Effect of Wall Thicknesses on Broadband Design of Ka-Band TE21-Mode Coupler

Wei Zheng| Chao Wang | Wen-Li Yang | Chun-Bang Wu

Abstract—Commonly,the classical formulas are suitable for designing the TE21-mode coupler for the operating frequency under Ka-band by ignoring the wall thickness.However,in practice,for the one operated in the Ka-band,such classical formulas are not valid and the effect of wall thicknesses should be considered.Herein,we propose a design method for the Ka-band TE21-mode coupler via computer simulations,taking into account the wall thickness.The experimental results show that using the linear twice-weighted algorithm to optimize the coupling hole size can improve the coupler performance.And the bandwidth of such coupler increases by 10% with lower coupling loss(<0.5 dB) and higher isolation (>40 dB).

Index Terms—Coupling loss,isolation,TE21-mode coupler,useless hole.

1.lntroduction

In satellite communications,a certain mechanism is needed to track satellites through ground-station antennas.Such mechanism will generate so-called “error signals” whose amplitudes are proportional to the deviations between the pointing direction of the ground station antennas and the actual position of the satellite.

Usually,ground-station antennas with narrow microwave beams are used to communicate with the satellite,and the communications will become worse when the main microwave beam of the antenna is not aligned with the direction to the satellite.Therefore,most of the ground-stations have the tracking ability to point at the satellite.The techniques with the tracking mode,using the TE21mode,has been widely used because of its accuracy and coupling compact characteristics[1]-[4].In the multi-mode horns,a combination of several higher-order modes can be used,but usually only single or two orthogonal TE21and TE11modes(used as communications modes[5]-[9]) are adopted.The TE21mode as a single multi-mode conical horn antenna is used to generate the difference signal[7],[10]-[12].

Classical formulas for designing TE21-mode couplers have a precondition that the waveguide wall thickness (h) can be ignored in the coupling region between the circular and the rectangular waveguides[11]-[17],but only when the wall thickness satisfiesh≤ 0.035λ,whereλis the operating wavelength.When the operating frequency is the Ka-band,the actual waveguide wall thickness cannot meet this requirement.Thus,the classical formulas are no longer applicable,and it is necessary to improve the original coupling distribution or design a new coupling distribution[11],[15]-[18].In this work,the effect of wall thicknesses is investigated to improve the formulas via computer simulations,and a linear twice-weighted algorithm for the coupling hole size is applied to improve coupler performance.And in this paper,the TE21-mode coupler is designed to evaluate the proposed method.As an oriented mode coupler,the TE21-mode coupler is used to couple the circular waveguide’s TE21mode to the rectangular waveguide’s TE10mode.Four coupling arms are jointed through a network to obtain a single TE21-mode coupler.The two TE21-mode couplers then can realize the circular polarization through a 90° hybrid to separate the azimuth and elevation error signals.

2.Methodology

2.1.Design of TE21-Mode Coupler

The simulation for a TE21-mode coupler is carried out to evaluate the energy transmission in the circular waveguide by the Computer Simulation Technology (CST) software.The simulated TE21-mode coupler is shown inFig.1(a).The coupler consists of eight coupling arms and four of them are summed through a network to obtain a single TE21-mode coupler.The formed two TE21-mode couplers are then undertaken to generate circular polarization through a 90° hybrid to separate the azimuth and elevation error signals.Figs.1(b) and (c) present the simulated energy transmission in the circular waveguide designed with the traditional method (ignoring the wall thickness) and the improved method (considering the wall thickness),respectively.Obviously,the energy is transmitted from right to left (Fig.1).And the deeper the red color,the greater the energy.The green indicates that there is no energy.In the traditional mode,the wall thickness is ignored,the energy of the TE21mode is not fully coupled,and some energy is transmitted in the circular waveguide after the coupler,as shown inFigs.1(b) and (d).However,using our improved method,the energy of the TE21mode is nearly fully coupled.After the coupler,no energy transmission exists in the circular waveguide (Figs.1(c) and (e)),indicating that the improved method is more effectively to reduce the useless energy transmission.

Fig.2shows the coupling loss of couplers with different wall thicknesses.As the frequency increases,the wall thickness of the coupling hole also increases with respect to the wavelength.When the diameter of the coupling hole is less than the critical value,the coupling effect will be cut off.Therefore,the coupling waveguide wall thickness has to be increasingly thin as the frequency increases,the design formula of the TE21-mode coupler is still applicable at the high-frequency region,if the waveguide wall thicknessh<0.05λand the bandwidth is relatively narrow[17].However,whenh≥ 0.05λ,the formula fails to apply at the Ka-band or higher band.

