Attenuation in 3 cm rectangular cross sectioned waveguides

Department of Electrical Engineering

Attenuation in 3 em rectangular cross sectioned waveguides

EEA-34-1968 M. ~lasbalg.•

,

Term report made in the group EEA. headed by Prof.dr. H. Groendijk. Coach: Ir. W. Versnel.

COlTENTS

page 1

2 :5-13

dies. att. factor ,

on V.S.W.R.

&

att. 4-5 5-9

9-1'

Insertion L08ses

Scattering ooeff1oient method SWDIIlary Prefaoe

§

I. Theoretioal Diecuaaion 1.1. Theoretioal value of 1.2 Refleotion influenoe 1.3

1.4

§lI.Practical Discussion

11.1 Attenuation in copper bronze wgd.

11.2 Attenuation as function of short

circuit variation

II.' Scattering coefficient measuring

and attenuation calculation Discu,sion and conclusion

Bibliography 14-24 14-17 18-21 21-24 25-26 27

- 1

-SUMMARY .

Several methods of attenuation measuring on two reotangular cross-sectioned waveguides 3x22.86x500mm in size are described in this report.

These methods- are all based on the measuring of the voltace standing wave ratio (V.S.W.R) and on the plaoement of the

t

minimum points and the 3dB pointe around them. The generaly applied system of varying a short oircuit has been used for finding the variation of attenuation a8 a function of

the short c~rcuit placement.

The scattering coefficient method has been carried out by

means of a computer program. Moreover it is shown that the substitution method of attenuation measuring can not be

used for such low attenuations as found in the above mentioned waveguides.

The importance of plating and construction qualities appears I

from the attenuation measuring results for a number of producing methods of guides.

2

-PREFACE

The task of this stage was to measure the attenuation factor (due to dissipation) of two narrowed waveguides

3x22.86x500mm in size. The standard sizes of a rectangular waveguide are lO.16x22.86mm.

Both waweguides were produced in the workshop of the

,Eindhoven Universi~y of Technology. Every,guide was produced in ~wo parts ~ cover and ba8~. The two parts were plated separately and then mounted with screws. One of the parts was once more plated after having been mounted •. The plating

process was carried out with pure silver. Each layer had a thikness of about 8p.

Several methods of measuring the attenuation factor were used and will be given in this report in detail.

The attenuation·factor of the two gUides was expeced to be

~bout ten times higher than the measured factor.

This expectation was based on the supposition that the

measurement had been carried out with a similar wave guide, the result of which was'realy a 10 fold difference.

This waveguide was made of copper and bronze (3x22.86x20Omm in Size). The construction of the guide was bad from a

microwave point of

v~w;

this will be discussed further in this report.

The narrowed wavegUide has the characteristic of a good

bandwidth matching component, and is used in noise generators as for ex~ple in double cathode tubes.

The letter "B" written near formulae, is a symbol letter for Bibliography. The index for the bibliography can be found at the end of this report.

:3

-§

I.'

THEORETICAL DISCUSSION

1.1. The theoretical value of the attenuation factor due to di8Sipation.

The attenuation factor neopers/meter due to dis8ipatio~

in waveguide-walls for a TEIO (m=l D=~mode in a reotansu1ar

waveguide of width a meters (associated model index m) and height b meters (associated model index n) is:

•• •• • •• ••••

R_a~J~f~/~' surface r~1stivit1 of waveguide walls in oha.

,f wave frequency in Hertz

~ permeability in henrys/meter ,

t conductivity of waveguide walls in IIIbQ,.~t.r

a length of the rec tangular croS8-seQt1'o'n:'ji~a.tars

b wid th " " n i t " I t "

'7.

=

/JA-/E.

i =120lY' intrinsic impedance of free spsoe

.m}-'

real part of the relative die1eotr1Q o~n.~ani

of tpe material filling the waveguide

wavelength in free space (vacuum) in ••~.r8

cut-off wavelength in a TE₁₀ mode wave ii),mre.

The calculation: .

for f.8.8895·109Hrz (measured wi th frequency meter mod.X5,2hp)

H_s for

silve~

2.52'.10-7 f ohms ••••••••••.•.

:e(2}p_289

Rs for copper 2.61-.10-7 f ohms • • • • • • • •• • • • • B

fal,'"

289

~(Ag)=~(CU)~4r·10-7Henry/meter

b=3·10-3meter' a=22.86·10-:3meter

\=3-10S/S.8895·10 9=3. 374·10-2meter

~,=4.

