Mikrodalga tümleşik devre teknikleriyle gerçekleştirilen QPSK modülatörleri

Abstract

Bu tezde mikroşerit hatlarla gerçekleştirilen mikrodalga faz kaydıncılarmın tasarım yöntemleri araştırılmıştır. 90° ve 180° için tasarlanan faz kaydracılar daha sonra kaskad bağlanarak tezin başlangıcında hedeflenen QPSK Modülatörü oluşturulacaktır. Hedeflenen faz hatası merkez frekansı olarak seçilen 7. 51 GHz civarındaki 150MHz lik bir band içinde bulunan her bir 5MHz lik kanal içinde 5° dir. Tasarım için seçilen konfigürasyon, anahtarlama elemam olarak pin diyotian ve faz kaydırma elemanı olarak sonu açık devre transmisyon hatları içeren yansıma tipi faz kaydıncılardır. Yapıda güç bölücü/birleştirici olarak kullanılan bir de iki-yan hatiı kuplör vardır. Faz kaydırma miktarı sonu açık devre transmisyon hatlarının boylan ile ayarlanacaktır. İki-yan hatiı kuplörün ikili simetrisinden yararlanarak ideal durumdaki S Matrisi, simetri düzlemlerinde açık ve kısa devre koşullarım uygulayarak elde edilen dörttebirlik kısımların giriş yansıma katsayılarının türetilmesi yoluyla belirlenmiştir. Daha sonra yan hatiı kuplörün küple kapılan, pin diyotian ile sonu açık devre transmisyon hatlarına bağlanarak toplam devre iki-kapıh hale getirilir. Ek olarak getirilen devrenin giriş yansıma katsayılan yan hatiı kuplör için elde edilen bağıntıda küple kapılardan çıkan işaretin, bu kapılara giren işarete oram olduğu düşünülerek dört-kapıh için elde edilen S matrisi iki-kapıh S matrisine indirgenir. Yapıda bulunan T jonksiyonu ve açık devre süreksizlMerinin, tasarımı etkileyen yönleri vardır. Bu süreksizliklerin eşdeğer devreleri kullanılarak, getirdikleri referans düzlemi kaymalan ve ek reaktanslar yaklaşık olarak hesaplanabilir. Referans düzlemi kaymalarının etkisi hat boylarını uygun biçimde ayarlayarak giderilebilir. Ek reaktanslann etkisinin giderilmesi için literatürde çeşitli yöntemler vardır. Diğer bir bozucu etki de diyot parametrelerinden gelir. Diyot parametrelerine duyarlılığın azalması için kullanılan hatların karakteristik empedanslanmn arttırılması iyi sonuç verir. Süreksizliklerin ve diyot parametrelerindeki değişmelerin performansa etkisi sayısal olarak hesaplanmıştır. Bozucu etkilerin mümkün olduğunca düzeltilmesi ile elde edilen QPSK modülatörünün yapısı ve sayısal sonuçlan tezin içinde yer almaktadır. Diyotlann beslenmesi için bir örnek devre yapışma da değinilmiştir.

