ELECTRONICS AND ELECTRICAL ENGINEERING ISSN 1392 – 1215 2012. No. 6(122) ELEKTRONIKA IR ELEKTROTECHNIKA
HIGH FREQUENCY TECHNOLOGY, MICROWAVES T 191 AUKŠTŲJŲ DAŽNIŲ TECHNOLOGIJA, MIKROBANGOS
The Investigation of Gyroelectric n-InAs Phase Shifters Characteristics
V. Malisauskas, D. Plonis Department of Electronic Systems, Vilnius Gediminas Technical University, Naugarduko St., 41-425, LT-03227, Vilnius, Lithuania, phone: +370 5 2744766, e-mail: [email protected]
http://dx.doi.org/10.5755/j01.eee.122.6.1836
Introduction 0 s s j j 1.emr , r B 0 The microwave phase shifters can be manufactured d1 d1 2.1 emr , r 1 using microstrip lines and open cylindrical waveguides [1]. d2 d2 21 The propagation and attenuation of phase wave’s cha- 2.2 emr , r 22 racteristics may vary in ferrite and semiconductor aa z r 3 3.emrr , waveguides by changing longitudinal magnetic flux den- s sity, external dielectric layer width and permittivity of r R1 dielectric layer, semiconductor temperature, the concentra- d1 tion of the free charge carriers. R 2 Nowadays the investigation of the semiconductor and d2 semiconductor-dielectric waveguides is very relevant and important for the sake of science. The usage and possibili- Fig. 1. Structure of the gyroelectric open cylindrical phase shifter ties of latter mentioned waveguides in gyroelectric phase with two dielectric layers: 1 – semiconductor core, 21 and 22 – external non-magnetic dielectric layers, 3 – air shifters are not known [2–4].
n-InAs semiconductor has been selected for the pur- The structure area 2, consists of two (area 2 and 2 ) pose of investigation. The super high frequency transistors 1 2 external non-magnetic dielectric layers complex relative are manufactured using n-InAs semiconductors, which eedd12, d1,2 =.1m have the higher concentration of electrons. permittivities rr and the permeability r The influence of external dielectric layer on the pa- Third area of the structure is the air which surrounds rameters of gyroelectric n-InAs semiconductor and semi- the whole structure of phase shifter (an upper index “a”). conductor-dielectric phase shifters has been hardly investi- Maxwell complex differential equations and gated in this paper. The aim is to maximize the differential boundary condition method are used to obtain the complex phase shift module at a relatively low concentration of dispersion equation. electrons. Dispersion and phase characteristics calculation The dispersion, phase and attenuation charac- algorithm and results of the analysis are presented in the teristics of the phase shifters are investigated, when the article [5]. main type hybrid mode HE11 propagates in phase shifters. Attenuation calculation algorithm Structure of phase shifter The attenuation calculation algorithm of gyroelectric General structure of the open cylindrical gyroelectric phase shifters, consists of three stages. Initial analysis it it phase shifter in coordinate rz,,j system is presented in parameters and frequency []ff min max , and phase it it the Fig. 1. constant []hh¢¢min max (it is the number of iterations) In the structure (Fig. 1), area 1 is exposed by a values are entered during the stage A. The frequency and constant longitudinal magnetic field, which is defined as a phase constant values are calculated using in [5] presented magnetic flux density vector B 0. It is the semiconductor algorithm. The complex dispersion equation is evaluated (an upper index “s”) core – gyroelectric material, which during the stage B. The complex propagation constant s can be described by using complex permittivity tensor er hh=i¢¢ - h¢ (here h¢ is the phase constant, h¢¢is the s attenuation coefficient) is found at the stage C. and a real relative permeability mr = 1.