572-1O-2.eter

~r(Ag)=35.16'10-3nep~er/met~r

4(CU)=36.42'lO-3nep,er/meter

4

-l

1.2. Refleotion influence on the VSWR and attenuation measuring It can be seen from the following figure and evaluation that

the attenuation measuring by means of measuring the voltage

standing wawe ratio (VSWR) yields an attenuation factor due to

dissipation and reflection. In this case the only point or

interest here is the dissipation attenuation factor.

I I I I I I I I I • I I I I 1--1--I I ' I I I I I--J,l. ~I I I ~.---J.

..

--l' I I " I I 1""'1..

t---4 - - - --"

~rl----Jb

- - - -

--11

If y+ ( 0 )

=

V~(O) P.·-i

,;-:'

hexp.(jwt) incident wave seen at point 1 == ()

reflected wave from point l=li ' seen at point 1=0 reflection coefficient at point i

1. j waveguide length between points i and j

1, ,

then according to the above figure the following equations eXist:

1. waveguide 0-1 without 10S8 v+(il)=A.exp~(wt-Sll) V-(ll)=Af~xp.j(wt-Bll) Vl(O)=Ap~xp.j(wt-2Bll) 2. waveguide 1-2 without 10S8 + -V (1 2)=Aoexp.j(wt-SI 2) .V (12)=A~exp.j(wt-S12) Y2(O)=A~exp.j(wt-2aI2) .

3. waveguide 2-3 with an attenuation factor~

V+(13):Aoexp.j(wt-SI

3) exp.(- 123 ); V-(13)=Af3exp.j(wt-Sl,).exp~2')

5

-4. waveguide 3-4 without 1088

V+(14)=A.exp.j(wt-a14i·exp.(-~123)

.V-(14)=Af4exp.j(wt-a14)·exp.(-~123) V4(O)=Af4exp.j(wt-2G14)·exp.(-2~123) 5. waveguide 4-5 without 10S8 V+(15)=A·exp.j(wt-a15)·exp.(~123) V-(15)=Af5exp.j(wt-a15)·exp.(-~123) V5(O)=Af5exp.j(wt-2a15)·exp.(-2~123) The VSWR

:-It can be seen from this evaluation that when the attenuation

factor is calculated from a VSWR measurement, the calculation

result gives the attenuation factor due to dissipation and reflection in one term. Hence this measuring method will not lead to our target:- separating the two attenuation factors.

I

1.3. Insertion 10sse8. 13[3"J

1.3.a. The definition

The dissipation and reflection loss in&Network is caused by the "insertion loss of the network".

This insertion loss is defined as the ratio of the maximum

available power (PI) delivered

frnr..

#..e

~/ wi thout a network

inserted, and the power (P2) delivered to

a

_~dload

when a network is inserted in between.

Z self impedance of the generator

g

Zl load impedance connected to the network

These two components ca1be seen in the following figure when the network is inserted.

.z,

I I I I P,~ I I I I I 6 -I I I I I NETWOIH'I ~~ I I I I I

If L is the insertion 10SB then according to the above mentioned definition and figure,

L=

_-15-

P,

l.

L(in dB)

=

lOlOg-j;

Here, L includes the dissipation and reflection losses caused by the mismatch between the network and the generator.

A distinguishment between these two typs of 108ses is required. In the high frequency band, it is necessary to take into

acount the impedances of the lines Network - Load and Generator - Network.

In relationship with the above-mentioned insertion-loBs

definition, the characteristic impedance of the transmission

line Generator - Network must be equal to the generator

impedance, and the load impedance must be equal to the

characteristic impedance of the transmission line Network - Load.

This can' be shown in a circuit ~iagram

2, WETWORt<

!

uco",.p nt. l.iAlt: ' - - - -... I

... "l -.

If Zl is the obaraoteristic impedanccof the transmission

line Generator - Network

Z2 is the characteristic impedance of the trana.1881on,

line Load - Hetwo'rk

vi=a1 the incident voltage wave

propagatin~

from the

generator to the network

r .

Vl=bl the reflected wave from the network to the ,senerator

due to mismatc~ betwee~ network in-put impedance and

Zl

r

V₂=a₂ the reflected voltage wave from the load to the

network due to mismatch of Z2 and

ZL

V~=V~lI:b2

the incident voltage wave from network to load

from generator to the network

are confermed, cirquit; generator to the load if ZL=Z2 • r r then V_{l=V 2}=a 2=b1=O

Iv~t

'a1.

