Microwave bandpass filter
I United States Patent l wt in l 3,875,538 Minet et al. Apr. 1, 1975 l5 MICROWAVE BANDPASS FILTER 3.345.58 l(l/l9h7 Di Piazza a. 333/73 R l7h| Inventors: Roger I. Minet, (1) Residence (&#39;urlay; J an 09MB&#34;. 26 Fri/mm [hammer-James Wv Lawrence Residence (orlay both of Lannion ASA&#39;lS/(IH! litumim&#39;rMarvin Nusshaum 223m EIIIE I L- &#39;lhepault. 2 Rue Allm&#39;m&#39;y. Agent, or l-&#39;irmAhraham A Saffitz till Docteur Roux Pcrros-(iuircc 22700. all of France |22 Filed: Feb. 20. 1974 I ABSTRACT [2| l Appl. No.: 444.140 Microwave filter of strip transmission line structure. It comprises a main rectilinear strip conductor and a plurality ol&#39;open-cndetl strip line stubs all having one 333/73 2635 3 ;l: .f m half wave length at the mid frequency of the filter and Field of searchw 333/73 C 73 S 84 M 73 R parallel-connectetl to the mam strip conductor. lhe 1/84 R connecting POIHIS are regularly spacccl apart along the mam strip conductor and. on each strip line stub they I M References Cited jtculficuvely oflset wlth respect to the mldpomt of UNI&#39;I&#39;H) STATES PATENTS 2.532.003 lZ/WSU (arter 333/73 L 6 Claims. 6 Drawing Figures A it 5/2 (9 A// memo/15 uz mm, l l&#34;- 1 I 7 4208 w 4206 &#34;1 4m; 8/ 1W! 6&#34; MICROWAVE BAN DPASS FILTER The present invention generally concerns microwave filters and more particularly microwave bandpass filters of strip-line structure.  
  Microwave filters of strip-line structure having a plurality of shunt or series quarter wavelength stubs are known in the art. The text book Microwave Filters. Impedance-Matching Networks and Coupling Struclures by George L. MATTHAEI. Leo YOUNG and E. M. J. JONES. Mc GRAW-HILL BOOK COMPANY discloses:  
 at page 595. filters using parallel short-circuited stubs that are a quarter wave long;  
 at page 596, filters using series open-circuited stubs that are a quarter wave long; and  
 at page 599 filters using pairs of parallel short circuited stubs. each stub of a pair being a quarter wave long. In this latter case. the two stubs of a pair form half-wavelength long, short circuited shunt stubs connected at their middle to the connecting line.  
  In all these filters the connecting lines between the stubs are always quarter wavelength connecting lines. It results that the filters are physically of large size, the length of the filter being at least equal to (nA,./4) where n is the number of stubs and the wavelength in the connecting line at the midband frequency of the filter.  
  The principal object of the invention is the provide strip-line microwave filters of compact structure.  
  Another object of the invention is to provide stripline microwave filters in which the length of the con necting lines of the stubs can be predetermined at will and particularly can be taken much shorter than the quarter wavelength.  
  According to the invention, there is provided a microwave bandpass filter having a main strip transmission line and a plurality of open-ended half-wave strip line stubs perpendicular to the main strip line, and forming crosses with the same, spaced apart therebetween by a predetermined distance much smaller than the half-wavelength along said main line and connected in parallel to the main line, the point of connection of the stub to the main line being offset from the mid point of the stubs by predetermined quantities.  
  The invention will now be disclosed in detail in relation with the accompanying drawings in which:  
  FIG. 1a and ll) represent a two crossed cell microwave filter:  
  FIG. 2 represents a three crossed cell microwave filter in which the stubs are spaced by an electric spacing different from a quarter wavelength;  
  FIG. 3 represents a three crossed cell microwave filter with stubs of the same length but not of the same strip width;  
  FIG. 4 represents a three crossed microwave filter of a known type with stubs of the same strip width but not of the same length; and  
 FIG. 5 represents a five crossed cell microwave filter.  
  FIGS. la and lb show a microwave filter with two crossed cells according to the invention and which comprises a main strip transmission line having a metallic strip conductor 1 bonded to dielectric sheets 2 and 3 to the other side of which are bonded metallic ground plates 4 and 5. The two ground plates are electrically interconnected by means not shown in FIGS. la and lb.  
