Comparative electromagnetic analysis of ridge waveguide transitionsfor RF power couplers

Rajesh Kumar a,n, P. Singh a, Pratigya Mathur b, Girish Kumar b

a Ion Accelerator Development Division, Bhabha Atomic Research Centre, Mumbai 400085, Indiab Department of Electrical Engineering, IIT Bombay, Mumbai 400076, India

a r t i c l e i n f o

Article history:Received 2 July 2013Received in revised form20 September 2013Accepted 23 October 2013Available online 29 October 2013

Keywords:Waveguide iris couplerRidge waveguide couplerWaveguide to cavity couplerRF power couplerRidge waveguide transition

a b s t r a c t

Ridge waveguide transitions have been used in the high power couplers of many ongoing high intensityproton accelerator projects worldwide. Because of their smaller size and high energy densities, theyrequire strict dimensional tolerances during fabrication and operating conditions. In order to study theirelectromagnetic characteristics, two different types of transitions with a straight ridge and a taperedridge are compared using full wave simulations. Apart from the return loss and resonant frequencyvariation with dimensions, comparative studies on the phase shift, insertion losses, electric and magneticfield distributions and multipacting are also reported. This analysis will be useful in selecting theappropriate ridge waveguide transition for the RF couplers of accelerator cavities.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

RF coupler acts as an impedance matching component betweenthe incoming waveguide and an accelerator cavity. Room tem-perature cavities of the many ongoing high intensity proton RFLINAC projects operate at UHF frequencies. At these frequencies,the waveguide sizes are quite large. As the available port size onthe cavity is small, ridge waveguide transitions are useful in suchapplications. In these waveguide based coupling systems, an iris iscut in the end wall or side wall of the waveguide [1]. The RF poweris coupled to the cavity through the iris. Different ridge waveguidetransitions like constant impedance taper [2], tapered ridge with aconstant width [3] and a straight ridge taper [4] have been usedor are under consideration for the high power waveguide-cavitycouplers in different accelerators. It is found that these transitionsare very sensitive to the dimensional tolerances [4–6]. After thesuccessful design and testing of a constant impedance taper typecoupler [7], other implementations using constant width taper [8]are under active consideration. Though, these designs have beenconsidered in different accelerator projects, there is no report of acomparative study on their dimensional tolerances. In order tostudy this dependence, a numerical study is carried out on thestraight ridge and the linearly tapered ridge transitions using acommercial EM Solver CST Microwave Studio (CST-MWS). It is

found that the linearly tapered ridge is less sensitive to most ofthe dimensional changes as compared to the straight ridge taper.It is also shown that the linearly tapered ridge waveguide transi-tion is superior to the straight ridge transition in terms of thereturn loss bandwidth, lower insertion loss, phase shift and the EMfield concentrations. However, because of its simpler design andrecently proposed tuning scheme to relax its dimensional toler-ances [4], the straight ridge transition is also expected to be a goodalternative.

2. Comparative analysis of the straight and tapered ridgewaveguide transitions

In this work, a detailed numerical analysis is carried out for thelinear taper using CST Microwave Studio (CST-MWS). The resultsare compared to the already reported results for the straight ridgetaper [4]. For the purpose of this discussion, input waveguide ofWR2300 size and half height is considered. The design frequencyis taken as 352.2 MHz. Fig. 1(a) shows the top and cross-sectionalviews of tapered transition. Three dimensional simulation modelof the tapered transition is shown in Fig. 1(b). Side view of thetransition is shown in Fig. 1(c). As it can be seen from return lossplot of Fig. 1(d), the transition is optimized for 352.2 MHz.

All the important dimensions of tapered ridge transition aresummarized in Table 1. The equivalent dimensions for the straightridge transition are also given as reported in [4]. For the sake ofcompleteness, a 3D CST model of straight ridge taper is shown

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Nuclear Instruments and Methods inPhysics Research A

0168-9002/$ - see front matter & 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.nima.2013.10.050

n Corresponding author.E-mail addresses: krajesh@barc.gov.in, rkthakur_iitk@yahoo.com (R. Kumar).