2 to network; P l

= --_ =

_

Zl Z1

IV~12

l

b 2

f

2) Power delivered froa network to load; P2= ---

=

---Z2 Z2

Maximum power is delivered if Zi_{• p.}network = Zl • Maximum power is delivered

If these two conditions

Power delivering in the

1) Power delivered from

of the insertion lOBS. in dB:-;- L

=

lO.lOgl~~I~~~

b 2 Zl

r

a

2-L

=

lO·log

_1

~Bl

.•..

eq.I.'.a.l

b 2

I.'.b. Evaluation of insertion 1088 in terms of soattering ooeffioients

~~b~'---b

NETWOAK:d

-

•

~

The scattering matrix equation for a reciprocity network (Sl~S2J:)

~b~

=

~11

9

11 ·

[a~l

•

b_l = 8₁₁a

1 + 812a2

,

b 2 ~12 8 22 &2 b2 = 812&1 + 322&2

8₁₁

=

bl ••• •• • • ••• eq. I.'.b.1. &1 &2=0 8₁₂ == b₂ I.3.b.2. • • • ••• •• •• eq. &1 a₂=0

From eq. I.3.,a.l. and, eq. I.3.b.l/2 it can be seen that

L = 10·log

-~-

[cle)

I

12r • •

• • • • • • ••

1.3.c. Definition and evaluation of reflection and dissipation losses

where

Ln

are the reflection 106ses.

1

---~--,-1 -

!Slll~

in dB:

L.

=

lO·log----~----­

9

-where

Ln

are the dissipation 10ss8s

r

a_{l '\2/Zl}

-~.

_{bl; ,2/ Z2} LD= ---~2·

---

for =Zl = Z2 ' b21/Z2 in dB: Concluaion: L . L R +

~

{,Vn.

d..B ) •

The insertion 10s8e8 of the network are the sum of reflection and disSipation 108ses.

In dB:- L',= lO·log---~1 +

1 +ISl~

•

1.4. The scattering coeffiCient method for dissipation

1088 measuring ,

1.4.a. Scattering coefficients in terms of impedances

¥rom network analysis it is known that every four-pole

network can be substituted by the following circuit:

Zll" - Z12 Z22 -

2.'2-in-pu:-t---lc::J Z12

C

out~ut

Z impedance seen in the in-put while the load impedance

<>c

at the out-put is equal to infinity

Zsc impedance seen in the in-put while the load impedance

at the out-put equals tO,zero

Z~ impedance seen in the in-put while the load relative

10

-It can be easily seen that Zoe - Z. Z .. ---... 22 Z - Z m sc •... " 1.4 '. ~) chap.4.l, p.4.

further information oan be found under ~. ohap.4.13

p.4 •

The folloving equations could be reached by means of the scattering coefficient deffinition:

2 (Z11- 1)(Z22+ 1) - (Z12) Zm - 1 S

=

---~ = --- •••••••••••••••••••••1.4.&.2. 11 (Zll+ 1)(Z22+ 1) -(Z12) Zm + 1 2 2 4(Z12) (91.2) =

[~~l)(z~;;l):-~~>7

From the above , sets of equations, it can be seen that

for finding the scattering coefficients,

3

points are

required:-Zoc ' Zsc ' Zm ' but for more accuracy 8 points of measur1na

were taken.

I.4.b. Scattering coefficients - measuring and drawing procedure

SWR.

.easuring Nr.

"1ST"""!! OF

short circuit from ntwk.

8

7

6 5 4 3 .2 1

7

it

6fl 5fg 4ft

,~ 2~

1ft

OTt

--f--V

~ t -~ ~ +

t

~

t

t

t

T

The calibrated moving.ahort circuit S.C. is moved in steps

of

~

from

,o~

to

7~

(8 measuring points).

Every step, the standing

wave

ratio and minimum points on the

length axis are noted down ( 8_i and 1 i_{m n, ,}i for i=1, ••••

8).

Two sets of 8 points each can be drawn on the Smith chart

(ref.dwg. 1.4.c). The first set: 1,2, •••• 8 is the root loous

of impedances while a variable short circ~it is moved from

~

- 11

-I.E.1 ...n1")lrc},~~)a~L81.·~1 .. TIT LE .', ..,'....~,~..:::.,'J.~~;.''-r',~J.r " .,'1' ".•J \..""1'_1. C.; ....t ',-.\ ":."._'r__ 'l',·. ,'."~-,",', ".".J.r. (-," '.,'..P.. '-~ .~..,....,. 1-, ,".'.~- DWG. NO. _\.• ,.

