DE2408634A1 - MICROWAVE FILTER - Google Patents

Description

Patentee "microwave filter"

Registrant: ROGER MINET, 60 Residence Corlay, 22300 LANNION Jean Debeau, 26 Residence Corlay, 22300 LANNION Ernst Louis TfIEPAULT, 2 rue du Docteur Roux, 22700 PERROS-GUIIiEC (France)

Microwave filters

This invention relates generally to microwave filters and stripline microwave filters in particular.

Microwave filters in stripline design, consisting of several quarter-wave stub lines connected in parallel or in series exist are already known to the person skilled in the art. In the textbook "Microwave Filters, Impedance-Matching Networks and Coupling Structures "by George L. Matthaei, Leo Young, and E.M. J. Jones, McGraw-Hill Book Company described:

- on page 595 filters consisting of parallel, short-circuited There are stub lines with a length of a quarter wavelength,

509834/0527

ipl.-lng. G. Schliebs

Dipl.-Ing,

Patent attorney

- on page 596 filters that are made in series, not short-circuited stubs with a length of a quarter wavelength exist, and

- on page 599 Filters that consist of pairs of parallel, short-circuited stub lines, with each stub line of a pair is a quarter wavelength long.

Ιίη the last-mentioned case, the two stub lines form one Pair of half a wavelength long, parallel, short-circuited stub lines, which are connected in their middle to the connecting line.

In all of these filters, the connecting lines are between the stub lines always have quarter-wavelength connecting lines, from which it follows that the dimensions of the filter

are large, since the length of the filter is at least equal to c

where η is the number of stubs and X is the

Wavelength in the medium of propagation at band center frequency of the filter.

The main object of this invention is to provide stripline microwave filters with small external dimensions.

Another object of the invention is to provide stripline microwave filters in which the length of the connecting lines of the stub lines can be freely selected and in particular can be less than a quarter wavelength.

According to the invention, a microwave filter is obtained from a strip main transmission line and multiple, open ended, half-wave ribbon stub lines which are at right angles are arranged to the main strip line and together with

509834/0527

Dipl.-Ing. G. Sdiliebs

Patent attorney

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the latter form crosses separated by a predetermined distance and connected in parallel with the main line are connected, the connection point between the main line and the branch line opposite the center point the stub lines are offset by specified amounts.

The invention will now be explained in more detail with reference to the accompanying drawings. Show:

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

2 shows a microwave filter consisting of three crossed cells, in which the stub lines are separated from one another by an electrical distance which deviates from π / 2; 3 shows a microwave filter consisting of three crossed cells, the stub lines of which have the same length but consist of strips of different widths; FIG. K shows a three-crossed microwave filter, the stub lines of which have the same strip width but not the same length and
5 shows a microwave filter composed of five crossed cells.

1a and 1b show a microwave filter according to the invention with two crossed cells, which comprises a main strip transmission line with a metallic strip conductor 1 which is bonded to dielectric foils 2 and 3, on the other side of which metallic grounding plates k and 5 are attached. The two grounding plates are electrically connected to one another by means not shown in FIG. 1 a and FIG. 1 b.

B09834 / 0527

Dipl.-Ing. G. Sdiliebs

Patent attorney

Each cell of the filter includes two arms or stubs 6 and 7 for the first cell and 16 and 17 for the second cell, arranged on either side of the strip transmission line and are connected in parallel with the letiziren. Every this stub is about a quarter wavelength long and not short-circuited, and the two are aligned with each other A pair of stubs represent a piece of stripline that is about half a wavelength long. the two stub lines of a pair do not have exactly the same length, i.e. the strip line pieces formed by the stub pipe pairs are not connected to the strip main transmission line exactly in the middle.

The lengths JL and £ _ of the stub lines 6 and 7 are like this chosen that

I ₁ - 4 ₀ (ι- ε)

(D

H ε)

where £ is a coefficient much less than one.

According to the theory of radio frequency transmission lines is the distributed admittance of the cell divided by the characteristic admittance of the strip main transmission line, i.e. the relative conductance of cell -j given by:

Y (F) β 2 sh ^

ch (9

- F denotes the frequency,

the figure of merit of that formed by the cell

^ n ⁼ "'Tl

ό ία Jt ₀
Resonators is, $ 09834/0627

Dipl.-Ing. G. Schliebs

Patent attorney

- α is the effective value of the data type constant,

- Fq is the resonance frequency of the cell given by

F ₀ = p = - (3)

where S is the relative dielectric constant and c is the Speed of Light.

