DOI 10.1007/s11141-016-9651-4
Radiophysics and Quantum Electronics, Vol. 58, No. 10, March, 2016 (Russian Original Vol. 58, No. 10, October, 2015)
USING THE TALBOT EFFECT FOR SUMMATION OF MICROWAVE SIGNALS IN THE MILLIMETER-WAVELENGTH BAND G. G. Denisov1,2 and M. Yu. Shmelyov1∗
UDC 537.86
We consider the problem of summing the power produced by several coherent sources of microwaves and propose to use the Talbot effect in an oversized rectangular waveguide to solve it. The operating frequency of the summator is 94.4 GHz. The calculated coefficient of summation of individual signals is equal to 2.8 dB in the 800 MHz frequency range with allowance for the ohmic loss. Computer simulation of the summator has been performed, and its characteristics have been studied at a low power level.
1.
INTRODUCTION
The gyroklystron is an amplifier capable of producing multimegawatt level power at frequencies near 100 GHz. However, as of now there are no sufficiently strong microwave sources, which allow one to ensure the above-specified power level in the input signal at realistic values of the gyroklystron amplification ratio (25–30 dB). To solve this problem, we propose a scheme of synchronization of several independent sources (magnetrons), which can ensure an output signal power equal to several tens of kilowatts. This scheme was implemented in the balance summator of magnetron power, which is based on the single-mode waveguide at a frequency of about 34 GHz [1]. In this case, as a small fraction of radiation produced by one magnetron is reflected to another one, mutual frequency locking occurs, and the magnetrons become coherent. The frequency increase complicates application of single-mode waveguides at a high power level (about 10 kW). Using oversized waveguides allows one to solve this problem. In this paper, we propose to use the Talbot effect in an oversized waveguide to sum up the radiation power. It was shown in the works dealing with studying and using the Talbot effect [2] that as a paraxial wave beam is injected into an oversized waveguide, it can be repeated, reflected symmetrically, split into several symmetric beams, etc. [3]. The devices, which allowed one to control the output radiation by varying phase relationships at the waveguide output, were described in [4, 5]. These phenomena are connected with interference of the modes, into which the field of the input beam can be decomposed. Phase increments for each mode become multiples of π at certain fixed distances. For example, in a planar waveguide at the distances z = (p/q) (a2 /λ), the phase increment between the modes with the transverse indices m and n is determined approximately by the following formula [4]: Δϕnm =
π p 2 (n − m2 ). 4 q
Here, p and q are integer positive numbers, a is the transverse size of the waveguide, and λ is the wavelength in free space. For the waveguide length z = 2a2 /λ, two wave beams, which have identical amplitudes A0 , ∗
[email protected] 1
Institute of Applied Physics of the Russian Academy of Sciences, 2 N. I. Lobachevsky State University of Nizhny Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 58, No. 10, pp. 881– 885, October 2015. Original article submitted June 2, 2015; accepted September 22, 2015. c 2016 Springer Science+Business Media New York 0033-8443/16/5810-0789 789
Fig. 1. Quasioptical directed coupler.
Fig. 2. Distribution of the electric field in the summator.
Fig. 3. Summation coefficient in a “closed” system with four ports (a) and in an “open” system with the fifth port and an absorber (b).
Fig. 4. Calculated (a) and measured (b) coefficients of transmission of signals from ports 1 (S14 , solid line) and 2 (S24 , dashed line). but different phases (with the phase shift Δϕ) at the waveguide input, are converted into two beams with different amplitudes A1 and A2 at the output of the converter (see Fig. 1). Specifically, if one sends two identical coherent beams with phase shift equal to π/2 to this device, then one will have a waveguide power summator: A21 (π/2) = 2A20 and A22 (π/2) = 0. 2.