_":'-'~--_---'::=----+---t[D)i.Ai:lTrEE~l'::'C~••-:J:-_-:.--::l-:·~::-..·7.·~---·­

TH CHARTFORM5301-7560-N GENERAL RADIO COMPANY, WEST CONCORD, MASSACHUSETTS

IMPEDANCE OR. ADMITTANCE COOR.DINATES

RADIALLY SCALED PARAMETERS

B !',! I ! ' , ! TOWARD GENERATOR . . -q '" '"I I-', o , " " , - - TOWARD LOAD ~ ~ 0 , II IIIIII III III ~ :. _is 0 B~ 0 0 !i '" '" II II 'I II III II I B 0Of 0_'" 2 qn

Elec'ronics-Yol. 17.No.1,PP. 130-133,318-325, Jan. 1944

CENTER

I

12

-The second set: 1',2', ••••••• 8' is the root locus of

impedances measured wi~h a network inserted while a

~ariable short circuit varies from

o1r

to ~ •

Two circles can be seen in dwg. 1.4.c. : Circle I (points 1 •••• 8) - "base circle" Circle ll(points l' •••

(1) -

"image circle" points 1 and l' are short-circuit points

points

5

and

5'

are open-circuit points

~J ~ dwg.

1.4.0)

- the image 8 11 (~J p.341 iconocenter 0' center). 1.4.c Graphical evaluation of It is necessary to locate the point of "0" (the Smith chart_{. ,}

The chorda ~-;' 2'-6' •••••• 4'-8' have a common cross over

point A. Point M is the center of the image circle

(not the iconocentert). Points F,G, are the intersection points betweeb the image circle and the perpendiculars to . AM theough M and A. The intersection between FC and AM is

the iconocenter point 0'. Point 0 corresponds with an

impedance seen at the Qutput of a network when a matched load is connected. Point 0' corresponds with an impedance Been at the in-put side when the out-put 1s matched.

Hence the diatanoe 0 - 0' corresponds with the value of

the scattering coefficient 811

=

~~H8=o

•

If R is the radius of the image circle,

where H is the intersection point between the perpendicular

(to MO' through point

0')

and the image circle.

The evaluation of the last two formulae and angles of

l'

-I.4.~Scattering coefficient computer calculation

A special program was worked out by Mr. J.D.Pieterse ~7}!

The in-put dates for this program are:

la) The V.S.W.R. for a matched load connected to the nwk.

o.p.

Ib) The lOyation of two points around the minimum that shoY

the aame out-put on the o.p. meter, when a ma.tched load i8 connected to the network out-put.

2 ) The location of the 'dB points around the minimum given

in mm for the 8 points (short circuit, varying in steps of

~ ~ ' s , c , . ' )

16

from 0 to 2 while is oonnected to the network out-put •

, ) The wave length ~ in mm.

~l~ and ISl21~re among the various results given by the computer;

their values were used for calculating

La

and

Ln

according

to equations 1.3.c.l. and 1.3.c.2 • •

1.4.e. The computing method in general

:-According to ,the eight points given in the in-put band.

the computer finds an optimal image circle. The eight measured

points are projected through the center 0' of the circle

-on the circle itself. and an optimal cross-over point is

found by means of the projected points. The iconocenter is_,

then found (method in 1.4.c.) • Through the iconocenter lin.a

are drawn that crose the optimal circle on 8 points. TheBe

are the corners of an irregular Ootagon. These corners are moved on the image optimal circle until a regular Octagon

is reached. From the new H pointe (the corners of the regular

Octagon) lines are drawn back through the iconocenter.

crossing the image optimal circle at points 1', 2' ••••8· •

Three of these 8 points are used by the computer for

calculating the scattering coefficientsa

Z --. l' Z --- 5' and Z... O· • Eight points were taken in

sc oc III

order to find the optimal value of the above-mentioned three points. The optimal points in every case are found by the

condi tion that the sum of the squa1'"e' distances is minimal •

.4

~

el, /

~

dl, =

~

i~ ~ 4"

14

-§ 11. PRACTICAL DISCUSSION

.11.1. Attenuation factor in a Copper Bronze waveguide

First a Copper Bronze waveguide was measured. The waveguide

was made from two parts, Copper and ~ronz~ a8 indicated in

the figure below.

This construction yields a relatively high resistance

tor

the wall-current••

The aeasuring oonstruction:

ovr-PUT" • "Hell

'\

e

_{o 0} o osloi....u _..."'y. "••, c..,rry

...

