The Optimization Synthesis Of Matching Network And Idler Circuit For Varactor Frequency Multipliers

T h i s pape r d e s c r i b e s a new method t o s y n t h e s i z e a v a r a c t o r f r equency m u l t i p l i e r , w h i c h i s based on q u a s i l i n e a r a n a l y s i s of t h e m u l t i p l i e r as a whole w i t h t h e h e l p of computer o p t i m i z a t i o n , i n s t e a d of d e s i g n i n g t h e i n p u t and o u t p u t matching networks as w e l l a:; i d l e r c i r c u i t s e p a r a t e l y . The o p t i m i z a t i o n and experiment examples i n this; pape r have shown t h a t t h e approach i s v e r y e f f e c t i v e and s u c c e s s f u l . I n t r o d u c t i o n A s w e know, t h e d e s i g n of v a r a c t o r f r equency m u l t i p l i e r s i n e s s e n c e i s a network s y n t h e s i s problem,,once t h e v a r a c t o r dynamic impedance a t i n p u t , o u t p u t and i d l e r f r e q u e n c i e s have been c a l c u l a t e d i n t h e l i s t f o r m [ l ] . I n o r d e r t o e n s u r e h igh conve r s ion e f f i c i e n c y , t h e i n p u t and o u t p u t networks are conjug a t e l y matched t o t h e v a r a c t o r dynamic impedance a t i n p u t and o u t p u t f requenc i e s r e s p e c t i v e l y . Moreover,, t h e i d l e r c i r c u i t i s r e s o n a t e d a t i d l e r f requency t o a l l o w i d l e r energy t o ex t r eme ly d r i v e v a r a c t o r . Of c o u r s e , t h e above mentioned c a l c u l a t i o n s of v a r a c t o r dynamic impedance are based on t h e f o l l o w i n g assumpt i o n s , .The i n p u t and o u t p u t p o s s e s s i d e a l i s o l a t i o n . .The v a r a c t o r c u r r e n t i s c o n s t r a i n e d t o f low o n l y a t t h e i n p u t , o u t p u t and d e s i r e d i d l e frequency., A s a m a t t e r of f a c t , t h e m u l t i p l i e r f i l t e r s do n o t p o s s i b l y p r o v i d e i d e a l open o r s h o r t performances a t co r re spond ing f r e q u e n c i e s and have n o n n e g l i g i b l e rea c t a n c e . On t h e o t h e r hand, because of t h e v a r a c t o r p a r a s i t i c p a r a m e t e r s , t h e i d l e r c i r c u i t , such as a q u a r t e r wavelength open s t u b , i s n o t r e a l l y resonan t a t i d l e r frequency.As a r e s u l t , o t h e r harmonic c u r r e n t s b e s i d e s i n p u t l o u t p u t and i d l e f r equency may occur i n t h e v a r a c t o r . The i n p u t and o u t p u t c i r c u i t s w i l l i n t e r f e r e w i t h each o t h e r . For e x a m p l e , a d j u s t i n g t h e o u t p u t c i r c u i t may change i n p u t impedance of f-requency m u l t i p l i e r o r v a r a c t o r o p e r a t i n g s t a t e . Cons ide r ing t h e s e s i t u a t i o n , t h e m u l t i p l i e r d e s i g n becomes much more complicated. D e s c r i p t i o n of o p t i m i z a t i o n t e c h n i q u e The m u l t i p l i e r a n a l y s i s i s based upon ABCD pa rame te r s of t h e c i r c u i t elements. T h i s i s a s t a n d a r d network a n a l y s i s t e c h n i q u e . The advan tages of ABCD m a t r i x l ies i n t h e ease, i n which cascaded networks may b e r e p r e s e n t e d and a n a l y z e d [ 2 ] . A t y p i c a l b l o c k diagram of v a r a c t o r f r equency m u l t i p l i e r o p e r a t i n g i n shunt mode is shown in Fig.1, Where F i = I n p u t l o w pass f i l t . e r , Fo= Output band pass f i l t e r , N i = I n p u t matching network, No = Output matching network, Nm = I d l e r c i r c u i t , 6 2 9 Ls = lead inductor of varactor, Cp= Packaged capacetances of varactor, R = Ri,Rn,FUn are varactor dynamic resistances at input, output and idler C = Ci,Cn,Cm are varactor dynamic capacitances at input, output and idler Zr = Input impedance of cascaded networks by No and Fo, Z1 = Output impedance of cascaded networks by Fi, Ni, Nm and Cp, Zin = Total input impedance at input frequency f, Zout = Total output impedance at output frequency Nf, Zpp‘ = Equivalent impedance of overall network except for L s , R and C, X = Total reactance of varactor internal loop, which is shown in Fig.2 frequency f , Nf and Mf respictively, frequency f, Nf and Mf respictively, It is obvious that X can be calculated by, 1 X(r’)=2nFLs ~ + Im(Zpp‘) Where Im(2pp’) is reactance of Zpp’ Generally speaking, the requirements for frequency multiplier synthesis 2 nFC can be summarized as follows, (1)Perfect input and output impedance matching, Zin(f)=Rg at input frequency f, Zout(Nf)=RL at output frequency Nf, (2)Good isolation between input and output, 1 1 =O at input frequency f , = O at output frequency Nf , I W f ) I IZ1(Nf) 1 (3)Full resonance of idler circuit, X(Mf)=O at idler frequency Mf, (4)Effective suppression of undesired harmonics. 1 =O at undesired harmonic frequency Kf I X W ) 1 At this point, the optimization synthesis of the frequency multiplier can be formulated as the minimization of a objective function, which is written as F(X1 , X2 , .. . . . . , XJ )=W11 Zin( f) -Rgl +W2 1 Zout (Nf) -RLI +W3 I X(Mf) I 1 1 WP + w4 + w5 + c I Zr(f1 I I Z1(Nf) I IX(Kf) I where F(Xl,X2, ......, Xj) is the objective function, Xl,X2, ......, Xj are element values of the input, output matching networks Ni, No and idler circuit Nm (characteristic impedance or electrical length zl, ....,Lj),which are determined by minimizing the above objective function. Wl,W2, ... Wp are weighting coefficients, which are able to adjust according the relative emphasis on some terms. The constrained element limits are chosen as For electrical length L 10