диафрагмированные волноводные фильтры / 6e4d641b-f0c7-4d05-abc2-e2264161bc1f

In spite of its low loss and superior power handling capability, the waveguide filter cannot have broad bandwidth due to the strong frequency dependence of the reactance values for coupling of the cavity resonators and the guide wavelength. To achieve a broadband design of the iris-coupled waveguide bandpass filter with the Chebyshev function as the transfer function, the susceptance value of the inductive iris is optimized by specifying the ideal zero frequency of the reflection. Based on this method, a diplexer is trial fabricated and a broadband diplexing characteristic is realized. In addition, agreement with numerical results is demonstrated, confirming the effectiveness and validity of the method. The tested diplexer has a VSWR of less than 1.24 and an isolation of more than 53 dB at passband bandwidths of 32 and 7% relative to the wavelength. © 2000 Scripta Technica, Electron Comm Jpn Pt 2, 83(7): 59ñ67, 2000

Key words: Waveguide filter; diplexer; optimization; iris susceptance; broadband.

In satellite communication, the need for a broadband antenna feed system is increasing in connection with requirements for expansion of communication capacity and for system flexibility. In the diplexing circuit of the feed systems of the satellite-borne or ground station antennas, waveguide bandpass filters or diplexers made of combinations of these are widely used due to their low loss and good power handling characteristics [1, 2]. However, it is difficult to obtain broadband waveguide bandpass filters since the frequency dependence of the reactance values for coupling of cavity resonators and the guide wavelength are significant. Of the waveguide bandpass filters, those capable of a relatively broad bandwidth include the stub-type waveguide bandpass filter, the E-plane waveguide bandpass filter, and the iris-coupled waveguide bandpass filter [3ñ5]. A passband width of 20% has been reported for the stubtype waveguide bandpass filter, which is large in size and requires delicate fabrication. On the other hand, the E-plane waveguide bandpass filter and the iris-coupled waveguide bandpass filter have good manufacturability and are suitable for size reduction. However, in the previous design method, in which the element values of the equivalent circuit are determined at the center frequency, the return loss is degraded at the passband edge frequencies if the relative passband width is more than 10%. One design

© 2000 Scripta Technica

method taking account of the entire passband characteristic involves the use of an optimization method in which the equivalent circuit and the physical dimensions are determined in such a way that the desired frequency characteristic is obtained [3, 6]. However, in the previous examples of optimization, the frequencies to be selected and the number of points used to specify the characteristic cannot be determined uniquely. Depending on the settings of these frequencies and the performance function, the desired converged solution may not be obtained or a large computation time may be required.

In this paper we propose a broadband design method that optimizes the susceptance of the inductive iris so that the reflection zero frequency of the ideal bandpass filter derived from the frequency transformation from the lowpass prototype filter coincides with the reflection zero frequency of the filter to be designed. In the present design method, the deviation of the reflection zero frequency in the return loss characteristic from the ideal value is compensated by the optimization of the susceptance of the iris. In this method, the selected frequency is determined uniquely and a convergent solution can be obtained within a short time. The computed filter characteristic based on the optimized parameters approaches the original Chebyshev characteristic. Further, an equivalent circuit that is suitable for the design of a thick inductive iris is proposed. By accurately determining the physical dimensions of the element values in this circuit by mode matching, the filter analysis and design are made more accurate. In the following, the configuration of the iris-coupled waveguide bandpass filter and the broadband design method with idealization of the reflection zero frequencies are described. Next, an accurate analysis by the mode matching method that is suitable for the actual filter shape is presented. Further, a broadband diplexer without a need for tuning is fabricated for the Ku band and the effectiveness and validity of the present method are confirmed.

2. Filter Structure

The iris-coupled waveguide bandpass filter structure is shown in Fig. 1. In a rectangular waveguide, inductive irises are placed at intervals of about 1/2 wavelength so that a cavity resonator is formed between adjacent inductive irises in the waveguide. The resonant mode of the cavity resonator is TE101. The amount of coupling between resonators is controlled by the size of the inductive iris. In order to allow high-precision machining by NC machines, the corners between the iris and the waveguide are rounded. In order to attempt broadband, adjustment-free operation of the filter in Fig. 1, a high-precision analytical design including the effect of the thickness and the rounded corners of the inductive iris is needed.

Fig. 1. Iris-coupled waveguide bandpass filter.