  Each cell of the filter comprises a pair of arms or stubs 6 and 7 for the first cell and 16 and 17 for the second cell, which are located on both sides of the strip transmission line 1 and connected in parallel to the same. Each of these stubs is about a quarter wavelength long and is open-circuited and the two aligned stubs of a pair form a section of strip line which is one halfwavelength long. The two stubs of a pair have not exactly the same length or in other words the strip line sections formed by the stub pairs are not connected exactly at their mid point to the main strip transmission line. The spacing length along said main line of the connection points of the stub pairs is designated by L and the choice of its value will be explained later on.  
  The respective lengths I and of the stubs 6 and 7 are such that:  
 Zsinh ch cosh (s Di where:  
 F denotes frequency,j is M I and y is the characteristic admittance of the stubs, while e is the number defined by equation I) Q 1-r/4ozl is the Q factor of the resonator formed by the cell,  
 a being the real part of the attenuation constant F denotes the resonance frequency of the cell equal e being the relative dielectric constant and c the velocity of light.  
  By assuming that the cells are lossless and in the vicinity of F expression (2) can be reduced to:  
 where (5) Combination of equations (4) and (5) gives:  
  Synthesis ofcrossed cell filters can he made either hy calculating the amplitude-frequenc response of the filter or by using the general synthesis theory of bandpass filters. The first method can he applied to the lilters comprising at most three cells since farther the calculations become inextricahle. Applications of the two methods are given in the following.  
  Let us consider a non-dissipative filter comprising two or three crossed cells separated by sections of connecting strip line. fed at its input terminals h a signal generator and connected at its output terminals to a load. the impedance ofthe generator and load heing re spectively matched to the input and output impedances of the filter. that is to the characteristic impedance of the main strip transmission line. The attenuation A is equal to the ratio of the availahle generator power to the power actually deli\ered to the load; it can he written in the form of &#39;l&#39;schehyscheff polynominal.  
 Two Crossed (ell Filter In the case of a two cell filter. the attenuation is given h the formula:  
 \\herc H is related to the length of the main connecting line section and to the mid frequenc F. ofthe filter h the relationship:  
 0 ZrrL/A,  
 it&#39;ll where l. is the phtsical length of the connecting line section and A. the wavelength at the mid frequenc} F, of the filter.  
 The quantits h of equation (7| is given by:  
 The ripple amplitude in the passhand is:  
 cos ti ll 4 sin-f l l I the resonance frequency drift is:  
 l&#39;.. +ll tlll and the passhand is defined h Al- IV I (it l The passhand is defined h 41 V3 ll+ iz tanlil The ripple amplitude in the pass hand is defined h and the resonance frequency drift is defined by:  
  ln equations l5). lb] and t 18). represents 3 or and 5 represents 6, or 6 Case B k 7 2 9 17/2 \vherefrom cost-l 0 Then the attenuation is given h the formula:  
 The ripple amplitude in the passhand is defined by:  
 R T I t and the resonance frequency drift is defined as previ ously by equation l3] and since cot 6 there is no drift of the resonance frequency The resonance frequency of the filter is the same as the resonance frequency of the cells. In equations and (II v represents y, or v,,, and 6 represents 6,. or e,,,.  
  Let us assume it is desired to design a passhand filter having the following characteristics:  
 tuna MHI 4 MH/ l0 it I n Ripple in the passhand 0.20103 wherel&#39;rom R L04- 7. lirst and Second lisantplc corresponding to Case A.  
  By replacing R h L047 in equation (l7). are ohtains:  
 By replacing Al /F and 0 by their values in equation 1 lhl. one obtains:  
  By replacing I! and v,./e,. by their values in equation (IX). one obtains:  
 Axl  
  D 4000 m 1 h. Hmmu use? Mlt/ As I. 2:  
  \&#39;,,,/e,,,&#39; lip/6, I ZXIUZ? 3854 First example:  
 Equation (23) is satisfied by taking:  
  v,. l 5,. e,,, 00228 Let us select as dielectric material for the dielectric sheets of the strip line the so-cal|ed Rexolite 1422&#34; having a dielectric constant e,.= 2.3. Then equation 3) gives for l.,:  
 II itmun.  
 equation 4) gives:  
  0 I JI,,&#39; 012mm.  
 and equation l3) givei 0&#39; a \aluc of 50 ohms is selected for the impedance of the end ecll stuhs and a thickness of 3 nuns for the dielectric sheet of the strip-line. then: X z titl and the graph of page lb) of the text hook referred to (ill Then equations 13) give:  
 I... l2.08 mm l,.- 12.64 min and the width of the strip does not depend on the cell concerned The filter is thus completely defined and is represented in FIG. 3. Third [Example corresponding to case B By replacing R by 1,047 in equation (19). one ohtatns:  
  By replacing Al /F,- and It h their values in equation (2| l. one obtains:  
  The resonance frequency ofthe cells is the resonance frequency of the filter (2-H As in the first and second examples. equation (24) can he satisfied by making the end cell stuhs and the mid cell stuhs with the same strip lines and taking different 6,. and e or by giving 6.- and e, the same value i.e.. by giving the stuhs the same length and by varying the admittance of the strip line they are made of. Only the first case will he discussed.  