Nuclear Instruments and Methods in Physics Research A 736 (2014) 99–106

in Fig. 2(a). This is the same coupler which is reported by theauthor's in [4].

Simulation model of the tapered coupler with meshing isshown in Fig. 2(b). In the parametric studies for tapered coupler,frequency domain solver of CST MWS is used with tetrahedralmeshing. Twenty points per wavelength are assigned for meshingwhich results in approximately 30,000 tetrahedrons. The solveraccuracy is set at 1e�5.

2.1. Parametric studies for the return loss and resonant frequencyvariation

The end ridge gap is varied in steps of 0.1 mm for linearlytapered ridge waveguide transition. The plot of return loss fordesign frequency of 352.2 MHz is shown in Fig. 3(a). For thecomparison purpose, the variation for straight ridge waveguide asreported in [4] is also given on the same plot. Similarly, theminimum return loss frequency plots are given in Fig. 3(b). Wecan notice that the dependence of return loss variation with endgap is almost same in the straight ridge and linearly tapered ridgewaveguide transition.

We can notice from Fig. 3(b), that there is more frequencyvariation for tapered coupler. This is due to the fact that variationof end gap not only changes the end ridge impedance, it changesthe taper angle as well. This is not the case in straight ridgecoupler as the central ridge gap remains same during simulations.The variations in end gap only change the end ridge impedance instraight ridge coupler. As the central ridge dimensions remainsame in straight ridge coupler, frequency variation is flat. However,return loss varies in straight ridge coupler because of the change inend ridge impedance.

The variation of return loss at 352.2 MHz with central ridge gapis shown in Fig. 4(a). The corresponding plots for minimum returnloss frequency are shown in Fig. 4(b). The central ridge gapparameter ‘cg’ is varied during this simulation whereas ‘eg’ and‘sg’ are kept constant.

Similarly, the variation of return loss at 352.2 MHz with thecentral ridge width and the length is shown in Fig. 5(a) andFig. 6(a) respectively. The dimensions are changed by 71.0 mm.The corresponding plots for the minimum return loss frequencyare shown in Figs. 5(b) and 6(b). It can be seen that the return lossdeterioration is less in a tapered ridge waveguide as compared tothe straight ridge. Except end ridge gap and central ridge gap(where parametric step is 70.1 mm), all other parametric varia-tions in steps of 1.0 mm show a return loss of better than �20 dBfor linearly tapered structure.

Fig. 1. (a) Top view and cross-sectional view of the tapered ridge coupler; (b) CST MWS simulation model of coupler; (c) side view of coupler; and (d) S11 parameters plotobtained from simulations for optimized geometry.

Table 1Dimensions of the optimized tapered and straight ridge transition.

Parameter Value for taperedcoupler (mm)

Value for straight ridgecoupler (mm) [4]

Description

w 584.2 584.2 WR2300 widthh 146.05 146.05 WR2300 heightwl 160 160 Input Port lengthc-ow 584.2 to 189 334 Central section-

overall widthcw 89 69.4 Central ridge

widthcl 321.7 315 Central ridge

lengthcg 22.2 to 1.55 11.5 Central ridge gapch 146.05 to 35 64 Central ridge

heightew 89 89 End ridge widthe-ow 189 189 End section-

overall widtheg 1.55 1.55 End ridge gapeh 35 35 End ridge heightel 20 20 Output port

lengthsw 89 — Starting ridge

widthsl 10 — Starting ridge

lengthsg 15.65 — Starting ridge

gap

R. Kumar et al. / Nuclear Instruments and Methods in Physics Research A 736 (2014) 99–106100

Finally, the variation of return loss at 352.2 MHz with WR2300width and height are simulated by varying the dimensions in stepsof 71.0 mm. The plots are shown in Figs. 7(a) and 8(a) respectively.The corresponding plots for the minimum return loss frequency areshown in Figs. 7(b) and 8(b). It can be seen that the return lossdeterioration is slightly more in tapered ridge waveguide as com-pared to straight ridge. However, the return loss still remains betterthan �25 dB in a tapered ridge.