3.Design Method

3.1.Equivalent circuit

In general, in the design of a waveguide bandpass filter with inductive irises based on the equivalent circuit, frequency transformation of the low-pass prototype filter and equivalent transformation of the circuit are carried out to yield the ideal bandpass filter consisting of lumped elements [4]. Figure 2 shows an ideal bandpass filter. Next, an equivalent circuit is given for the actual filter structure and the element values of the equivalent circuit are determined such that the characteristic coincides with that of the ideal filter at the passband center frequency. The equivalent circuit of the iris-coupled waveguide bandpass filter is shown in Fig. 3. This circuit consists of transmission lines corresponding to the cavity resonators and parallel susceptances corresponding to the inductive irises. The equivalent circuit shown in Fig. 3 is proposed for the inductive iris. This circuit has transmission lines with an electrical length of fi / 2 and with the propagation constant equal to that of the input and output waveguides on both sides of the parallel susceptance Bi. Since the iris has a nonzero thickness, the reference plane at which the input admittance of this iris appears to be a pure susceptance exists inside the

Fig. 2. Ideal bandpass filter.

Fig. 3. Equivalent circuit of iris-coupled waveguide bandpass filter.

(3)

(4)

Then, fi is the electrical length of the i-th iris in the equivalent circuit at the center frequency.

The parallel susceptance Bi0 of the iris at the center frequency is given by [8]

iris surface. In this equivalent circuit, the section from the reference plane to the iris surface is approximated by a transmission line with an electrical length of fi / 2. By letting the propagation constant of this transmission line be identical to that of the waveguide, the electrical length fi obtained in the design can be used directly as the variation of the electrical length of the adjacent cavity resonator. If the iris is sufficiently thin, the susceptance Bi is given by [7]

Here, Y0 is the characteristic admittance of the waveguide, a is the waveguide width, lg is the guide wavelength, and d is the iris size. The electrical length fi is a function of the iris thickness. The values of Bi and fi of an iris with nonzero thickness can be derived by electromagnetic field analysis such as the mode matching method.

Next, the LC series resonant circuit in Fig. 2 can be expressed approximately in terms of a 1/2 wavelength cavity resonator near the resonant frequency [8]. Then, the electrical length Q0t between the adjacent parallel induc- tances Li,i 1 and Li,i 1 is

(1)

Similarly, the electrical length Qi between the adjacent parallel susceptances Bi and Bi 1 is

(2)

In order for the circuits in Figs. 2 and 3 to be equivalent near the resonant frequency, it is necessary that Q0i in Eq. (1) and Qi in Eq. (2) be equal at the passband center frequency of the filter. From this condition, the electrical length qi0 of the cavity resonator at the passband center frequency of the filter is given by

61

(5)

where gi is the element value of the low-pass prototype filter, lg1 and lg2 are the guide wavelengths at the lower bound and upper bound of the passband of the filter, and lg0 is the guide wavelength at the center frequency of the passband.

3.2.Broadband design by reflection zero correction

In the waveguide bandpass filter using inductive irises, the frequency dependence of the susceptance of the iris and of the guide wavelength in the cavity resonator is strong. Therefore, in broadband operation, the characteristics of the equivalent circuit degrade significantly from those of the ideal filter at the passband edges.

Figure 4 shows the computed return loss characteristics of an 11-stage Chebyshev bandpass filter with 0.01 dB ripple. In the figure, the solid line indicates the characteristic of the waveguide bandpass filter represented by the equivalent circuit in Fig. 3 while the dotted line indicates the characteristic of the ideal filter in Fig. 2. Since the passband is wide with a 32% bandwidth to wavelength ratio, the characteristic indicated by the solid line has greater reflection at the passband edges. In the following, a method is presented for improving this return loss.

The insertion loss LA of the Chebyshev low-pass prototype in the passband is given by [8]

(6)

Fig. 4. Calculated reflection characteristics of bandpass filter (before compensation for iris susceptance).

where n is the number of stages of the resonators, H is the inband ripple, wc is the angular frequency, and wg1 is the cutoff angular frequency. From Eq. (6), the zero angular frequency wgp of the return loss of the low-pass prototype filter is

(7)

Also, in the case of the waveguide filter, the frequency transformation from the low-pass filter to the bandpass filter is given by [8]

(8)

From Eqs. (7) and (8), the guide wavelength lrgpm of the ideal reflection zero in the waveguide bandpass filter is given by

(9)

The frequency obtained from Eq. (9) is specified as the reflection zero frequency and the susceptance of the iris is corrected by an optimization method. As the optimization method, the conjugate gradient method [9] is used. The constraint is the return loss at the specified reflection zero frequency, and the initial susceptance is that used in the