121 19- 3 Algorithm. Attenuation calculation algorithm in paper [5], when concentration N =×510 m . A. Initialization of system parameters. The main mode HE11 dispersion characteristics of the n-InAs semiconductor-dielectric phase shifters are shown eedd1 ,,,,,[2 esn mm* fit f it ],[ h¢¢ it h it ], rr k minmax minmax in the Fig. 2, when the concentration of electrons is small s 19- 3 BNRRr0,,m ,12 , , . N =×110 m and magnetic flux density is varied B. Solving transcendental linear dispersion equation B 0 0, 0.25, 0.5, 0.75, 1 T, also only one external system. dielectric layer is used. it it it for f ¬ ff min, max do For external dielectric layer TM-15 type dielectric is 1) Calculation of the relative complex permittivity used [4]. The external dielectric layer relative complex d1, 2 4 tensor. permittivity is er 15(i 1 10 ) and the relative 2) Calculation of the coefficients [4]: s thickness of dielectric layer is dr1, 2 /0.15.= ¢¢¢ithh¢¢¢¢¢ it¢¢¢¢¢ it h¢ for hhhh¬, min D, max do On the basis of dispersion characteristics (Fig. 2), it hh=i¢¢it - h¢ ith¢¢; can be seen that, when we change magnetic flux density the main mode HE phase constant also changes at ss ad B 0 , 11 emD,, ,,,kk k ,,, k k s ef ef PF 12 normalized frequency fr =×0.0325 GHz m, which is in abs, ,1414 , ..., s , v , ..., v . working frequency range fr s 0.018 GHz m and here 3) Calculation of the cylindrical functions. we have a phase shift. 4) Calculation of the determinant elements: In Fig. 3, the mode HE11 dispersion characteristics is a jk , when j = 0, 1, ..., 12 and k = 0, 1, ..., 12. presented, when normalized dielectric layer thickness is dr/0.15.s = The first dielectric layer relative sd, 1, 2 5) Evaluation of the determinant Da det(jk ). d1 permittivity is a equal to air er 1, and the second sd, 6) Saving determinant values D . d2 4 ith, it dielectric layer permittivity is er 15(i 1 10 ). Comparing Fig. 2 and Fig. 3, it can be seen that the end for cut-off frequencies of the main mode HE move to higher end for 11 frequencies. When we change external dielectric layer C. The complex wave propagation constant hh=i¢¢ - h¢ width and permittivities. evaluation. it it for it¬ 0,1, [ f min f max ] do
for ith¢¢¢¬-0,1, h ¢ith¢¢ 1 do
sd,, sd sd,, sd if DD and DD ithh1, it it , it ithh+ 1, it it , it
hh=i¢¢it - h¢ ith¢¢; hr¢¢ ss(). fr end if
end for Fig. 2. Dispersion characteristics of the n-InAs phase shifter, end for d1, 2 when N =×11019 m- 3 ,dr/0.15,s = e 15(i 1 104 ) 1, 2 r Investigation of n-InAs phase shifters with two external dielectric layers
Gyroelectric phase shifters dispersion characteristics are presented as normalized phase constant hr s dependences on the normalized frequency fr s . The polarization of the hybrid modes is left-hand (eim j ). The investigation of the n-InAs semiconductor and semiconductor-dielectric phase shifters is performed by taking electron mobility m=4 mVs2 / × , effective mass * mm= 0.02 e (m e – is mass of free carrier) and material sn Fig. 3. Dispersion characteristics of modes HE11 of the n-InAs background constant e=k 15.2 [6]. phase shifter, when N =×11019 m- 3 ,dr/0.15,1sd=e=1 and The dispersion characteristics of the phase shifters, 1 r s s d2 4 without external dielectric layer dr1, 2 /0= is presented dr2 / 0.(i) 15,er 15 1 10