The measuring preparation:

1) The Itlystron Hepeler was adjusted to maximum power o.p~

on the Bcope (for a oertain mode).

2) The oscilator frequency was adjusted around 1Khz. to

15

-=

3.6dB + K 1 . 0, = 1.2dB + K 2 . 0, 2.4dB +

(K

_0,l-K_0,

2).

+ K 1_0, + K_0,2 K_r,2

=

=

K 1_s, 11: Ke,2

K 1-

_r,

By means of the attenuator A, the out-pu.t meter vas adjusted

to an out-put mea~uring "V", while the 1209 long narrowed

Bronze Copper waveguide "Gil and its tva adapters formed

part of the circuit. Then "G" and the two adapters were

substituted by a standard attenuator (PP4l50xNo.70,).

The out-put meter was adjusted to the 8ame deflection "W"

by means of varring the attenuation of the standard attenua\Qr.

Tne Bcale indicated an attenuation of K~l. 3.6dB , wh~l~

K.,i is the attenuation indicated by the standard attenuator

(i - measuring index).

The same measuring was carried out for the two adapters

only (Without the marrowed waveguide). The measured attenuation

on the standard attenuator was

K

_s2 c 1.2dB •

Assuming the attenuator has a self attenuation Ko,i a t(K

a,1)

due to the influence of its /rJ,utlaIllLoSs , then

Kill: K i_r, + K i where K i is the real attenuation

8, 0, r,

(1 measuring index).

For adapte~waveguideK_r,l

For adapten only K

r,2

For waveguide only

K

=

g

In order to know the variation of the real attenuation as

s function of the measured attenuat~on, t~e attenuator

characteristic was measured.

By refering to figure 11.1. , the calibrating characteristio

can be seen, where K '1_s, the measured attenuation, K i the

0,

calculated attenuation from the V.S.V.R.,

8

i +l

K 1:11: 10· l o g . and ..:1K = K_{8 ,}1 - Kc;.1 :.

K... '

s, 8

1-1

16

-Characte~istic measured data

i _{Ks,i(dB) Kc,i(dB) AK--K i (dB)}

0, 1 0 , . 0.52 _-0.52 2 0.2 0.66 -0.46 3 0.4 0.86 -0.46 4 0.6 1.04 -0.44 5 0.8 1.24 -0.44 6 1.0 1.44 -0.44 7 2.0 2.42 -0.42 8 3.0 3.42 -0.42 9 4.0 4.36 -0.36 10 _{5.0 5.30 -0.30} 11 6.0 6.24 -0.24 12 7.0 7.10 -0.10 13 8.0 8.10 -0.10 14 9.0 8.96 +0.04 15 10 9.60 +0.40 16 11 10.6 +0.40 17 12 11.5 +0.50 18 13 12.4 +0.60 19 14 13.1 +0.90 20 15 13.6 "'1.40

(Data for fig. 11.1.)

The pOints listed in the above table were used for piloting

the characteristic of th~ ~ttenuator ( fig. 1.1.).

From this characteristic we see that for K 1=3.6dB_s, and

Ks ,2=1.2dB, Ko ,1=Ko ,2=O.45dB.

Then K 1=4.05dB_r, and K 2=1.65dB yielding a guide_r,

attenuation of Kg-4.05-1.65=2.4dB and an attenuation factor of«1cO.2dB/cm (3x22.86x120mm - Copper Bronze).

Remark. The V.S.W.R. measured for soa1e attenuating above

lOdB cannot be used to calculate K i because the

_r,

V.S.w.R.

is too low and the reflections along the equipment have dominant influehce parts on the measuring result.

3 4 5 6 7 8 910' 2 3 4 5 6 7 8 910' 2 3 4 5 6 7 8 910' 2 3 4 5 6 7 8 910' 2 .5 I

i

I

i

iii

I" I T T 'I T

i"I

I T T

i

T T '1

Til

II

.0

II

s

.0 .5 , .0

_rnm

s

...

-.

_r.v

-"

'J 'J ~-t-d:t t : f· .. ₊ .. .5 .. ..

·.nl

t - 4 -- - ~ _-I t-4' .. t + ~ + j -3.0

..

-I-- ~. "W . . . ~ .. 1: + t ., -- _{i i '} l~ .5' +

.-..ct: ...

t=t: fH ~ + 2..v - . . 1.5 -- .. _-- -- .. .. 1.0 + --t 0$ -0." _I

I

I

~

l

I So

~ ~~~Ioe

I

!