2.2. Random and systematic dimensional variations

Considering the fact that a tapered ridge coupler is lesssensitive to the most of the dimensional changes, both randomand systematic changes were applied to the parameters as given inTable 2. All the parameters were changed by 71.0 mm except theend ridge and central ridge gap. The ridge gaps were changed by70.2 mm during this simulation. These changes correspond to

Fig. 2. (a) CST MWS simulation model of straight coupler and (b) simulation model of tapered coupler with meshing.

Dimensional variation in mm

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0

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Ret

urn

loss

(dB

)

[Ref. 4]-End ridge gap (eg)

End ridge gap-Tapered Ridge (eg)

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Freq

uenc

y (M

Hz)

Dimensional variation in mm

Ref[4] End ridge gap (eg) End ridge gap (eg)

Fig. 3. (a) Variation of return loss at design frequency (of 352.2 MHz) with end gap changes and (b) corresponding minimum return loss frequency variation.

348

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Dimensional variation in mm -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

Dimensional variation in mm

[Ref.4] Central ridge gap (cg) Central ridge gap (cg)

Fig. 4. (a) Variation of return loss at design frequency (of 352.2 MHz) with central gap changes and (b) corresponding minimum return loss frequency variation.

R. Kumar et al. / Nuclear Instruments and Methods in Physics Research A 736 (2014) 99–106 101

random and systematic variation no. 6 as given in [4].We can seefrom Table 2 that the variation of return loss and frequency ismuch less in the tapered coupler than a straight ridge coupler.

It should be noted here that only maximum shift is consideredhere because for smaller dimensional shifts, the return loss oftapered ridge doesn’t deteriorate beyond �20 dB.

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Ref[4] Central ridge width Central ridge width (cw)

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Dimensional variation in mm

Ref[4]Central ridge width

Central ridge width (cw)

Fig. 5. (a) Variation of return loss at design frequency (of 352.2 MHz) with central ridge width changes and (b) corresponding minimum return loss frequency variation.

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Dimensional variation in mm

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Central ridge length (cl)

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Ref[4]-Central ridge length

Central ridge length (cl)

Fig. 6. (a) Variation of return loss at design frequency (of 352.2 MHz) with central ridge length changes and (b) corresponding minimum return loss frequency variation.

351

351.25

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Dimensional variation in mm

Ref[4] WR2300 width

WR2300 width (w)

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Dimensional variation in mm

Ref[4] WR2300 width WR 2300 width (w)

Fig. 7. (a) Variation of return loss at design frequency (of 352.2 MHz) with WR 2300 width changes and (b) corresponding minimum return loss frequency variation.

R. Kumar et al. / Nuclear Instruments and Methods in Physics Research A 736 (2014) 99–106102

2.3. Transmission phase and insertion loss

Amplitude and phase balance are also important parameters inmultiple coupler based cavity systems as the cavity acts as a powercombiner in such applications [9]. Hence, a comparative study wascarried out to study the effect of dimensional changes on thetransmission phase and insertion loss. Insertion loss is also impor-tant for thermal management in high CW power applications.

As the return loss is quite sensitive to the end gap and centralridge gap, the corresponding study for transmission phase wasalso made. The plots for phase shift with end gap and central ridgegap are given in Fig. 9(a) and 9(b) respectively. Similarly, plots forthe phase shift with central ridge length variation are given inFig. 10.

It can be observed from Fig. 9(a) that the transmission phaseshift is more for the tapered ridge as compared to the straightridge in case of end ridge variation. However, as can be seen fromFigs. 9(b) and 10, the phase shift is lesser in a tapered ridge couplerfor central ridge gap and central ridge length variation.

The insertion loss for the tapered ridge coupler is found usingthermal loss calculations available in post processing module ofCST-MWS. It is found to be 0.135% of input power for tapered ridgecoupler. The corresponding value for the straight ridge coupler is0.155%.

