The article provides a comparative description of some approaches to assessing the coefficient of performance (COP) of antennas and antenna systems based on the results of electromagnetic computer simulation, taking into account losses. The possibilities of calculating the antenna efficiency using the MMANA program are shown and a description of the program for calculating the efficiency based on the simulation results is given. Introduction Computer modeling provides useful opportunities for evaluating the efficiency of existing antennas and predicting the efficiency of antennas under development. If objects of the near environment of the antenna (supports, braces, roof) participate in the radiation process, then it is possible to estimate the influence of these objects, in other words, the efficiency of the entire antenna system. Efficiency estimation is of particular interest for electrically small antennas (ESA) due to the difficulty of obtaining high efficiency at small wave (i.e., expressed in fractions of a wavelength) size The most general definition of efficiency is the ratio of the radiation power P∑ to the excitation power PE in the transmission mode:
where PL is the power loss in the materials of the conductors and dielectrics of the antenna. It follows from the principle of reciprocity that in the receive mode the efficiency of the antenna is the same as in the transmit mode. Another definition of efficiency (by circuit equivalent) is the ratio of the radiation resistance R∑, reduced to the antenna connection point, to the active part of the input impedance (impedance) RA, which is the sum of R∑ and the equivalent loss resistance RL:
Methods for calculating efficiency in simulation 1. Use of drive power and power loss data The excitation power (power supplied to the antenna) PE is easily calculated from the simulation results:
where lE is the effective (effective) value of the excitation current. If, knowing the currents In and the active components Rn of the impedances of all individual segments of the antenna, calculate the power loss
then you can get the radiation power as the difference between the excitation power and the loss power:
Efficiency is calculated according to formula (1). The method is of little use for assessing low efficiency (a few percent or less), especially when the errors in determining the loss power and excitation power are large. Often negative values of P∑ and hence efficiency are obtained (for example, in the NEC2d program). 2. Analytical calculation of radiation resistance or its determination by analyzing the model of an ideal antenna without taking into account losses For simple antennas, the radiation resistance can be calculated using known formulas or obtained by modeling an ideal antenna. This is better than having it as the difference between very close numbers obtained with large errors. Efficiency is calculated according to formula (2). It should be borne in mind that in some cases the current distribution and, consequently, the reduced radiation resistance strongly depend on losses, and formula (2) when determining R∑ by modeling an ideal structure can give an efficiency with a large error (for example, an efficiency greater than unity will be obtained). This happens, for example, when modeling a dipole with a length of one wavelength. 3. Comparison of the maximum gain values of a real antenna and a lossless antenna similar in structure The maximum antenna gain, as is known, is related to the maximum directivity factor (DFA) Dmax through the efficiency:
From here, the efficiency is directly obtained if there is confidence that the shape of the radiation pattern (RP) without taking into account losses is similar to the shape of the RP of a real antenna. The value is obtained as a result of modeling an ideal antenna with a unit efficiency (η = 1). When determining the efficiency from relation (6), Gmax and Dmax must be expressed in relative units, not in decibels. To move from decibels to ratios of the quantities under consideration, formulas are used
You can also find the efficiency value from the analysis results in decibels directly:
If the antenna system contains wires of significantly different diameters or from different materials, then the radiation patterns of lossy and lossless antennas can differ markedly in shape, and this method also leads to errors. 4. Using data on the input power and determining the radiation power using the Poynting vector method The best and most universal method for calculating the radiation power of any antenna is the Poynting vector method [1]. Consider the mode of operation of the antenna in free space (Fig. 1).
The Poynting vector P, as you know, is the vector product of the vectors of the electric E and magnetic H components of the electromagnetic field
Its direction at each point M of the far zone coincides with the direction of radiation of radio waves, and its value On a sphere of radius R, in the vicinity of the point M, we single out an area bounded by small increments ΔΘ and Δφ (Fig. 1). Its area is determined from the expression
Radiation power through this pad
By dividing the entire sphere into a sufficiently large number of small areas and summing the radiation powers through all the areas, one can obtain a value very close to the antenna radiation power through the entire spherical surface:
Here M is the number of steps along the coordinate φ; N is the number of steps along the Θ coordinate. If we take the same steps A in degrees in Θ and φ, then we get М = 360/Δ and N = 180/Δ. For free space, the value of the radius R of this surface does not matter. Having calculated the power supplied to the antenna according to the formula (3), we obtain the efficiency ie (1). The disadvantage of this method is that in real conditions the result depends on the losses in the propagation medium. In modeling, this can be circumvented by using free space or ideal ground conditions. Note that for an ideal earth, it is necessary to consider not the entire sphere, but only the upper hemisphere, and N = 90/Δ. Peculiarities of efficiency calculation based on the results of the MMANA program Calculation according to paragraphs. 2 and 3 is possible with the above reservations directly from the results of the analysis of a lossy antenna and a lossless antenna. The only condition: the mode of free space or ideal land. MMANA does not allow you to display the impedances of individual segments for analysis. This makes the first path (item 1), which has serious drawbacks, inaccessible. Far-field strength values are also not displayed, which could be used to calculate the radiation power using the Poynting vector method. The results tables give the gain in decibels GA(Θ, φ) (dBi) in a given direction for a given antenna relative to an ideal isotropic radiator at the same input power. However, this is still sufficient to determine the efficiency. And even according to a simpler algorithm than in accordance with (12), (3), (1):
Here and below, the values of GA(Θ, φ) must be in relative units:
In accordance with algorithm (13), a program was compiled for calculating the antenna efficiency. Antenna efficiency calculation program The program for calculating the antenna efficiency based on the results of analysis in the MMANA program is written in Turbo Basic and is available on the website of the Radio magazine. The kpdmm.exe file is placed in any directory and run on MS DOS or MS Windows without any special installation. The program uses a file of the form name.csv, which is created by the MMANA program by choosing "Angle/Reinforcement Table" from the "File" menu. Efficiency can be calculated after analysis in free space mode or in ideal ground mode. The steps for the azimuth and zenith angles are set the same. The program provides only two possible step values: 2° or 10°. For estimated calculations, a step of 10° is recommended, and for accurate calculations, a step of 2°. (Further step reduction in the case of the MMANA program does not lead to a significant improvement in accuracy, but it requires a large amount of memory and significantly slows down the calculation process.) Table 1 shows the mandatory values of the initial angles, the step, and the number of steps in the corners for all four possible situations.
