DE2408634C3 - Microwave filters - Google Patents

Description

The invention relates to ribbon line microwave filters and relates to a microwave filter consisting of a main line v. ^ u several open Halbwellcn stubs is the band center frequency, which are arranged at right angles to the main line and, together with these crosses, which are separated, and by a predetermined distance (L) voneinande · connected in parallel with the main line. A spur line is to be understood as the cross piece of a cross consisting of two branches.

Microwave filters of this design, consisting of several quarter-wave stub lines connected in parallel or in series exist are already known. In the textbook »Microwave Filters, Impedance-Matching Networks and Coupling Structures by George L. Ma 11 haei, Leo Young and E. M. J. J ones, McGraw-Hill Book Company, N.Y. 1964, pages 595-599 various Executions described.

In all of these filters, the connecting pieces of the main line are between the stub lines, that is the distances between the stub lines, always a quarter wavelength long, from which it follows that the dimensions of the filters are large because of the length

of the filter is at least equal to ^ ', where η is the

Number of stub lines is and /.,. the wavelength in the propagation medium at the center band frequency of the filter.

The same is true of a coaxial line microwave filter according to US-PS 25 32 993 and in a band line microwave filter according to US-PS 33 45 589 the case. In the former, the stubs are equal to the wavelength, in the latter case equal to a quarter wavelength of the band center frequency; in both cases the connection points of the stub lines are opposite to the main line the center of the stitch lines offset by specified amounts, d. i.e., the branches of a stitch line are different length.

The object of the invention is to provide microwave filters of the type mentioned at the beginning with small external dimensions to obtain, in which in particular the length of the connecting lines of the stub lines

can be freely selected and can preferably be much less than a quarter wavelength.

This object is achieved according to the invention in such a way that the distance (L) is much smaller than a quarter wavelength and

ίο the amounts (>) in relation to this distance (L) and the specified bandwidth of the pass band are selected. In this way, the natural frequencies the cells of the filter, which are to be regarded as resonators, differ significantly from the Mitlen-

is to adjust the frequency of the filter as a whole.

The distance (f) is preferably essentially one eighth of the wavelength of the center frequency of the pass band.

The invention is illustrated below with reference to

jo drawing explained in more detail; in this show

Fig. La and Fig. Ib one consisting of two cells Microwave filters,

F i g. 2 a microwave filter consisting of three cells, with aem the stub lines through one

■ s electrical distance are separated from each other, the deviates from .7 / 2,

F i g. 3 a three-cell microwave filter, whose stub lines have the same length but consist of strips of different widths,

4 shows a microwave filter made up of five cells.
FIGS. 1 a and 1b show a microwave filter according to the invention with two cells, which has a strip-shaped transmission line with one meter.

is metallic strip conductor 1 comprises, which is connected to dielectric Foils 2 and 3 is bound, on the other side of which metallic grounding straps 4 and 5 are attached. The two ground straps are electrically connected to one another (not shown).

Each cell of the filter comprises a stub with two branches 6 and 7 for the first cell and 16 and 17 for the second cell, which is arranged on both sides of the transmission line and connected in parallel with the latter are. Each of these branches of a branch line is about a quarter wavelength long and not short-circuited, and the two aligned branches of a pair form a piece of stripline which is about half a wavelength long. The two branches of a pair are not exactly the same Length, d. H. a stitch line is not connected to the transmission line exactly in its center.

The lengths /, or I _{2 of} the two branches 6 and 6 are rooted so that

/ 2 = Od H),

fio where f is a coffin that is much smaller than funs. 2 and 3 show a microwave filter according to the invention with three cross cells. Let the parameters of the outer cells be / ", L ₂ , Y _e ,> _e unc 'those of the middle cells / _ml , / _m2 , Y _n ,> _m .

fts The following can be derived from the teaching theory Derive equations (2) to (6):

The distributed admittance Y [F) of a cell divided by the characteristic admittance of the transmission

management, d. H. the relative conductance of the cell, is given a more descriptive method of calculating the Fredurch quenzganges the amplitude leads in the filter area

too confusing even with three-cell filters

- ^s i "h '/'. borrowed calculations, - The polynomial H is a func-

cosh 'Λ + cnsh (''/') s tion of Y _e (equation (6a)) with coefficients that are a

Are functions of k and ti. It is
where F denotes the frequency,

.τ. F ^k - γ '

- "(1 Ml IO

and (8)

ν the characteristic admiltance of the Slichleitiinu,

.τ " ti = 2.tL// _y ,

15 where )., The wavelength at the center frequency of the

is the quality factor of the Reso filter formed by the cell.

nators, \ the active value of the damping constant, The mathematical treatment of the Tchebyscheff and F _{0 is} the resonance frequency of the cell, the given polynomial leads to two physically meaningful solutions:

_c 20th

μ, =. (3) FaIlA: k = 2; cos βφ O (Fig. 2, 3).