3. Comparison of return loss bandwidth

A comparative study on return loss bandwidth shows that thetapered ridge coupler has more bandwidth than the straight ridgecoupler. The return loss plots for the straight ridge and the taperedridge coupler are given in Fig. 11. We can see that the bandwidthfor a tapered ridge coupler is more than the straight ridge coupler.The �20 dB return loss bandwidth of tapered coupler is found to

be 11.26 MHz (i.e 3.2% of 352.2 MHz) whereas it is 4.03 MHz(1.14%) for the straight ridge coupler. The transmission phase shift(i.e S21 phase) in the tapered ridge coupler is only 1.34 deg/MHzwhereas it is 3.05 deg/MHz for the straight ridge coupler.

4. Electric and magnetic field distributions

The electric and magnetic field distributions were obtainedfrom the time domain solver of CST-MWS at 352.2 MHz. The plotof electric field distribution is shown in Fig. 12(a) whereas mag-netic field distribution is shown in Fig. 12(b). We can see fromFig. 12(a) that the electric field is almost constant along the centralregion of tapered coupler whereas the magnetic field is varyingalong the coupler length. This is clearly evident from line plots ofFig. 13. These plots are obtained from CST for 1 W of input power.We can observe from Fig. 13(a) that electric field is much lower inthe central region of the tapered coupler as compared to thestraight ridge coupler. Also, the magnetic field intensity is lesser inmost of the central region of the tapered coupler as shown inFig. 13(b). In fact, this results in lower RF losses in tapered couplerthan the straight ridge coupler.

5. Comparison of multipacting behavior

Tapered ridge couplers are prone to multipacting problems [7].However, it will be important to briefly discuss the multipactingbehavior of straight ridge and tapered ridge couplers. Multipactingscaling laws described in [10] have been used by many researchersincluding [11] for coaxial lines and [12] for rectangular waveguides. Ingeneral, two side multipacing power levels in coaxial and rectangularwaveguides scales as f 4d4, where ‘f’ is the frequency and ‘d’ is the gapbetween multipacting surfaces. Recently, scaling laws have beenreported for multipacting onset in ridge waveguides as well [13].We have used the scaling laws for ridge waveguides reported in [13]to carry out multipacting comparison. The design frequency of352.2 MHz is considered for this comparison.

As the straight coupler consists of rectangular waveguide inputand two ridge waveguide sections (central ridge and end ridge),there should be three distinct power levels at which multipactingcan start. In the tapered ridge waveguide, central ridge gap changesalong the length and hence multipacting onset will have manypower levels. Such behavior has also been observed in tapered ridgewaveguide couplers [7].

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Ref[4] WR2300 height WR2300 height (h)

Fig. 8. (a) Variation of return loss at design frequency (of 352.2 MHz) with WR 2300 height changes and (b) corresponding minimum return loss frequency variation.

Table 2Simulations for random and systematic dimensional changes.

Random/systematicshift number

Taperedcoupler returnLoss (dB)

Straight ridgecoupler returnLoss (dB) [4]

Tapered ridgefrequency(MHz)

Straight ridgefrequency(MHz) [4]

Randomshift 6

�18.68 �13.61 353.14 348.01

Systematicshift 6

�20.9 �16.99 353.3 349.3

R. Kumar et al. / Nuclear Instruments and Methods in Physics Research A 736 (2014) 99–106 103

The multipacting onset levels for the straight ridge and taperedridge are calculated using scaling laws given in [13]. For straightridge coupler, multipacting onset voltage is estimated to be around55 V and 300 V for end ridge and central ridge respectively. Thecorresponding power levels are calculated by CST-MWS port

simulation with 1 W input power for end ridge and central ridgesections. As the end ridge and central ridge gaps are known, thevoltage levels can be estimated from electric field plots of Fig. 13 (a).The voltage level for 1 W input varies from 25.3 V to 2.3 along thecentral ridge section of straight ridge coupler. Similarly, it variesfrom 17 V to 2.8 V in the central ridge section for tapered coupler.Hence, corresponding power level for multipacting voltages levelscan be calculated. For input rectangular waveguide, reported datafor 16 in. by 9 in. waveguide at 476 MHz [12] is used for scaling toWR2300 half height waveguide. The calculated multipacting onsetpower levels are summarized in Table 3.