122 Differential phase shift module DJ frs const The lower concentration of electrons N =×11019 m- 3 is taken in our calculations, so that the dependence on the magnetic flux density B can be ob- 0 n-InAs semiconductor-dielectric phase shifters would not tained using dispersion characteristics of the phase shifters. work as a wave absorber. It can be calculated by drawing a vertical line in the phase The highest attenuation of main mode HE s 11 shifter working frequency range fr , for example at the propagated in semiconductor n-InAs phase shifters can be normalized frequency fr s 0.0325 GHz·m. The vertical s obtained without external dielectric layer ()dr1, 2 /0.= lines are drawn in Fig. 2 and Fig. 3. The attenuation characteristics are presented in Fig. 5. Differential phase shift module in degrees can be ob- tained using equation [4]
sss DJs hr h r/ r L 360 / 2 p , (1) fr const 0 B0
s where hr0 is the normalized phase constant, when B 0T; hr s is the normalized phase constant, when 0 B0 B0 0T; L is the length of the phase shifter. In Fig. 4, the differential phase shift module depen- dences on the magnetic flux density is presented. From Fig. 5. Attenuation characteristics of modes HE of the n-InAs Fig. 4, it is seen that the phase shifters have wide working 11 phase shifter, when N =×11019 m- 3 , dr/0s = range without external dielectric layer dr/0s = and 1, 2 1, 2 s d1, 2 4 Attenuation characteristics of the n-InAs with it dr1, 2 /0.15,= e 15(i 1 10 ). r semiconductor-dielectric phase shifters at different
magnetic flux densities B0 are shown in Fig. 6. These characteristics show that EM wave attenuation in n-InAs phase shifters increases, when B0 decreases. It is seen he- re that the attenuation coefficient decreases after the main s mode cut-off frequency frcut0 =×0.0193 GHz m and the s attenuation stabilizes after frequency fr = 0.0325 GHz·m at B 0 and B 0.25 T. This phenomenon can be Fig. 4. The differential phase shift module dependences on the 0 0 explained by diagrams, shown in Fig. 7. magnetic flux density, where 1 – dr/0;s = 1, 2 s d1, 2 4 s 2 – dr1, 2 /0.15,= er 15(i 1 10 ) ; 3 – dr1 /0.15,=
d1 s d2 4 e=r 1, dr2 / 0.(i) 15,er 15 1 10
The widest working range of the n-InAs phase shifters can be obtained, when the magnetic flux density B0 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 Fig. 6. Attenuation characteristics of the n-InAs phase shifter, be noticed that, the external dielectric layer, when relative 19- 3 s d1, 2 4 s when N =×110 m , dr1, 2 /0.15,= er 15(i 1 10 ) thickness is dr1, 2 /0.15= and permittivity
d1, 2 4 er 15(i 1 10 ) , expands the conversion 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 dr/0.s = 1, 2 sss With external dielectric layer which relative Fig. 7. Im(, exxxyzz e , e ) dependences on magnetic flux permittivity is equal to air, DJ is less than 400°, frs const 19- 3 s density B 0 , when N =×110 m , fr =×0.0325 GHz m d it means that the dielectric layer with er = 1 reduces the ss phase shifter conversion range. The imaginary parts Im(,eexxzz ) of the complex
123 relative permittivity tensor of the n-InAs core Fig. 7 coin- Conclusions s cide, when B0 0T, and Im()exy value is equal to In this paper open cylindrical gyroelectric zero, when B0 0T. In this case the n-InAs semiconductor phase shifters with core without dielectric semiconductor-dielectric phase shifter transforms into layer and with one and two dielectric layers are layered dielectric waveguide. investigated. It is shown in Fig. 8 that attenuation coefficient of The highest n-InAs semiconductor and semiconduc- mode HE11 decreases after cut-off frequency tor-dielectric phase shifters DJ s can be obtained, s fr const frcut0 =×0.0225 GHz m. The mode (wave) attenuation when B are from 0 to 0.25 T. increases, when between the semiconductor core and the 0 dielectric there is an air space. It means that the electro- The attenuation in the phase shifters with one external magnetic waves are more concentrated in semiconductor d1, 2 4 dielectric layer with er 15(i 1 10 ) , is the lowest, core, so the mode attenuation increases more than using s it means that the EM waves are more concentrated in the one external dielectric layer dr1, 2 /0.15= (Fig. 6). The external dielectric layer than in the gyroelectric core. electromagnetic field concentrates more in the dielectric layer than in the air. The lower attenuation is in air and References higher in dielectric layer. 