It is assumed that the cells are lossless and that in the vicinity of F_ the expression (2) can be reduced to

FF y (F) _S JD «4 jQ _G J = T- ^ (4)

where Q _Q β 1 / π £ ² (5)

then the combination of equations (4) and (5) gives ί

y = 4 (F - F ₀ ) AC ² F ₀ (6)

For the synthesis of crossed line filters one can either calculate the "frequency response of the amplitude" or the general one Apply the theory of synthesis of passband filters.

The former method can be applied to filters with a maximum of three cells, since the calculations are inextricable are. Applications of the two methods are described below.

Let us consider a lossless filter made up of two or three cells crossed over by pieces of strip connection line are separated from each other, which is fed by a signal generator at its input terminals and is connected to a consumer at its output terminals, the impedance of the generator and consumer to the Input and output impedance of the filter, i.e. to the

509834/0527

Dipl.-Ing. G. Sdiliebs

Patent attorney

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characteristic impedance of the main tire line, are adjusted. The attenuation A is given by the ratio between the available generator line and the actual one Given the power delivered to the consumer and can be expressed by a Chebyshev polynomial.

Two cells crossed filter

In the case of a two-cell filter, the attenuation is given by the equation

. _Ί 1 cos θ Π _ο , b tan w> _Ί ι tu _fn \

A & Λ. + Ί £ g— I d K je / -JI l / J

sin θ

where θ is the length of the length of the main trunk line in electrical Degrees at the center frequency F of the filter, which is given by

O = 2πί / λ (8)

where L is the length dimension of the connecting line piece

and λ is the wavelength at the center frequency F of the filter,
cc

The quantity b in equation (7) is given by

4 (F - F)

z ~ = b + cot 0 (9)

π ε ² F ₀

The ripple amplitude in the pass band is

_{R =}

sin θ

The frequency drift is

and the passband is defined by

42 2 "Ti

F ^s 1
c G

609834 / 0'5 27

Dipl.-Ing. G. Sdiliebs

Patent attorney

Three cells crossed filter

The lengths of the stub lines of the end cells should start with Jt _

el

and £ ρ denote the lengths of the stub lines the middle cell with j? and G, . These lengths are then with jL. linked by the following equations:

kl = fo ⁽¹ - ^C e>

■ * ^ G 2 ^^^ j G

(13)

Q = 9 (1 - Γ)
* -ml * Ό m

i = 9. (1 + 6)

According to the words that the distance between the stubs has in electrical degrees and according to the ratio k between the admittance of the middle cell and the admittance of the end cells, a distinction must be made between two cases:

Case A

k = 2 9 £ π / 2 from which it follows that cos 9 ^ 0

The damping A is then given by the equation

■ J O 1 <. \ ^

A ₌ χ

97 ρ

^{i2 /} sin 9

\ jj - 2 tan 9 s - £ tan 9 4 - = - = ^ ~ 2 ~ ^{cot β} (! 5)

- ^{2 2} L ° J

The pass band is defined by

(16)

⁺ ^ ^{tan θ}

The ripple amplitude in the pass area is defined by

S0983A / 0527

Dipl.-Ing. G. Schliebs

Patent attorney

R.I + (I ₇ )

27 sin θ

and the resonance frequency drift is defined by

'P ■ P _n ■ + 1 (18)

C 0.

4 y

In equations (15), (16) and (Iu), y represents y or y and £ represents £ or £. ^J β mem

Case B

cos k ρ 2 θ = π / 2 from which it follows that G = O

The damping is then given by the equation

Α = 1 ₊ % ^ ί ( _4ω 3. ₃ *) ² U ₉ )

ΤΙ / 2 4 (F - F) 2Jt 0__ __jr ₍₂₀₎

The transmission range is given by

^V 2 - k ^'y
The ripple amplitude in the pass band is defined by

⁽²²⁾

and the resonance frequency drift is defined by equation (18) as before. Since cot 0 = 0 in this case, there is no migration of the resonance frequency and the resonance frequency of the filter is equal to the resonance frequency of the cells. In equations (20) and (21), £ represents or £ "and yy or y.

