broadband waveguide feed for parabolic ...downloads.hindawi.com/journals/apec/1994/053036.pdf14 p....

Active and Passive Elec. Comp., 1994, Vol. 17, pp. 9-19Reprints available directly from the publisherPhotocopying permitted by license only() 1994 Gordon and Breach Science Publishers S.A.Printed in Malaysia

BROADBAND WAVEGUIDE FEED FORPARABOLIC REFLECTORS

P. BHUSHAN MITALFellow Member LE. T.E. (INDIA)

CR State College of Engineering, Murthal (Sonepat). India-131039

(Received November 15, 1993; in final form January 4, 1994)

The broadband requirement in microwave systems has necessitated attention on components that canoperate over frequency ranges far broader than those of standard rectangular waveguides. This paperdescribes the design and development of an ridged horn to match the waveguide impedance to freespaceimpedance so that the horn could be used as a feed for an offset-fed parabolic reflector over a wideband of frequencies, i.e., C and X bands (4.2 to 10.2 GHZ). In the present case, a five stepped chebyshevtransformer has been used. Complete design required for horn feed as well for the ridged waveguidecomponents necessary for testing has been carried out. The results obtained are quite encouraging.Good agreement is found between the measured results and theoretical values.

I. INTRODUCTION

In a ridge waveguide, ridges on the top and bottom broadwalls of a waveguidecause a capacitive loading [1-10]. The electric lines of force tend to bunch up inthe space between the ridges, as shown in Fig. 1. This effectively lowers the cutofffrequency for the odd modes in which the electric field is maximum at the centerof the guide cross section having no effect on the even modes. It increases thebandwidth of a given waveguide in the direction of lower frequencies while main-taining the physical dimensions of the waveguide. The maximum bandwidth islimited by the closeness of the spacing between the ridges, which affects the powerhandling capability and mechanical tolerances on important dimensions.

Theoretical investigations show that the ridge waveguide gives wide bandwidthsfree from high mode interference. Frequency range of four to one (4:1) from thefundamental mode of operation are easily obtained with single and double ridgewaveguides.

(i) Calculation of Cutoff Wavelength (h) of Ridge Waveguide (TElo mode)

The cutoff condition of the waveguide corresponds to resonance of the equivalentlumped constant circuit as shown in Fig. 2, and the expression for the cutoff

10 P. BHUSHAN MITAL

FIGURE

wavelength of the ridge waveguide is given as

bl A’c a A’c 2

b (a ;tc)(1)

tanA’c

This equation is solved for first order root to obtain the cutoff wavelength of theTE0 mode. The discontinuity capacitance, Cd, is due to the fact that the ridges in

A

(,C’) EQVWALEN"I" LUMPED- (’NSTANT CKI"

FIGURE 2

BROADBAND WAVEGUIDE FEED 11

the waveguide present discontinuities to the electromagnetic waves and cause localor higher order waves. The effect of these local fields are included in the calculationby the addition (at the proper location) of the discontinuity susceptance, which iscapacitive in nature.

The discontinuity capacitance, Cd, is obtained by means of Schwarz-christoffeltransformation as

b2 dwhere X (2)

(ii) Calculation of Characteristic Impedance (Zoo)

The characteristic impedance of the ridge waveguide at the infinite frequency iscalculated from the expression given below.

V/,- A"-cs2 7c InCSC +

1 (2zrS d+ sin \----c/ + - C0S2 C

sin2 c (a- S)

s)2h’c

and Zo1

12oryo

zrS2h’c

1sin (2"rr(- S))4 ’c

a width of waveguideb height of waveguideS width of ridged height of ridge

A’c cutoff wavelength of ridge waveguide for TE0 mode.

(3)

The detailed derivation of this relation is given in Appendix I.The values of 2cd/E, cutoff wavelength A’c/Ac, and characteristic impedances

thus obtained at infinite frequency for different step ratios are summarised inTable I.

II. DESIGN AND FABRICATION OF HORN FEED

In a chebyshev transformer, there are stepped impedance sections proportionedto chebyshev polynomials that result in better broadband results for a given lengthand bandwidth than the use of tapers or binomial step functions.

12 P. BHUSHAN MITAL

TABLE

Impedance d/b ratio 2Cd Ae A

Ridge waveguide 274 ohms .6596 .2318948 1.1640Step No. 285.55 ohms .6917 .1919330 1.1413Step No. 2 307.30 ohms .7536 .1260418 1.1024Step No. 3 336.15 ohms .8930 .0551191 1.0562Step No. 4 361.75 ohms .9366 .0107073 1.0189Step No. 5 377 ohms 0

The structure consists of a symmetrical series of steps on the top and bottom ofthe inside of the waveguide walls with approximately quarter wavelength spacingbetween steps. Each section has a constant impedance throughout its length, i.e.,from one end of the section to the other end. Transition is made with smoothtapers in the outside dimensions and in the width of the ridges, thereby maintaininga constant ratio of ridge width to guide width (s/a ratio) throughout the length ofthe transformer.