1

_{~ ~ ~ ~}

_!

"0' ~ 0. Q3 0.4 Q5

0.'

o.:r~Ql 1J)' i 7 I 10' 0 0 40 3 6 7 2 7 5 4 3

"t.V. Drukkerij "Mercurius" Wormerveer No. 12TR X-as log. verdeeld 1·10' Eenheid 62.5 mm. Y·as verdeeld in mm.

18

-11.2. Attenuation as function of short circuit variation 11.2 ••• Measuring in a 47.12ma wavelength

ThiS method is baaed on mea8uring the standing wave ratio

when the short circuit is moved in 8teps of

3

mm from 0 to ~.

This was carried out for a waveguide

W

₂ 500mm length w1th

rectangular cross section 3x22.86mm in size. The wavesuide

W₂ was silver plated twice. For this waveguide the substitution

• method did not fit because of the high V.S~W.R. meaaured .

(low attenuation).

e

_o 0

•

s.c. --1...- A,

J:=:::==:::::t-::!A,.

~V-P,-R.-iA-'sL"-e---M...~Prf. _S.Alj)

w,.

~.APTIi.:-'-;CIiiQ-"--;;=::::~=;;-.~,---..,~bd..

SHORT c.illc.uir

Prior to the measuring, "the electrical tero point" vas aetablished. A short circuit plate was connected at the

end of the 9ircuit. The wavelength was measured and the

V.S.W.R. meter was positioned at a minimum point. Then the short circuit· plate was replaced by a varying short cirouit

PP4260xNo.980, (Without moving the V.S.W.R. meter).

After varying the short circuifoa minimum deflection point

on the V.S.W.R. meter the short circuit scale indicated.

length of R (mm). Refering to the figure and fact that

. e , m ,OPJTFiE rill/..5.C.. ~

the di8tan~e between two minimum pOln~s~ ~'[8 = ~ - R• •

~

•. «

t-""'·JiE:'

.,:j;.r.;L.

~

...

2.G7-

:'4...

---=---~

~~'

••

""".~m

~ 6.

- 19 - .

where

r.s

the d,istance between the electrical zero and the

measured zero on the short circa1t.

R i the length between shott circuit and electrical_e,

zero (in mm)

Ra,i the length pointed out on the variable ahort circu1 t (in mm).

Hence Re,i a Rs,i +

fa

Measuring result8:- (W 2)

•

R

i(mm)

att. fao. dB/em

e •

_.

0.01705 0 3 0.01608 6 0.01636 9 0.01740 12 0.01890 15 0.02046 18 0.01894 21 0.01760 24 0.01730 27 0.01689 '2

R_e.i(mm) att. fac. dB/OlD

0 _0.02337 3 0.02306 6 _0.02230 9 0.02040 12 _0.01953 15 _0.01968 18 _0.020~6 2·1 0.021 4 24 0.02306 27 0.02367

II.2.b. Variable short circuit attenuation measuring with minimum points located on the connections

This measuring was carried out on the same guide (W

2).

The frequenc~ waa set to 8.915GHz (~g 50mm). For this

wavelength the minimum points location was on the connection points of the waveguides in the circuit. This was possible because every waveguide in the cirouit had' a length of

n·2.5cm (0=1,2)3, •••• and ~_g/2

=

2.50m).

H-+t

cr_

_{+ .} -..-. . j.-+itt

•

.,

I

t + +I ' it

,1 t,' '++ ttl' t:I';'H'"th1_if'" 'Ii .._{it:; , " " : j ' l I~J, ·1 '~. 'I' I . - Hil iJ~;:.. .. .}

"er

,

:;

• 'I,

!milfl:it1

tlEi+ ,;

it!l:i ~, ~tki

..

:.}1,:

1.0':.·

!{~I "J,I~' ::ii:U: .. ~::! [7~i; dt~~ i:'~H ~1 i~~I;! n-4:mJiiti~~rttf~miili

ft

d lHi1

+iti

.r1 'l-hH ofTi: !~t .1- I. H

21

-On figure No.II.2 the two oaaracteristica are drawn. Alao in this oaBe it can be ·seen that the reflection and

dissipation attenuation 1s given in one term, and that the

distance between two minimums of the same graph is about.

A

s!2.

The attenuati~n varies as a function of the short oircuit

placement, aleo in case of locating the minimum points on

the several waveguide oonnections.