 Consequently let us assume: v)&#39;,. v l  
 &#39;lhen equation (13) gives:  
 I I108 mm 1. llbJ nun I, l2.07 min I,,,. [2.66 nnn The width of the strip-line are u&#39;,. u&#39;,,, 1 Lo min and the spacing between the stuhs is L A,./-t lilo Let us select a priori the electric length of the connecting lines equal to 77/41 which corresponds to a physical length of ./8.  
  It is known that an admittance inverter having a parameter l/sin 0 can be formed by a line section of electric length 6 connecting two identical elements having an admittance cotO. Thus:  
 - sin 1r/4 where J is the parameter of the admittance inverter between the first and the second cells. and so on.  
  The parameters of the admittance inverters are given at page 433 of the cited textbook.  
  I W .h&#39;l&#39;i l where p,- and p are the admittance slope parameters.  
  The admittance inverters at the ends of the filter have a ratio or parameter equal to unity. Thus:  
  Replacing AF. 1),. g,, g by their values in the expression of 1 gives: p. p 2674 Replacing AF, p g g by their values in the expression of J gives: p 2166 The admittance slope parameters are related to the admittance of the stubs by the relationship:  
  (25] Assuming equation (25) allows to determine the values of the e,- from the values of the p One finds:  
  The resonance frequency drift is given by the formula:  
 which give the resonance frequencies of the cells un m: lu F0; 3998.5 MHZ.  
  3998.15 MHZ from which the quarter wavelength 1., and the stub spacing are deduced 0,. ET (M8 mm II II II II II II 5 1 1 1: I258 mm For an impedance of 50 ohms, the width of the strip is taken equal to L6 mm and the thickness of the Rexolite&#34; sheet equal to 2 mm.  
  The filter is then completely defined and is represented in FIG. 5.  
 What we claim is:  
  l. A microwave bandpass filter of strip transmission line structure comprising a main rectilinear strip conductor, a plurality of open-ended strip line stubs all having one-half wave length at the mid frequency of the passband of said filter and parallel-connected to the main strip conductor at connecting points. said connecting points being regularly spaced apart along the main strip conductor and being, on each strip line stub. selectively offset with respect to the midpoint of the stub, and their spacing along said main conductor being much smaller than a quarter wavelength along said main conductor at said mid frequency.  
  2. A microwave bandpass filter of strip transmission line structure comprising a main rectilinear strip conductor having a given width. a plurality of open-ended strip line stubs all having one-half wave length at the mid frequency of the passband ofsaicl filter and formed by a stub strip conductor having the same width as the main strip conductor and parallel-connected to the main strip conductor at connecting points. said connecting points being regularly spaced apart along the main strip conductor and. on each strip line stub. selectively offset with respect to the midpoint of the stub. the distance between the connecting point and the midpoint of a stub being different for each stub. and the spacing of said connecting points along said main conductor being much smaller than a quarter wavelength along said main conductor at said mid frequency.  
  3. A microwave bandpass filter of the strip transmission line structure comprising a main rectilinear strip conductor having a given width. a plurality of openended strip line stubs all having one-halfwave length at the mid frequency of the passband of said filter and formed by stub strip conductors having different widths and parallel-connected to the main strip conductor at connecting points, said connecting points being regularly spaced apart along the main strip conductor and, on each strip line stub. selectively offset with respect to the midpoint of the stub. the distance between the connecting point and the midpoint ofa stub being the same for all the stubs and the spacing of said connecting points along said main conductor being much smaller than a quarter wavelength along said main conductor at said mid frequency.  
  4. A filter as claimed in claim I, in which said spacing is substantially equal to one-eighth of a wavelength along said main conductor.  
  5. A filter as claimed in claim 2, in which said spacing is substantially equal to one-eighth of a wavelength along said main conductor.  
  6. A filter as claimed in claim 3, in which said spacing is substantially equal to one-eighth of a wavelength along said main conductor.  
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