Let us assume that a passband filter should be constructed with the following characteristics:

509834/052 7

Dipl.-Ing. G. Schliebs

Patent attorney

F = 4000 MHz c

^ F = 4 MHz AF / P = 10 ~ ³

The ripple in the pass band is 0.20 dB, so that R

First and second example for case A

If one substitutes the value 1.047 for R in equation (17), one obtains

θ = 0.53 © = 43 ° 25 ^!

If one sets the corresponding values for & F / F and θ in equation (l6) Values, that's how you get

2 If one substitutes the corresponding values for θ and y / ζ in equation (lo), one obtains

ρ - ^t00 °, - 3998 * 27 MHz

¹ Q 1 + 0.000433 YYY ⁰ '*'

Since k = 2

^y n / ^£ m = ² y _e / He = ^{2 X 1927} = ³ * ^{5k (23)}

First example:

Equation (23) is satisfied if

V = I y =

° e m

c = £ s 0.0228 ^c e ^c m '

We want to choose the so-called "Rexolite 1422" as the dielectric material for the dielectric foils of the stripline, whose dielectric constant £ has a value of 2.3. Then equation (3) yields for jL _Q :

509834/0527

Dipl.-Ing. G. Sdiliebs

Patent attorney

4 F.

= 12.36 mm

Equation (S) yields

L =

27C

and equation (13) gives

= ^{12 '08 mn}

= ¹² x ⁶⁴

If a V7er t of Z_ = 50 ohms is selected for the impedance of the end cell stub lines and a thickness of 2 now for the dielectric film of the stripline, then Z _n ~ vE ^ 80

and the diagram on page 169 of the one mentioned in the introduction

Width of the strip w

Textbook provides for the relationship

Thickness of the dielectric sheet

a value which is 0.8 for the end cell stub lines and a value of 2 for the middle cell stub lines.

Thus, VT = 1.6 mm and xv = 4 mm.

e ^f m

As a result, the filter is completely defined and looks like in FIG. 2.

Second example

Equation (23) is satisfied if

ς = 0.0228 £ ₌ = 0.0l6l

Then equation (13) gives:

12.08 mm 12.64 mm mm

^L e2

ImI - ^{12 '16} _{£ m2} = 12.56 mm

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

509834/0527

Dipl.-Ing. G. Sdiliebs

Patent attorney

vr = w = 1 * 6 mm a '

Thereby the filter is completely defined and looks like in Fig. 3

Third example for case B

If one substitutes the value 1.047 for -R in equation (I9), one obtains man

k = 0.939

If one sets the corresponding for AF / F and k in equation (21) Values, so you get

y _e / £ I = 192ΰ

The resonance frequency of the cells is the resonance frequency of the filter

F = F 0 c

Since 3c = 0.939, one gets y / C ^ = 0.939 χ y / € ^ = 0.939 χ 1928 = 1810 (24)

111 111 CC

As in the first and second examples, equation (24) can be satisfied by using the end cell stubs and the center cell stubs from the same striplines and making ε and £ different, or by making em

£ and £ gives the same value, i.e. by connecting the stub lines are the same lengths and the admittance of the striplines that make them up varies. Below only the the former case will be treated.

Accordingly, it is assumed:

^ e = ^ m = ^X "£ s 0.0228 £ _m = 0.0235

509834/0527

Dipl.-Ing. G. Schliebs

Patent attorney

Then equation (13) gives
I .. = 12.03 mm

JL ₂ = 12.64

R.A.M

1 _ml β 12.07 mm
i _m2 = 12.65 mm

The widths of the stripline are

w = w = 1.6 mm
em '

and the distance between the stub lines is L = A. / 4

= 12.36 mm

So that the filter is completely defined and looks like in Fig. ¹ I.