2.2.lmproving on Coupling Hole Size

As for a 48-hole coupler (h≥0.05λ,the sampling pointN=24),the coupler requires a 10%-bandwidth increase with <0.5-dB coupling loss and >40-dB isolation.The simulated result shows that the isolation is acceptable under the traditional Bessel distributions[18],but the coupling loss is not satisfied.To realize a required coupling loss,the re-design on the distribution of the coupler is applied.Defining the inefficient coupling holes as useless holes,reducing the number of useless holes is the design goal.

Fig.1.Energy transfer in a TE21-mode coupler (the wall thickness cannot be negligible in practice):(a) TE21-mode coupler,(b) and (d) energy transfer with the traditional method,and (c) and (e) energy transfer with the improved method.Note that the wall thickness is 1 mm at 20 GHz in all CST simulation.

The wavelength range corresponding to the designing frequency band should guarantee that the TE21mode can be transferred and the TE01mode should be cut-off in the main waveguide,thus the radius of the circular waveguide (R) should satisfy

Fig.2.Coupling loss with different h.

whereλLandλHare the lowest wavelength and highest wavelength,respectively.AndR=1.15λL/2.06[19].

So the initial value of the coupling distribution was calculated based on the Bessel distribution,then the additional linear twice-weighted algorithm was used to optimize the coupling hole size to improve coupler efficiency:

whereB(di) is the hole diameter ratio distribution corresponding to the Bessel distribution;diis the hold diameter after using the twice-weighted algorithm;ieis the weighting factor withebeing the weight andidenoting theith hole (i=0,1,2,…).

3.Results and Discussion

The comparison of the coupling-hole size before and after applying the linear twice-weighted algorithm is shown inFig.3.When different distributions are adopted,differences emerge in the relationship between the number of holes and the size of the holes.Adopting the proposed twice-weighted distribution,when the number of holes increases,the size of the coupling holes continues decreasing.In the meanwhile,adopting the Bessel distribution[20],the number of holes increases.However,there is a critical value for the size of the coupling holes shown by the dotted line inFig.3.If the size of the coupling holes is lower than the critical value,the coupling holes become useless.Therefore,whenh ≥0.05λ,using the twiceweighted distribution is a better choice.

In the following experiment,the classical values in [20] are adopted as the sizes of the TE21-mode coupler rectangular waveguide.And the coupling hole size is designed based on the Bessel distribution[20].The simulated curves of TE11-mode isolation and TE21-mode coupling loss are shown inFigs.4(a) and (b),respectively.As the frequency increases,the isolation first decreases and then gradually rises,and there is a minimum value.The coupling loss first increases and then decreases as the frequency increases,and there is a maximum value.The simulation results show that the isolation is acceptable under the traditional Bessel distribution,but the coupling loss is too high (the requirement is shown at the beginning of subsection 2.2).Even with a general predistortion parameter design,the relation bandwidth is difficult to exceed 5%.

Fig.3.Coupling hole size vs.sampling-hole number.

Fig.4.Simulated curves:(a) TE11-mode isolation and (b) TE21-mode coupling loss.

A linear twice-weighted TE21-mode coupler is shown inFig.5.And the TE11-mode isolation and TE21-mode coupling loss using the linear twice-weighted algorithm are plotted inFigs.6(a) and (b),respectively.Similar to the Bessel weighted distribution,the simulation results show that as the frequency increases,the isolation first decreases and then increases,while the coupling loss first increases and then decreases.However,the measured data show that the TE11-mode isolation of the twice-weighted TE21-mode coupler in the whole frequency band is greater than 40 dB,and the coupling loss is always maintained within the range of 0.5 dB.Compared with the coupler using the traditional Bessel distribution,both the isolation and coupling loss satisfy the requirement(as shown at the beginning of subsection 2.2).The test results present that the linear twice-weighted TE21-mode coupler has a 10%-bandwidth increase with <0.5-dB coupling loss and >45-dB isolation,compared with other work[20].

Fig.5.Linear twice-weighted TE21-mode coupler.

Fig.6.Simulated and experimental results of the TE21-mode coupler using the linear twice-weighted algorithm:(a) TE11-mode isolation and (b) TE21-mode coupling loss.

4.Conclusions

A design method for the Ka-band TE21-mode coupler was investigated,and the computer simulation was carried out.A linear twice-weighted algorithm is proposed to optimize the coupling hole size,and the simulation results show that using this algorithm can effectively improve the coupler performance.The designed coupler can achieve a 10%-bandwidth increase with <0.5-dB coupling loss and >45-dB isolation.Although this method is only applied on the design of the TE21-mode coupler,it is also feasible for other coupler designs.

Disclosures

The authors declare no conflicts of interest.