The number of steps required for a given maximum VSWR are calculated fromthe equation given below.

In[Z"+I]ZlSmax- 1 / (4)

Tn- cosWhere Smax Maximum voltage standing wave ratioZ and Zn + 1 are the terminating characteristic impedancesb is the electrical spacing of the steps at the low frequency end of the band.

The ratios of the reflection coefficients of the steps must equal the ratios of a setof constants ’am’ i.e.

rl: r2:r3 rn al: a2:a3 an (5)

According to Hansen

rm= 21n[Zm+l]zm (6)

Hence, step ratios are given by

Z2" Z3 In zn / 1

lnl In Z-: Znal: a2" a3... an. (7)


The ratio at a given step may be computed in terms of the terminating impedancesand the ’am’ values by

Zn q- 1am In

Zm + 1 ZIn (8)Zm a + a2 + + an

Once the number of steps has been chosen, the chebyshev coefficients and theresulting characteristic impedances required for each section are calculated alongwith d/b ratios. As the d/b ratio is constant for the given step of the transformer,the step discontinuity capacitance 2Cd/e. AND Ac’/Ac are calculated and the valuesare given in Table I.

Calculation of the length required for each section is than undertaken. Sincethe a and b dimensions vary according to the outside tapers, the cutoff character-istics vary throughout the length of each section, thereby introducing varying Agvalues. To overcome this problem, the TE, mode cutoff frequencies are determinedfor both ends of each section. The mean Ag at each and of the section underconsideration is than calculated as follows

Agm212Ag21L. Ag21H(Ag21L + Ag21H) (9)

,gm222Ag22L Ag22H

(10)()tg22L + )tg22H)

where Agm21 Mean at small end of the sectionAgm22 Mean at big end of the section.Ag21L Guide wavelength at small end of section at low frequency end.Ag21H Guide wavelength at small end of section at high frequency endAg22L Guide wavelength at big end of section at low frequency end.Ag22H Guide wavelength at big end of section at high frequency end.

The actual length of the section(s) is found from the relation given below

gm21 gm22S2(Agm21 + Agm22) (11)

The detailed dimensions of the ridged horn are shown in Fig 3.

III. PERFORMANCE AND EVALUATION

Based on the design given in Part-II, a horn feed unit was fabricated locally fromaluminum material and its performance assessed. The experimental setup forVSWR measurements is shown in Fig. 4. An EC sweep generator Model UM 400has been used as a microwave signal source. The desired frequency range is obtained

14 P. BHUSHAN MITAL

FIGURE 3

from its RF-plug in units CA-400 and XA-400. A locally fabricated attenuator isalso included in the circuit, A probe is moved in the slot provided in a section ofdouble ridge wave guide to sample the voltage.

The output of the probe is detected and read on a VSWR meter. The probeentering in the slotted section is a discontinuity and, to avoid this, the penetrationdepth is kept as small as possible. For low VSWR, this is not a problem but forhigher values, the probe must be inserted deeper to read the minimum. The slotwidth is also kept vary small, i.e., 16% of the total ridge width. Values of theVSWRs obtained at different frequencies are tabulated in Table II. E & H planeradiation patterns obtained at 4.2 GHz, 7.0 GHz and 10.2 GHz are shown in Fig.5, 6 and 7.

EC SWEEPGENERATORMODELUM 4O0

TRANSITION

DETECTOR

PROBE

EC UA’2:O

DOUBLE RIDGE

WIG BASED

ATTENUATOR

DOUBLE RIDGEw/; BASEOSLOTTED LINECARRIAGE

VSWR METER

KL B MAKE

RIDGE W/G

HORN FEEDFIVE STEPPEDCHEBYSHEV

FIGURE 4 Experimental setup for measurement of VSWR.


TABLE II

Sr. No. Frequency in GHz VSWR

1. 4.2 1.42. 4.8 1.43. 5.2 1.34. 5.8 1.35. 6.2 1.36. 6.8 1.27. 7.0 1.28. 7.5 1.29. 8.0 1.2

10. 8.5 1.111. 9.0 1.212. 9.5 1.213. 10.0 1.214. 10.2 1.3

IV. SUMMARY AND CONCLUSION

Despite the simplifying assumptions and small errors in the design method, theunit exhibited the typical chebyshev ripple response, but the ripple varied betweenVSWR of approximately 1.1 to 1.4 over the frequency range 4.2 GHz to 10.2 GHz.From the radiation pattern at 7.0 GHz, it is seen that beam width at 3 db is 6 andat 10 db is 24. The cross-polarized component is approximately 20 db down.Mechanical tolerances presented some problems in the fabrication. In general, it

RADIATION PATTERNAT 4.20 GHZ J// ]-’’

-.

DI:.(IREES (01 I-:1 DEGREE100 90 80 71,0 4,0 3,0-: II.O "".o z,o a.o 4.o .