In this thesis we investigate the design of pin diode microwave phase shifters in microstrip configuration. The particular design problem that we pose ourselves is a phase shifter which will be utilized as the output stage of a QPSK modulator. Phase errors are to be kept to within 5° at any 5MHz channel over a bandwidth of 150 MHz around the design frequency of 7. 51 GHz. The configuration chosen in the design is a reflection type phase shifter which utilizes pin diodes as switching elements and lengths of transmission lines as phase shifting networks. Two branch line 3dB hybrid couplers are used as power divider/combiner which are connected to open ended transmission line sections via pin diodes operated in series configuration. These two sections which provide phase shifts of 90° and 180° respectively, are connected in series to obtain the required phase shifts of 0°, 90°, 180° and 270° required for the QPSK modulator. We begin by a formal analysis of the reflection type phase shifter depicted in Figure 1. The idealized 3dB branch line coupler represented by the 4-port in the figure is reduced to the 2-port reflection type phase shifter by terminating the coupled ports 3 and 4 with identical lossless phase shifters, i.e. by assuming that the reflection coefficients seen when looking into the terminating networks can be assumed to be equal to eM with Im{ $ }=0. Figure 1 Reflection type phase shifter obtained via lossless termination of the coupled parts of a branch line coupler. Figure 2 Single section branch line coupler and symmetry bisections. Consider the 3dB branch-line coupler shown in Figure 2. Neglecting discontinuity effects at the T junctions for the moment the S matrix representation can be obtained in a straightforward manner by utilizing symmetry bisections shown in the figure to reduce the problem to the determination the reflection coefficients of equivalent 1 -ports. One can then write with Y1=l, Y2 = V2 and a = 0/2 (1) o _Pcf+Pt,+P*+Pn S-~ 4 1 - 7(1+ Vatana " I+7Y1+V2) tana 1 - j( tan a - V2cot a\ 1 + j( tan a - V2 cot a j e _P"-Pç,+P*-Pn Ju - ~A £,= Pçç+Pn-Pç.-P* 1 - 7jv2 tan a - cot a J 1 + _/' I v2 tan a - cot a\ l+j(l+yfl\ cot a l-j'(l+V2)cota (2) (3) Upon terminating the coupled ports of the branch line coupler with identical impedances represented by reflection coefficient eJ* one obtains VI ,m _ =_ = su +s2neJ*(l-SneJ')+Snsl3s14e Sn *22 (l-2sneJ*+s2neJ2*-s2neJ2*) | s2ue«(l-2sne" +s^ -s2ne^)+Sususue^(l-sne^)s2uS21Ae (l - sne»)(l - 2sueM +s2ueJ2* - sfc»*) (4.a),J*i sn - su ~ J3f __ _ sn + s13sueJ* (l - sue» ) + sns2ue (1-25^+5^-4^) (l-.sue*)(l-2.sue* +4^" -4^") At the band center frequency (3.19) reduces to the S matrix of an ideal phase Je 0 je j* o j* a, a, (4.b) shifter: (5) As noted above pin diodes in series configuration will be used which switch in and out an open circuited transmission line section of electrical length /2 as phase shifting networks. Let the pin diode be characterized with series impedances of Zf and Zr corresponding to low (diode switched on) and high (diode switched off) impedance stages, respectively. The reflection coefficients seen looking into the phase shifting networks can be written as a = '-*+^(i-'-*) ; zf/z.«i A=l 2Z_ zjzr«i (6.a) (6.b) where Zo is the normalization impedance and above expressions are valid to the leading order in the small parameters indicated. Clearly in the limit of an ideal switching device one will have Zf - > 0, Zr -> oo and an ideal phase shifting element will be obtained. Several effects which severely impair the validity of the above described idealized treatment have "to be taken into consideration. Among those the effects of the discontinuities introduced by the T junctions, by the open ended transmission line sections, by the non-ideal switching diode characteristics are of primary importance. The T junctions can be modeled as in Figure 3 BT, n and the shifts dx, d2 of the reference planes can be obtained from the available empirical formulas [Bahl I and Bhartia P, "Microwave Solid Circuit Design, John Wiley & Sons, 1988] vu \ TO Î2 ?Ts 1 Z02İ )n:1 Figure 3 Microstrip T junction and its equivalent network model. In this case the 2-port S matrix representation for the phase shifter as given in (2) will again be valid provided that the reflection coefficients in (lc) are replaced by the expressions given below in (la), (lb) and in (2) : 1-7 Hçç 1 + 7 1-7 BT + tan(a - d^) + Jin2 tan(a - d2) Pçt = 1 + 7 1-7 BT + tan(a - dt) + 4ln2 tan(a - d2) BT + tan(a - dj - V2»2 cot(a - d2) Ptt 1 + 7 1 + 7 BT + tan(a - <7j - 4ln2 cot(a - d2) BT + V2«2 tan(a -d2)- cot(a - Jj 1-7 BT + v2w2 tan(or - d2) - cot(a - <7J BT.+ cot(a - JJ + V2«2 cot(a - d2) BT + cot(a - <7J + -v/2»2 cot(a - d2) (7.a) (7.b) (7.c) (7.d) The correction required to compensate for the non-ideal character of an open circuit on microstrip line involves only a modification of the design length of the line. To obtain the S parameter representation of the QPSK phase shifting section one has to replace the eJ* term the in (2) by (4a) and (4b) for the two states of the switching diode, respectively. The final refinement necessary consists of the modification of the y/ in equations 4 accordingly. The overall S parameter representation of the phase shifter is VUl herewith formulated explicitly in term of all parameters relating to the characteristics of the microstrip networks and of the switching diodes. The resulting symmetric two port is characterized by two parameters, i.e.sn =s22 and sn =s21. Our design objective is to minimize the insertion loss and the phase errors over the entire design bandwidth. This accounts to the simultaneous satisfaction of the following requirements arg{(^)/}-arg{(512)r} = ^ + ^2 «,«1 (8) The layout of the optimized circuit comprising of two BPSK sections to form a QPSK modulator is shown in Figure 4 together with /1/4 impedance transformers to match the 70.71 H branch line port impedances to the required value of 50 Q at the output ports of the modulator. IF paths to the diodes and low pass blocking filters are also shown in the figure. Figure 4 Layout for the QPSK modulator (scale 2:1) A typical performance of the modulator generated numerically is depicted in Figure 5. We conclude that with the present design we have been able to limit the insertion loss 0.085dB and the phase errors (in channel bandwidths of 5Mhz) to 2° IX f(GHz) ?*. !-;!?. &j ffi a) 320.^ £ s s 1^ f(GHz) b) UJ X O- Figure 5 Typical phase performances of the modulator (a) For (00) bite (b) For (01) bite We have modified an existing microwave CAD software to better suit our needs and performed extensive numerical calculations to determine the dependence of the performance in the variations of the electrical characteristics and design performances. Our computations indicate that with proper choice of the diodes and with easily achievable engineering tolerances in the order of 35 jum the realized modulator should perform in keeping with the design specifications.