11.3. Scattering coefficient measuring and attenuation calculation lIJ.a -+---k-~-­ -'--..,-i--""'-""--_""L . . . .,.·Itt. the gtbpo1nt of the 8 points t - - -...T - : - - - -__l..'AlIrTH "."is ~1 + +

-The same circuit was used as in 11.2.a.

A_l ,A₂ adapters between the measured waveguides and

the circuit.

W

l narrowed rectangular crose~.ection waveguide ('x22.86x500mm

in size) plated once.

W

2 narrowed rectangular cross-section waveguide (3x22.86x500mm

in Size) plated twice.

S.C. calibrated variable short circuit.

Xhe "electrical zero" of the variable short circuit was

. found in the way described in part 11.2.a.

The following measurements were carri~d out:

1) Wave frequ~ncy f and wavelength in the gUideA g

2) Location 11,1₂ of 3dB points around the minimum~n the

length axis for 8 points (in

it

steps).

3) The measuring"of the V.S.W.R. and the location of two

Out-put-equal

po1nu around the

minimum were taken for

th ,.

the 9, point - the matched load measuring point.

22

-Measuring resu1ts:- 8 points of the fundamental image circle.

f • 8.906GHz. ~g

=-

49.94mm ">'/16 • '.12laa I'UJlIBon ',UtI Inn ,rus

t,r.',

Ian JfU9 I'o.o~ IH.I" I,r.n-" 1..H IH·2.S' IIlL./l I'H.Ot I 'Z.}-O IIr.n 1f9.U I1U. 111·1.7 195.'2 IH.Of I~HO "'.59

",.(,,

) 'Holt '''' .10 0\116 2A, .J.b .J."'J .10 1 "l b ~oint Nr.

Results of the 9th point - the matched load measuring•

Imeasured network 11(DUll) . I2{1UI)

s

•

A1+A2+W1 186.65 175.84 1.146 A1+A2+"2 183.78 174.38 1.142 A₁+A₂+W₁+W 2 187.035 174.77 1.122 I A₁+A₂ 212.83 202.2 1.145

The measured data of the above two tables, were fed into a

computer after registration on an "in-put band" for a oomputer. The computer used these data for the calculation of the

scattering coefficients.

Computer calculation

reeu1ts:-~eaeured network _/Sl11

_I

S₁₂₁

_t

S₂₂₍

A_{1 + A2} + _W1 0.05874 0.8972 0.04729

Al + A2 + "2 0.C54698 0.8828 0.05275

A1 + A2 + W1 + W2 0.04664 0.8072 0.03678

2'

-According to eq~ations 1.3.c.1

&

1.3.c.2 (given in the

theoretical part) the ?alcu1ation results are:

_essured network Lo(dBl olo(dB/cm) ~(dB) . ~R(dB/oa)

A_l+A_{2+W1 0.9268 0.01853 0.01472 0.00029}

A

l+A2+W2 1.0690 0.02135 0.01257 0.00025

Al +A;l+W1+W2 1.1698 0.03539 0.0091' 0.00018

A_{l+A2 0.1928 0.00964 0.03288 0.001644}

The measuring accuracy could be ohecked by evaluating

t.he erro r

f.

.

f=

_{\Ln(W l +Al +A2) + Lu(W2+A1+A2 ) - Ln(Al +A2) -}

Ln(Al+A2+Wl+W2~

~= 0.9~685 + 1.06904 - 0.19284 - 1.16989

f=

0.03316. This is an error of about 1.5% from

Ln(A

l+A2+W1+W2} + Ln(Al +A2 ) or LD(W1+A1+A2) + 1n(W2 +A1+A2)

Further calculation of the various attenuation constants

yields ~o the following results:

~D(Wl)=~D(Al+A2+Wl+W2)- ~D(Al+A2+W2)

=

0.03539-0.0213~O.01404dR/ol

~D(W2)=~D(Al+A2+W1+W2) _{- <n(A l +A2+W1 )}

=

0.03539-0.0185"O.01686dB/~

olD(Wl+W2)=ac:'D(Al+~2+Wl+W2) _{- "'D(Al +A2) :: 0.03539-0.00964=0.02575d13/01}

The graphical method ( Dwg. 11.3.) was carried out in order to compare it with the computer method. The drawing was made

for W₂

(A

_g=41.12mm~ It can be seen in this oase that it is

impossible to find the scattering coefficients from the drawing because of the low attenuation in the wavegUide.

