The Investigation of Gyroelectric nInAs Phase Shifters Characteristics

The microwave phase shifters can be manufactured using microstrip lines and open cylindrical waveguides [1]. The propagation and attenuation of phase wave’s characteristics may vary in ferrite and semiconductor waveguides by changing longitudinal magnetic flux density, external dielectric layer width and permittivity of dielectric layer, semiconductor temperature, the concentration of the free charge carriers. Nowadays the investigation of the semiconductor and semiconductor-dielectric waveguides is very relevant and important for the sake of science. The usage and possibilities of latter mentioned waveguides in gyroelectric phase shifters are not known [2–4]. n-InAs semiconductor has been selected for the purpose of investigation. The super high frequency transistors are manufactured using n-InAs semiconductors, which have the higher concentration of electrons. The influence of external dielectric layer on the parameters of gyroelectric n-InAs semiconductor and semiconductor-dielectric phase shifters has been hardly investigated in this paper. The aim is to maximize the differential phase shift module at a relatively low concentration of electrons. The dispersion, phase and attenuation characteristics of the phase shifters are investigated, when the main type hybrid mode HE11 propagates in phase shifters.


Introduction
The microwave phase shifters can be manufactured using microstrip lines and open cylindrical waveguides [1].The propagation and attenuation of phase wave's characteristics may vary in ferrite and semiconductor waveguides by changing longitudinal magnetic flux density, external dielectric layer width and permittivity of dielectric layer, semiconductor temperature, the concentration of the free charge carriers.
Nowadays the investigation of the semiconductor and semiconductor-dielectric waveguides is very relevant and important for the sake of science.The usage and possibilities of latter mentioned waveguides in gyroelectric phase shifters are not known [2][3][4].
n-InAs semiconductor has been selected for the purpose of investigation.The super high frequency transistors are manufactured using n-InAs semiconductors, which have the higher concentration of electrons.
The influence of external dielectric layer on the parameters of gyroelectric n-InAs semiconductor and semiconductor-dielectric phase shifters has been hardly investigated in this paper.The aim is to maximize the differential phase shift module at a relatively low concentration of electrons.
The dispersion, phase and attenuation characteristics of the phase shifters are investigated, when the main type hybrid mode HE 11 propagates in phase shifters.

Structure of phase shifter
General structure of the open cylindrical gyroelectric phase shifter in coordinate , , r z j system is presented in the Fig. 1.
In the structure (Fig. 1), area 1 is exposed by a constant longitudinal magnetic field, which is defined as a magnetic flux density vector .0 B It is the semiconductor (an upper index "s") core -gyroelectric material, which can be described by using complex permittivity tensor  e s r and a real relative permeability 1.
, Third area of the structure is the air which surrounds the whole structure of phase shifter (an upper index "a").
Maxwell complex differential equations and boundary condition method are used to obtain the complex dispersion equation.
Dispersion and phase characteristics calculation algorithm and results of the analysis are presented in the article [5].

Attenuation calculation algorithm
The attenuation calculation algorithm of gyroelectric phase shifters, consists of three stages.Initial analysis parameters and frequency [ ] (it is the number of iterations) values are entered during the stage A. The frequency and phase constant values are calculated using in [5] presented algorithm.The complex dispersion equation is evaluated during the stage B. The complex propagation constant Algorithm.Attenuation calculation algorithm A. Initialization of system parameters.
Solving transcendental linear dispersion equation system.
3) Calculation of the cylindrical functions.4) Calculation of the determinant elements: For external dielectric layer TM-15 type dielectric is used [4].The external dielectric layer relative complex permittivity is On the basis of dispersion characteristics (Fig. 2), it can be seen that, when we change magnetic flux density 0 , B the main mode HE 11 phase constant also changes at normalized frequency 0.0325 GHz m, fr s = × which is in working frequency range 0.018 GHz m    fr s and here we have a phase shift.
In Fig. 3, the mode HE 11 dispersion characteristics is presented, when normalized dielectric layer thickness is ).Comparing Fig. 2 and Fig. 3, it can be seen that the cut-off frequencies of the main mode HE 11 move to higher frequencies.When we change external dielectric layer width and permittivities.B can be obtained using dispersion characteristics of the phase shifters.It can be calculated by drawing a vertical line in the phase shifter working frequency range , fr s for example at the normalized frequency 0.0325  fr s GHz•m.The vertical lines are drawn in Fig. 2 and Fig. 3.
Differential phase shift module in degrees can be obtained using equation [4]   where 0  h r s is the normalized phase constant, when L is the length of the phase shifter.In Fig. 4, the differential phase shift module dependences on the magnetic flux density is presented.From Fig. 4, it is seen that the phase shifters have wide working  The widest working range of the n-InAs phase shifters can be obtained, when the magnetic flux density 0 B is varied from 0 to 0.25 T. Then the maximum is obtained with external dielectric layer and without it, for example when phase shifter core length is L = 50 mm.
Referring to the characteristics shown in Fig. 4, it can be noticed that, the external dielectric layer, when relative is taken in our calculations, so that the n-InAs semiconductor-dielectric phase shifters would not work as a wave absorber.
The highest attenuation of main mode HE 11 propagated in semiconductor n-InAs phase shifters can be obtained without external dielectric layer 1, 2 / 0. d r s ( ) = The attenuation characteristics are presented in Fig. 5.

Fig. 1 .
Fig. 1.Structure of the gyroelectric open cylindrical phase shifter with two dielectric layers: 1 -semiconductor core, 2 1 and 2 2external non-magnetic dielectric layers, 3 -air The structure area 2, consists of two (area 2 1 and 2 2 ) external non-magnetic dielectric layers complex relative permittivities 1 2 , d d r r e e and the permeability 1, 2 1 m d r = .Third area of the structure is the air which surrounds the whole structure of phase shifter (an upper index "a").Maxwell complex differential equations and boundary condition method are used to obtain the complex dispersion equation.Dispersion and phase characteristics calculation algorithm and results of the analysis are presented in the article[5].
jk a , when j = 0, 1, ..., 12 and k = 0, 1, ..., 12. 5) Evaluation of the determinant , n-InAs phase shifters with two external dielectric layers Gyroelectric phase shifters dispersion characteristics are presented as normalized phase constant  s h r dependences on the normalized frequency .fr s The polarization of the hybrid modes is left-hand .the n-InAs semiconductor and semiconductor-dielectric phase shifters is performed by taking electron m -is mass of free carrier) and material background constant 15.2 n s k e = [6].The dispersion characteristics of the phase shifters, without external dielectric layer 1, 2 / 0 d r s = is presented in paper [5]main mode HE 11 dispersion characteristics of the n-InAs semiconductor-dielectric phase shifters are shown in the Fig. 2, when the concentration of electrons is small

Fig. 4 .
Fig. 4. The differential phase shift module dependences on the magnetic flux density, where 1 -1, 2 / 0; d r s = 2 -1, 2 / 0.15, = d r s 1, 2 4 15 1 10 ;     d r ( i ) e 3 -1 / 0.15, = d r s range of phase shifters and reinforce quite thin and fragile phase shifters cores.Also the external dielectric layer decreases attenuation of electromagnetic (EM) waves in phase shifters, because the highest EM wave attenuation can be obtained without external dielectric layer 1, 2 / 0. d r s = With external dielectric layer which relative permittivity is equal to air,  fr DJ s const is less than 400°, it means that the dielectric layer with 1 e d r = reduces the phase shifter conversion range.

Fig. 5 .
Fig. 5. Attenuation characteristics of modes HE 11 of the n-InAs phase shifter, when