We can observe from Table 3 that multipacting onset takes placein the end ridge section at very low power level of .38 kW in bothcouplers as end ridge is same. The multipacting onset in centralsection takes place at power levels of .57 kW and .38 kW in straightridge and tapered ridge coupler respectively. Multipacting onset incentral section moves toward end ridge side as the power level isincreased up to 17 kW in straight ridge coupler. This behavior will bemore complex in central ridge section of tapered coupler becauseonset voltage also decreases with gap. The multipacting onset takesplace in rectangular waveguide input of couplers at 22.4 kW.

From these studies, we can conclude that both couplers areequally prone to the multipacting onset. As the couplers areexpected to work at high power levels of 250 kW, both designswill suffer from multipacting. RF conditioning will be required toachieve designed power levels. Prediction of higher order multi-pacting levels in these couplers will need further numerical andexperimental studies.

6. Conclusion

The tapered ridge transition is compared with the straightridge transition for power couplers of accelerator cavities. The EManalysis results for the return loss and the frequency variation arereported for tapered coupler and compared with the straight ridgecoupler. The insertion losses, sensitivity of transmission phaseshift with dimensions and frequency, return loss bandwidth,local field enhancements and multipacting comparison are alsoreported. It is found that the tapered coupler has some desirablecharacteristics like lower RF losses, higher return loss bandwidth,lower variation in phase and lower fields in the central region.However, because of the simplicity of the straight ridge design and

130 132 134 136 138 140 142 144 146 148 150 152 154

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Tra

nsm

issio

n Ph

ase

(deg

rees

)

Dimensional variation in mm

Ref[4]central ridge length central ridge length (cl)

Fig. 10. Variation of transmission phase at design frequency (of 352.2 MHz) withcentral ridge length changes.

Frequency (GHz)Fig. 11. Return loss and transmission plots for straight ridge coupler and taperedridge coupler.

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central gap (cg)

Fig. 9. (a) Variation of transmission phase at design frequency (of 352.2 MHz) with end gap changes and (b) corresponding variation of transmission phase with central gapchanges.

R. Kumar et al. / Nuclear Instruments and Methods in Physics Research A 736 (2014) 99–106104

the proposed tuners by the author's for straight ridge couplers inearlier work, the straight ridge transition still remains an attractivechoice. The reported studies will help the RF power coupler

designers in choosing the desired ridge waveguide based couplingstructures for accelerator cavities.

Acknowledgments

Authors would like to thank Dr. S. Kailas, ex-director PhysicsGroup and Dr. S.L Chaplot, director Physics Group BARC for theirkeen interest in the research efforts towards development of RFpower couplers at IADD, BARC. Authors would also like to thankDr. M.S. Bhatia (L&PTD, BARC ) and Dr. S.R Jain (NPD, BARC) foruseful discussions. Authors are grateful to reviewers for usefulcomments and suggestions.

Fig. 12. (a) Electric field arrow plot for tapered ridge coupler and (b) magnetic field arrow plot for tapered ridge coupler.

Distance along the coupler (mm) Distance along the coupler (mm)

Fig. 13. (a) Variation of electric field (V/m) along the coupler length for tapered and straight ridge coupler and (b) corresponding plots for magnetic field intensity (A/m).

Table 3Comparison of multipacting power levels.

Couplertype

Multipacting onsetpower level inrectangular WG (kW)

Multipacting onsetpower level in centralridge WG (kW)

Multipacting onsetpower level in endridge WG (kW)

Straightridge

22.4 .57–17 .38

Taperedridge

22.4 .38–17 .38

R. Kumar et al. / Nuclear Instruments and Methods in Physics Research A 736 (2014) 99–106 105

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