FIGURE 5

16 P. BHUSHAN MITAL

RADIATION PATTERNAT 7 GHZ

DEGREI-" S (0) II II DEGR[ !I-’S (0)100 90 80 70 60 5) 40 30 2 10 |0 10 0 30 40 ,0 60 7...0 80 90 100

FIGURE 6

RADIATION PATTERNAT 10.2 GHZ

--’4---

---20-22

100 90 80 70 60 50 40 30 20 10 10 20 30 40 50 60 70 80 90 100-,,--..--DEGREES (o)

FIGURE 7


was found that the distance between steps was relatively uncritical but the heightof the steps proved to be quite critical. Tolerances of the order of __.0.004" werefound to be adequate for the section length but changes as small as 0.0015 inch inthe step heights introduced measurable differences in the VSWR patterns. Thisbeing the first experimental model, the results, although not absolutely perfect,are still considered encouraging.

REFERENCES

1. S.B. Cohn, Properties of Ridge Waveguide, Proc. I.R.E., Aug. 1947, 783-788.2. Peter Lubell, Design Innovation Using Double-Ridge Waveguide.3. T. Anderson, Standardization of Ridged Waveguides, Microwave Journal, April 1961, 74-78.4. T.S. Chen, Calculation of the Parameters of Ridge Waveguides. I.RE Trans M.T.T., Jan. 1957,

12-17.5. S.B. Cohn, Optimum Design of Stepped Transmission Line Transformers, I.RE. Trans. MTT.,

April 1955.6. Hensperger, Broadband Stepper Transformer from Rectangular to Double Ridge Waveguide,

IRE Trans. MTI’., July 1958, 311-314.7. R.E. Collin, The Optimum Tapered Transmission Line Matching Section, Proc. IRE., April 1956,

539-548.8. S.B. Cohn, Design of Simple Broadband Waveguide to Coaxial Line Junctions, Proc. IRE., Sept.

1947, 920-926.9. Walton Sundberg, Broadband Ridged Horn Design, Microwave Journal, March 1964, 96-101.

10. S.A. Schelkunoff, Electromagnetic Waves, Von Nostrand, 1943, 494-496.

APPENDIX I

DERIVATION OF EXPRESSION FOR THE CHARACTERISTICIMPEDANCE OF RIDGE WAVEGUIDE

The average power carried by the ridge waveguide is given by

p= XA Eo /c2 fm 71-/ ,Tl-d 71-1, A 2 fl cos2y In CSC + 2

+ sin 2[sin 2 k 4

sin 4

k

hc2h E/3 {A}hg 2r

V0where E0 Electric field intensity -d- at the center of the ridged gap

V0 Instant peak voltage across the center of the guided ridged gap heightrn 1 for double ridge waveguide

2 for single ridge waveguide

(1)

18 P. BHUSHAN MITAL

b s Ac da =-v=-k =--/3 =-a a a a

/3 d/a d v s/a sk hc/a hc k hc/a hc

1 s/a Ac2 P=-- (2)

(3)

a s2a a s

k hc/a 2he

The ridge guide impedance is defined as

V0 EoEd2Zo 2- 2p

1 2p 2 pYo Z, Eo d

(4)

Putting the value of P from eqn (1), we get

2 1 e A 1 EdYo ’i E- Ag 2r cc" AcE {A}

Ac{A}2

Ag 2"/rd

At infinite frequency A Ag- Ac’Vo** 2 {A}

2 r Ac’ {2d (rs) rd rs 1 (2rs2r---- A"- cs2 c In CSC-- + + sin

\ h’c]

d cos2 rs/h’c [r(a s) 1 (2r(a s)]}+ [’n’(a s)] 2h’c- sin \ ,sin2

h’c

(5)

This is the required expression for ridge waveguide admittance at infinite frequencyon pv concept. The characteristic impedance at any other frequency f can becalculated from the relation

Zo** (6)


We can verify the characteristic impedance of ordinary waveguide (without ridges)from the above formula given by eqn (5) as follows.

Case I No ridges i.e. d b, s 0.2 a

wdCosec cosec 7r/2 1

22a{d 1 [Y* 3772-trdx x

2

2 2a 7r a

377 2"rrd 2 x 2 377 x 2b

x 2a

2b.’.Z, 377 x-

a

Case ll d b,s a

22a{YI 377 27rb0

2 a rr377 "rrb 4

ra+ aa + 0 + 1[0- O]

a377 x 2b

2b.’.Z, 377 -a

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttp://www.hindawi.com Volume 2010

RoboticsJournal of

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation http://www.hindawi.com

Journal ofEngineeringVolume 2014

Submit your manuscripts athttp://www.hindawi.com

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation http://www.hindawi.com

Volume 2014

The Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014

SensorsJournal of


Modelling & Simulation in EngineeringHindawi Publishing Corporation http://www.hindawi.com Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks


broadband waveguide feed for parabolic ...downloads.hindawi.com/journals/apec/1994/053036.pdf14 p....

Documents