1. Pomarnacki R., Krukonis A., Urbanavičius V. Parallel Algorithm for the Quasi–TEM Analysis of Microstrip Multiconductor Line // Electronics and Electrical Engineering. – Kaunas: Technologija, 2010. – No. 5(101). – P. 83–86. 2. Iqbal S. S. Novel Semiconductor Phase Shifters for Millimeter–Wave Devices // Microwave and Optical Technology Letters. – Wiley Periodicals, Inc., 2003. – No. 39(4). – P. 300–303. 3. Zhang Q., Jiang T., Feng Y. Slow–light Propagation in a Cylindrical Dielectric Waveguide with Metamaterial
Cladding // Journal of Physics D: Applied Physics. – IOP Fig. 8. Attenuation characteristics of modes HE11 of the n-InAs Publishing. 2011. – No. 44(2011). – P. 1–6. phase shifter, when N =×11019 m- 3 ,dr/015,1sd.e1 and 4. Nickelson L., Ašmontas S., Mališauskas V., Šugurovas V. 1 r The Open Cylindrical Gyrotropic Waveguides. – Vilnius: s d2 4 Technika, 2007. – 248 p. (in Lithuanian). dr2 / 0.(i) 15,er 15 1 10 5. Mališauskas V., Plonis D. Dispersion Characteristics of the The attenuation characteristics shown in Fig. 8 reveal, Propagation Waves in the Gyroelectric Semiconductor Waveguides // Electronics and Electrical Engineering. – that the attenuation maximum at the main mode HE11 cut- off frequency increases approximately by 1.5 times, when Kaunas: Technologija. 2010. – No. 10(106). – P. 87–90. B is varied from 0 to 1 T. The high EM wave attenuation 6. Sze S. M. Physics of Semiconductor Devices. – USA: John 0 Wiley & Sons, 1981. – 868 p. is undesirable because it reduces the transmission of EM wave power.
Received 2012 01 17 Accepted after revision 2012 04 19
V. Malisauskas, D. Plonis. The Investigation of Gyroelectric n-InAs Phase Shifters Characteristics // Electronics and Electrical Engineering. – Kaunas: Technologija, 2012. – No. 6(122). – P. 121–124. In this paper the open cylindrical gyroelectric phase shifters characteristics are investigated. The investigation is performed by changing their parameters: the magnetic flux density, the number of layers of dielectric, width and permittivities. The highest differential phase shift in n-InAs semiconductor and semiconductor-dielectric phase shifters can be obtained in range of magnetic flux density from 0 to 0.25 T. The minimum attenuation in phase shifters is obtained with one external dielectric layer. Ill. 8, bibl. 6 (in English; abstracts in English and Lithuanian).
V. Mališauskas, D. Plonis. Giroelektrinių n-InAs fazės keitiklių charakteristikų tyrimas // Elektronika ir elektrotechnika. – Kaunas: Technologija, 2012. – Nr. 6(122). – P. 121–124. Straipsnyje tiriamos atvirųjų cilindrinių giroelektrinių fazės keitiklių charakteristikos, keičiant jų parametrus: magnetinio srauto tankį, dielektrikų sluoksnių skaičių, storius ir dielektrines skvarbas. Nustatyta, kad n-InAs puslaidininkiniuose ir puslaidininkiniuose- dielektriniuose fazės keitikliuose didžiausias diferencinis fazės pokytis gaunamas, kai magnetinio srauto tankis yra nuo 0 iki 0,25 T. Mažiausiai elektromagnetinės bangos slopinamos keitikliuose su vienu išorinio dielektriko sluoksniu. Il. 8, bibl. 6 (anglų kalba; santraukos anglų ir lietuvių k.).
124