CALCULATIONS AND MEASUREMENTS
For calculations, the model of the summator at a frequency of 94.4 GHz was chosen. The input ports (1 and 2 in Fig. 2) were single-mode waveguide transitions from the 2.4 × 1.2 mm cross section to the 6 × 2 mm cross section. Port 4, in which the summation was performed, has an output size of 3.0 × 1.5 mm. The width of the middle part of the summator was a = 12 mm, while the length of the summator was 790
equal to 94.6 mm. This length was found by optimizing it to achieve the maximum summation coefficient in port 4 and is slightly different from the length yielded by the formula z = 2a2 /λ = 91 mm. Detailed calculations of this summator using the CST Studio software [6] showed that some higher modes turned to be locked in the central part of the summator, which led to resonance absorption of radiation inside the device. To avoid this effect, we decided to “open” the system. For this purpose, port 5 was made in the side wall of the summator near inoperative port 3, in the region of the weak field. This supplementary port is a 15 × 2 waveguide with a matched load. Individual (0 dB) signals with phase difference equal to π/2 are fed to ports 1 and 2. Summation takes place in port 4. Figure 2 shows the field distribution in the summator. The ports are marked with numbers. Figure 3 presents the frequency dependences of the summation coefficient F , which corresponds to the value of the first-mode signal in port 4 in the case of feeding ports 1 and 2 with individual signals at a frequency of 94.4 GHz with phase shift equal to π/2. One can see that the total signal in the open system is less strong (2.8 dB, rather than 2.9 dB), while the resonance dips disappear, and the operating band of the summator grows to achieve 800 MHz. Calculated values of the reflection coefficients S11 and S22 and transition coefficients S21 and S12 do not exceed −20 dB. Thus, the loss in the system are determined by absorption, in port 5, mainly. Due to the absence of two coherent sources with controlled phases, the device was tested experimentally on an example of splitting a single signal (0 dB) fed to port 4 between ports 1 and 2. A preliminary numerical experiment yielded a field distribution which is almost identical with that for the summation problem (see Fig. 2). The experimentally measured parameters S14 and S24 were calculated (see Fig. 4a). The calculation showed asymmetry between channels 1 and 2, which was due to the asymmetry of the problem per se (presence of port 5 with an absorber). The experimental data obtained by using a vector Fig. 5. Photo of summators (a) and measureanalyzer (see Fig. 5) were very close to the calculated val- ment of summator characteristics by a vector anues (Fig. 4b). A small decrease in the transmission coeffi- alyzer (b). cient was due to the manufacturing quality of the waveguide surface of the summator. Efficiency of operation of port 5 with an absorbing inset was also confirmed experimentally. The presence of an additional absorption center eliminates resonance dips, and due to its location in the weak-field region it has almost no decreasing effect on the signal level (see Fig. 6). The measured reflection coefficients S11 and S22 , and the transition coefficient S21 did not exceed −20 dB (see Fig. 7).
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Fig. 6. Measured transmission coefficient S14 in the presence of port 5 with an absorber (solid line) and in the absence of port 5 (dashed line). 3.
Fig. 7. Measured reflection coefficients S11 (solid line) and S22 (dashed line), and the transition coefficient S21 (dashed line).
CONCLUSIONS
This paper presents the results of calculating and measuring the characteristics of a quasioptical power summator, which is based on the Talbot effect in an oversized waveguide. Supplementing the summator with an absorbing unit in the form of an additional port with a matched load allowed one to eliminate spurious resonances and ensure an operating frequency band of up to 800 MHz. Experimental tests of the manufactured summator using one source yielded a result which was close to that obtained by numerical modeling. This work was supported by the Russian Science Foundation (Project No.14–29–00192). REFERENCES
1. E. M. Guttsait, I. M. Ivanov, and A. A. Kurushin, in: Proc. “Problems of Microwave Electronics” Conf., Moscow, 24–25 October 2013, p. 52. 2. H. F. Talbot, J. Sci., 9, 401 (1836). 3. L. A. Rivlin and V. S. Shil’dyaev, Radiophys. Quantum Electron., 11, No. 4, 318 (1968). 4. G. G. Denisov and S. V. Kuzikov, in: Proc. Int. Workshop Strong Microwaves in Plasmas, Nizhny Novgorod, 2–9 August 1999. V. 2, p. 960. 5. S. V. Kuzikov, Int. J. Infrared and Millimeter Waves, 19, No. 11, 1523 (1998). 6. http://www.cst.com/ .
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