Five cells crossed filter

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

The table on page 100 of the aforementioned textbook contains the values of the reactive elements for filters of the Chebyshev type with five elements for different, in dB specified ripples. You can find there:

^S 0 ^{= S} 6 ^{= X} S ₁ = S ₅ = Ii 3394

S ₂ = g ₄ = 1.3370 g ₃ = 2.1660

The electrical length of the connecting lines should be defined a priori as Tl / k , and this corresponds to a physical length of λ _ο / 8, ie O ₁ ^ ₂ = ^e 2.3 ^{= Θ} 3.4 ^{= 6} 4 5 ^{= π} / ^Ζ * · As is well known, an admittance reverser with a parameter l / sin θ can be produced from a piece of line with the

509834/0527

Dipl.-Ing. 6. Closes

Patent attorney

• 43.

electrical length θ, which is two identical elements with the Admittance cot 6 connects. So is

2 _ 2 _ 2 _, 2 1 _ ρ

^J 1.2 - ^J 2.3 ~ 3.4 "4.5 ~" ~ 2 TT "-

⁵ '^''sm π / 4

where J _{1 is} the parameter of the admittance reverser between the χ, δ

first and second cells, etc. is.

The parameters of the admittance reverser are on page of the textbook mentioned.

^ ^Ρ 1 ^Ρ · »

where p. and P ·. which are admittance rise parameters. The admittance inverters at the ends of the filter have a ratio or parameter that is equal to one is. It follows:

5.6 = i ^; - gg

and that results

_π ^Λ - _n - ^g ° ^gl - 3- 3c 1.3394 _ ^p l - ^P 5 - ^ F ^ - ₁₀ -3 -! 339.4

2 If one puts in the expression for J _{1 o}

2 ^P 1 ^P 2 g

for ^ F, p-, g ₁ and g _o , one obtains the corresponding values P ₂ = Pz ₁ = 2674.

For ^ F, P ₂ , g and g_ become at

2.3 g ₂ g ₃

insert the appropriate values; one then obtains p_ a 2166.

50 9834/0527

2408834

Dipl.-Ing. G. Schliebs

Patent attorney

The admittance rise parameters are related to the aiimittance of the Branch lines linked by the relationship:

P = 2 y./nC ² . (25)

3 3 3

If one sets - y, = y "= y" = 1

with the help of equation (25) one can find the values of £. from the values of ρ. to calculate.

You get

ε _Ί - o, o2i8

ε ₃ = o, oi7i

The resonance migration is given by the equation:

F - F_. cot θ. _Ί . + cot θ. .,., c 0, J _ 3-1, J 3.3 + 1

F "2 y. 0.
c J «j

F-F,

c 0 »l _ 0 + 1 _ ο _{73 10} " ⁴
F "2x1339.4"^J>'- *

^F c- ^F 0.2 1 + 1 _{= 3t73 10} -4

c 0.3 _ itl _ a
F "* 2x2166"'

which give the resonance frequencies of the cells

^F 0, l = ^F 0.2 = ^Ρ 0, /, = ^F 0.5

^F 0.3 ^{= 3} " ^{8 '15 miz}

from which the quarter wavelength jL · and the stub spacing can be derived:

0 = ? -: = 12.37 mm

^k fc
θ

L _ s 6.18 mm

50 9834/0527

2403634

Dipl.-Ing. G. Schlieb *

Patent attorney

_{Ί Ί} = Jt _{1 r} t = 12.10 mm

The lengths of the stub lines are derived from the fourths of JL · and from the C values'. One thus finds:

\, XX,

H ₂ ± - Q * or = 12.64 mm

^ l 2 ⁼ ^ l k ^{= 12} J ¹ ^ ^mm

Ln ο - in;, = 12.56 mm

£ _Ί "= 12.16 mm

jt _o - 12.58 mm

For an "impedance" of 50 ohms, the width of the strip becomes set equal to 1.6 mm and the thickness of the "Rexolite" film equal to 2 mm «

As a result, the filter is completely defined and looks as in FIG. 5 off.

509 8 3 4/0527

Claims (1)

Dipl.-Ing. G. Schliebs Patent attorney PATE NTAN'S PRICE Microwave filter, characterized in that it consists from a strip main transmission line and several, open-ended half-wave ribbon stub lines arranged at right angles to the main strip line and together with the latter form crosses which are separated from each other by a predetermined distance itnd in parallel with the main line are connected, the junction between the main line and the branch line opposite the midpoint the stub lines are offset by specified amounts. 609834/0527 Blank page