⁴ * »I '' Case B: k φ 2; cos ti = O.

where f _{r is} the relative dielectric constant and in case B - to deal with this case first -

c is the speed of light. 25 will

Assume that the cells are lossless and .7

that in the vicinity of F _n the expression (2) '~ ~ ϊ ⁺ " ⁿ

lets reduce to

FF ^and

Y (F) = AjQ ₁ , "- y. (4) .10

Ml f ^ c_ ι. ^ r

where ^

Q = I / t ¹ ISl

"'' 'i.e. the distances between the stub lines on the main

.15 lines are odd integer multiples of a

is. this results in the combination of equation (4) quarter wavelength, as in the case of the

imd (5) forms according to the American ones mentioned at the beginning

r · _ ρ γ patent specifications is the case.

YiF) = 4; , / "·%. 16)

^{f »yr} 40 Case A

From (6) follows for the normalized admittance and door k = 2, ti φ .τ / 2, from which it follows that cos ti ψ 0. the characteristic admittance of the main line “.. .... _,.

of the three-cell filter I-.lter with three, crossed cells

_t . _ _{2 r} 45 The lengths of the branches of the branch lines of the end

-, · - 4 / V ₁ . (/ · - / - ,, V-Ti ₁ , »· ■“, (6a) cells should be denoted by / ,,, and l _el and the

Y _m = 4j y _m {F- F ") / nt ² _m F ₀ . Lengths of the branches of the branch line of the central cell with

l _ml and l _m2 . These lengths are then linked with / ₀ through the fin such a filter is equivalent to a quadrupole linked to the following equations:

₅ o / "= ui-a (i3)

Input V, \ Y _m \ Y ₁

Output, l _e2 = Ό (l + '' Λ

I __ I / I ν

55 As the electrical length of the connector

where ti is the electrical length of the two cells vcr- adjacent stub lines ti Φ .τ / 2

binding main is; the mechanical length L whose distances are less than >. _{cli can be} chosen,

results from this (see equation (8)). The values ι The attenuation A is then given by

and ti are to be optimized. equation

To solve this problem, the considerations fto _h .

based on the theory of the Tchcbyschcff filter and \ -_ \ 4. ^tos / ' (4 ^{,, · 1} - 1 m) ¹ , (14)

examine its attenuation A, which can be found in general

my form can be written as,.

whereby

I - I ■) ·. II ¹ ■ Π) ^(1S i3 /> 13 Γ. I- -μ, ν Ί

4 '"=, do W =' tan H 4,."'-Cot M.

2 2 L mi - "2 J

where H is a Tchcbyscheffschcs polynomial. The (15)

The passage area ht is defined by

IFF ⁴ 1161

The wavy wedge in the passage area is defined by

27 sin- <-> ''

and the ResDiian / frequen / deviation If ·, / ,, I is defined by

/ "

7, - ent ()

MXl

In the (jequations 115). (16) and (18) ν stands for: <> the values y ,. or y _m and ■ for the values. · ,. or .- ", the end or middle / rush.

Numerical example

It is said to be a continuous band filter with the following - < Characteristics are constructed:

F ₁ = 4 (XH) MHz.
I, = 4 MHz.
IFF, = Hl '■

The ripple in the pass band should be 0.2OdB, so that

R = 1,047.

If you insert the value of 1.047 for R in equation (17), you get

cos ² (-) = 0.53. <-> = 43 25 '.

v-

If one substitutes the corresponding values for IF F, and <-> in equation (16). so you get

\ ,. Ί = 1927.

If one sets in equation (18) for (-) and V ₁ . ² . the corresponding values. so you get

^r » , - ;, (HH, 433 = ³⁹⁹⁸ - ²⁷ ^ H,
SinceA: = 2.
y _m > ² "= 2>, - '* = 2-1927 = 3854.

(23)

(ileichung | X | returns
i)

2 -,

and equation (13) gives

6.1 2 mm

'■ • ι =' mi = 12.0X mm. / ,, - 1, " ₂ - 12.64 mm.

If a value of / ,, = 50 Ohm is chosen for the impedance of the end / ellen stub lines and a thickness of 2 mm for the dielectric film of the strip line. then Z _n <, * 80. and the diagram on page 169 of the textbook mentioned in the introduction provides for the relationship

Width of the strip »v

a value which is 0.X for the 1 nd / ellen stub lines and the value 2 for the central cell stub lines. Thus »,, = 1.6 mm and w _m = 4 mm. This means that the filter is completely defined and looks like in! · 'I g. 2 off.

Second example (I ig. 3)
Same! -: vj 123) is fulfilled if one chooses

y, - y _n = ι.

. · ,. = 0.0228.
", = 0.0161.

Then equation (13) gives

/,., = 12.08 mm.

/ ,. _: = 12.64 mm.

L ₁ = 12.16 mm.

i "i = 12.56 mm.

and the width of the strip does not depend on the cell in question. so that

W ₁ . = n _m = 1.6 mm

is. As a result, the filter is completely defined and looks like in FIG. 3.