Immediately after launch, the program prompts you to select the working language of the dialogue: Russian (DOS 866 encoding) or English. After that, you need to specify in which mode the antenna analysis was performed in MMANA (free space or ideal ground). Incorrect indication of the mode, together with incorrect data entry into the table, may not be detected by the program and lead to a significant error in calculating the efficiency. Then enter the name of the file containing the "Angles/reinforcement" table. The file name must contain no more than eight characters without Cyrillic. If the file is not in the working directory, you must specify the path to it. The program detects erroneously specified files, as well as errors in input of initial data (inconsistency of data in Table 1) and issues appropriate comments. If the file or its path is not found, a message is displayed. If the input is successful, after processing the file, the result of calculating the efficiency in relative units and in percent is displayed. Comparison and evaluation of methods for calculating efficiency after simulation by the MMANA program Table 2 shows the results of efficiency calculations using the methods discussed above for some antenna models from the MMANA archive made of lossless material, good conductor, and iron.
Model 1 had loss-tolerant current distribution shapes and patterns. Therefore, the results of efficiency calculations by all methods practically coincide. For model 2, we have a noticeable difference only for iron according to the first method. The reason is a significant change in the currents in the wire where the excitation source is turned on. The third model, in contrast to the original one, had a 10 times smaller thickness of passive vibrators. This greatly affected both the current distribution and the radiation pattern, especially in the case of iron. Therefore, there are significant deviations of the results for the first two methods from the third. The directional pattern of the 4th model turned out to be strongly jagged under the influence of the ideal earth, so there was a difference even between the results of the program obtained with different angle steps. The most trustworthy are the results obtained by the program with a step of 2°. Of the other methods, the 2nd method (by amplification) provides a smaller error. AGT - simulation convergence test If you use the proposed program to calculate the antenna efficiency without losses, then the result will be the closer to unity, the more successfully the geometric modeling of the wire structure is performed. This applies in particular to segmentation, modeling closely spaced wires, small frames, and sharply angled wire connections. This test is known as the AGT (Average Gain Test) or APG (Average Power Gain) test of the convergence of the analysis by the average gain. The quality of modeling should be considered unsatisfactory if the result is outside the limits of 0,95 ... 1,05. The better the simulation quality, the closer the result is to unity. However, there may be situations where the test result is exactly one, and the model fails. AGT - verification is necessary but not sufficient. A good sign of the convergence and stability of the model is the weak dependence of the model parameters on increasing the number of segments (improving the accuracy of the simulation). If the AGT test available in the program is applied to a lossy antenna model, the result will be the antenna efficiency. Such a possibility, in particular, is available in the NEC2d program, where the efficiency factor is also calculated separately according to the method (5) with all its minuses. Efficiency calculation taking into account the influence of the earth and the environment Calculating the efficiency of an antenna over ideal ground is useful when the antenna system is so close to the ground or other surface, such as a conductive surface, that this surface has a significant effect on the distribution of currents through the wires and the radiation pattern. In the "Ideal ground" mode, the program can process files obtained in real ground conditions. The result of processing will be the efficiency value calculated taking into account losses not only in the antenna itself, but also when reflected from a non-ideal surface. Therefore, in the message "Perfect (?) Ground" there is a question mark warning about a possible error that the program cannot detect. The calculation of efficiency over real ground will give more or less correct results only for programs that take into account the effect of ground on the input impedance (this is not done by the programs M IN IN EC and its derivatives). Calculation of the efficiency taking into account the environment is possible only under the condition of an appropriate (taking into account the properties of the material) electromagnetic modeling of objects located in the near field of the antenna. Difficulties may arise when it is impossible to set different material parameters for different wires (as, for example, in the MMANA program). This problem can be partly solved by specifying a much smaller (or larger) wire diameter. Conclusion The issues discussed in the article do not affect losses in feeder lines and matching devices. The efficiency of the antenna-feeder device as a whole is the product of the antenna efficiency and the efficiency of the feeder line with the matching device. The application of the described methodology is not limited to these programs. The errors in determining the efficiency using the Poynting vector method are related to the quality of the simulation, as well as to the rounding of the data in the file for the far field. Unfortunately, the output data after simulation by the MMANA program is not very accurate. It is hoped that in new versions of the MMANA program this shortcoming will be eliminated, and the developers of new antenna modeling programs will not forget to include the determination of efficiency among the tasks to be solved, taking into account the wishes expressed here. Literature
Authors: A. Grechikhin, I. Karetnikova, D. Proskuryakov, Nizhny Novgorod
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(3)
represents the radiation energy flux density (W/m2) at a given distance (R) in a given direction (Θ, φ). Here Z0 = 120π (Ohm) is the wave impedance of free space; E(Θ, φ, R) - intensity (V/m) of the electric field component at a given point.
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