24

-WEST CONCORD, MASSACHUSETTS GENERAL RADIO COMPANY,

H CHARTFORM5301·7560·N

_E_I'_i_o_B_]_"~_~,_s_·_G_""r_=t_l_b_cr +_ T

_'T_L_E_~_·;_C_O_'_L_o__C_C_'_c_'_f_f_o__i_'_ll_ _'_,:-1::>=--_f_O_I'_A--7':-_=-_-_~_;_7_._J_._~_·;_-1_~;_1_ _

-I;

~~NO• 1>:1

IMPEDANCE OR ADMITTANCE COORDINATES

'" ~ b 0 0 I,III, I '" !" 0 0

Copyright 1949 by Kay Electric Co" Pine Brook,N~wJersey

...

'"

Uo _g '" 0 0 0 0 II I I II IIII IIIIII III III III ,II II,III I .1 I lil iV a; _'"0 _~ ...0 g o ,.; r I TOWARD GENERATOR : >

-El.ct~nics·Vol. 17, No.1, PP. \30-133,318 - 325, Jan. 1944

e~ 0 0 _!! '" N 1, ,,\ I I , +-1 II, " IIi I e 0 0 _~ 0 0 " N ,.;

..

RADIALLY SCALED PARAMETERS

e g 2 ~ ~ ~ ~ ~ ~ ~ - ~Io ~ ~ _l--J-_Lll.LJ--,+'--'--_l'J'J-'J'T'-'-..1'->-'-,-I~~I !, !,' II Ii h"'rTn-+_L~1 I1 \ I ,I I! - TOWARD LOAD

t

~ g ~ ~ ~ ~ ~ T.~~ 9 ~ f'J P 6 b b i l l II II I) 1 ' , - 1 'I j'll! ' 1 ' - T - 1 , ' r l l ' , ' I ' [ ' 1 ~ ~ ~ ~ C\! ~o 9 ~ b CENTER I

25

-DISCUSSIOK AND CONCLUSION

During the attenuation measuring of the two waveguides examined, several measuring problems cropped up.

The main problem was to distinguish between reflection and dissipation influences on the V.S.W.R. measuring. The optimal method found for solving this problem was the calculation by means of a computer program.

This was possible because of the availability of such a calculation program for scattering coefficients.

When a network with a low attenuation factor is measured the influence of reflections, inner surface discontinuities,

inaccuracy in power adjustment and con~ection between

guides are. important factors •.

For this reason special attention was paid to the construotion, plating, and connections of the waveguides in the circuit.

This experiment was started in the expectation that the praotical attenuation factor could be 100 times the

theoretical value (due to the bronze copper waveguide measuring). The main conclusion in this point is that

the attenuation factor is largely influenced by the

mechanical construction and plating quality of the waveguides. The best method for finding the attenuation factor in

such waveguides would certainly be USing a variable

calibrated short circuit with the cross section dimensions of the waveguides examined.

By means of auch a short circuit it is possible to

measure every examined waveguide and addapt~r separately.

Such a short circuit was not available in the laboratory. The cause of the difference between the theoretical and practical values of the attenuation factor ·found in this

stage (0.003 ~ 0.015 dB/em) may be the inaccuraoy of

the ctoBs-section dimentions, the imperfect galvanic

connection between the cover and base of the waveguides

_,

_,

on the one hand, and the imperfect waveguide oonnections in the circuit on the other.

26

-However, the differenoe between theoretioal and measured attenuation faotor was reduoed from a difference faotor

of 100 to a differenoe faotor of 4-5~~

dB).

This oonolusion for oirouits where thee, types of waveguides are used !s surely an· important oonolusion.

21

-BIBLIOGRAPHY

·B 1 M.Sucher J.Fox Handbook of Miorowave measurement.

Volume I third Edition, Polytechnic Press of the Polytechnic Institute of Brooklyn (1963)

B 2 S.Ramo J.R.Whinery T.Van Duzer, Pields and Waves

in Comm~icat1on E1ectronios, John Wiley

&

Sons,Inc.(1965)

·B 3 E.L.Ginzton, Miorowave Measurements, Mo. Graw-Hi1l (1957)

B 4 H.Groendijk, Miorogo1f Techniek, T.R. Eindhoven (1968)

B 5 J.E.Storer, L.S.Steingo1d, S.Stein, A Simple Graphical

Analysis of a two 'port Waveguide Junction, Proc. I.R.E. 41 (1953) 1004 - 1013

...

B 6 Deschamps G.A. Journal of Applied Physics ~ (1953)

1046 - 1050

B 7 Pieterse J.D. , Het Equiva1ente T - Netwerk Van Een

I