The two examples were chosen so that the length L of the connecting piece between two stub lines or cells is / _fs : this length L can also be used within the scope of the invention for other fractions of >. _ci lie, and the amounts ι Air the individual stitch lines can be chosen differently, z. B. ■. _e ψ> _m (as in the case of FIG. 3) and also V ₁ , Φ Y _m . provided only the condition

k =

First example (Fig. 2)
Equation (23) is fulfilled if one chooses:

: _r =, "= 0.0228

For the dielectric films of the stripline, a dielectric material is selected whose dielectric constant ι has a value of 2.3. Then equation (3) yields for I _n : <*

is satisfied.

=! 2.36 mm

Filter made up of five cross cells (Fig. 4)

Assume that a passband filter is to be constructed which has the same characteristics as the already constructed filter, however consists of five cells instead of three cells.

The table on page 100 of the aforementioned Textbook contains the values of the reactive elements for filters of the type TchebyseheiT with five elements for different, in dB at Eecebenc toilet wedges.

1339.4 Qu, K) " ⁴ , O t- I
2674 ■ = 3.73 , 0-. I.
2 · + I
2166 IO \ 1
ϊ ■ = 4.62

The admittance rise parameters are found there with the

The admittance of the stub lines is linked by the relationship Rn = Ra = I. Ri = R ₅ = 1.3394

g ₂ = g ₄ = 1.3370. g, = 2.1660.

s ρ, = 2ν ^,). (25)

The electrical length of the connectors of the _{Selzt mun}

Hauptleit-.cig is a priori set equal to.-R / 4, and
this corresponds to a physical length of;. _r8 , ie> ί = Y ₁ = Y ₃ = I.

⁽ 'hi = ft> 2.j = Hu = ^ 4.5 = .7.4. ίο with the help of equation (25) the values

von) j from the values of p .

As is well known, an admittance reverser can be obtained with Man

a parameter l / sin · ² ft »produce from a Lei- _ qqtio

the electrical length ft », the two '' ~ η 0154 '

identical elements with the admittance cot ft »ver is! ² I 00171

binds. Hence 'i - · ■

The resonance migration is given by the ·> ii ji ii ' -1 C, \ firhnna

20 F ₁ - F ₀ · COt

where J _{1 2 is} the parameter of the admittance reverser f

between the first and second cells, etc. The parameters of the admittance reverser are up Page 433 of the textbook mentioned. ■. '

V KJ Win f _t - _Fii2

where Pj and pj. _yf the admittance rise parameters

are. The admittance reversers at the ends of the

Filters have a ratio or parameter, ^. ~ ^ 0.3

that is equal to one. From this it follows F.

P ₁ which give the resonance frequencies of the cells

RoR ₁ - ' ⁵ F _0. , = F ₀ . ₂ = F ₀ . ₄ = F ₀₅ = 3998.5 MHz,

F ₀₃ = 3998.15MHz,

- f \. Γα ₌ ι from which the quarter wavelength / "and the stitch

V F <J R5Rh line spacing can be derived

40
and that results in ^ ₌ ^c .. _ 12.37 mm.

P ₁ = Ps = ^F '* " ^g l = ^ll * ³³⁹⁴ ₌ , 3394 ^4f " ^[ ' ^r

1 1 / ■) ίο ₍₎

45 L = ^c - = 6.18 mm.

If we put in the expression for Jf, 2 .τ F ₁ . \> _r

ji _ yP ~ P \ Pi _ η The lengths of the stub lines are determined by the

¹ 'F ₁ ² gjg, * "values of I ₀ and derived from the f-values.

50 One finds thus

for IFiF ₁ . p ,. g, and g ₂ the corresponding values. _. - η 10

a, one obtains, ^u - ¹ · ⁵ --'-- '

"-" _ 2674 'υ = Ί * = 12.18mm,

P ₂ -Pi- 2674. _{t = / =}

r- ·· ■ r- 1 iL- Ii 1 = 12.16 mm,

For I F. p ₂ . g ₂ and g ₃ become be. , £ ₌

, 2 _ ! f P2P3 _ -> For an impedance of 50 ohms, the width becomes

² ■■ * ~ F ² g ₂ g ₃ "" ~ of the strip is set equal to 1.6 mm and the thickness of the

60 foil equals 2 mm.

insert the appropriate values; This means that the filter is fully defined and can be seen

then p ₃ = 2166. as in FIG. 4 off.

For this purpose 2 sheets of drawings

Claims (2)

Claims; 1. Microwave filter, which consists of a main line and several open half-wave Siichlinien for the band center frequency, which are arranged at right angles to the main line and together with this form crosses that are separated by a predetermined distance (L) and connected in parallel with the main line The junction between the main line and the branch line is offset by specified amounts (>) from the center point of the branch line, characterized in that the distance (L) is significantly smaller than a quarter wavelength and the amounts (r) in relation to this distance ( L) and the predetermined bandwidth of the passband are selected. 2. Mikroweüeafilter according to claim I, characterized in that the distance (L) is substantially is one eighth of the wavelength of the center frequency of the pass band.