Fig. 5. Calculated reflection characteristics of bandpass filter (after compensation for iris susceptance).

calculation of the characteristic indicated by the solid line in Fig. 4. The computed return loss characteristics of the filter with corrected susceptance values are shown in Fig. 5. Here, the design specifications, transfer function, and number of stages of the filter are identical to those in the corresponding filter in Fig. 4. In the figure, the solid line is the characteristic after correction and the dotted line is that before correction. By specifying the frequencies corresponding to the guide wavelength at the ideal reflection zeros as the zero frequencies, the return loss characteristic is significantly improved and the ripples are kept almost constant.

3.3.Analysis of the inductive iris by the mode matching method

Bi and fi in the equivalent circuit of the inductive iris shown in Fig. 3 can be computed accurately by deriving the scattering parameters of the iris by the mode matching method [3]. The inductive iris without rounded corners is formed of steps in the width direction of the waveguide and a narrow waveguide section in between (Fig. 6). Hence, when the scattering parameters for each mode at each step are derived and are connected for all of the modes in the expansion by using the scattering parameters of the waveguide section between the steps, the scattering parameters of the iris can be computed.

The configuration of the step is shown in Fig. 7. Since irises symmetric with respect to the waveguide axis are considered as the final objects of analysis, the structure of the step is symmetric with respect to x A1/2. When Port 1 is excited with the TEn0 mode, the transverse components of the electromagnetic field scattered at the step include only the y component of the electric field and the x compo-

Fig. 6. Inductive iris without rounded corner.

where w is the angular frequency, P0 is the free space permeability, H0 is the free space permittivity, and B is the waveguide height. Similarly,

Region (2):

(14)

(15)

nent of the magnetic field. Therefore, the electromagnetic fields in Regions (1) and (2) can be expressed in terms of superposition of the modal functions of TEn0 modes in the waveguide for each section. In the expansion with N modes, they are

Region (1):

(10)

(16)

(17)

where km1 is the propagation constant, Gm1 is the normalization coefficient, Fm1 and Bm1 are the coefficients of the modal functions, and A1 is the width of Region (1). Here, km1 and Gm1 are given by

(12)

(13)

(18)

(19) Substituting Eqs. (10) and (14) into (18), and Eqs. (11) and (15) into (19), then applying the Galerkin method, we obtain

(23)

We can rewrite Eq. (20) as

(24)

in which S11, S12, S21, and S22 are the step scattering parameters, given by

(25)

Next, let us derive the scattering parameters of the inductive iris by using the scattering parameters of the step. In Fig. 6, let P be the scattering parameters of the step between Regions (1) and (2), and let Q be those of the step between Regions (2) and (3). The following is assumed:

(26)

(27)

Further, let the scattering parameters of the waveguide in Region (2) be

(28)

where

Then, from Eqs. (26) to (28), the scattering parameters of the entire iris are given by

where S11 i , S12 i , S21 i , and S22 i are N u N matrices. The Sij i m, n component indicates the scattering parameter given as the output of the TEm0 mode at output port i when input port j is excited by the TEn0 mode.

The calculation of the scattering parameters of the single iris with rounded corners can be carried out by applying the mode matching method described above after the staircasing approximation of the circular arc with several steps is invoked. The staircasing approximation of the circular arc is shown in Fig. 8. Here, the x coordinate of the circular arc is equally divided and the step shapes are determined such that the centers of the steps are on a circular arc with radius R. The number of divisions of the circular arc in the z direction is NR.

3.4.Convergence of the numerical results by the mode matching method

For the analysis of a single iris without rounded corners by the mode matching method, the convergence of the amplitude |S11| of the reflection coefficient versus the number of modes N is shown in Figs. 9 and 10. In Fig. 9 the iris thickness L is the parameter, while in Fig. 10 the iris width A2 is the parameter. It is seen that convergence is slower in the case of different thickness L than in the case of different iris width A2. In each case, the variations of the amplitude are less than 0.05 dB for N t 25.

Next, for the single iris with rounded corners, the convergence of the amplitude |S21| of the transmission coefficient versus the number of arc divisions NR is shown in Fig. 11. From the results of Fig. 9, N = 25 is used. For NR t 10, the amplitude variations are less than 0.03 dB and hence convergence is reached.

Fig. 9. Convergence characteristics of |S11| by N. Parameter: L, frequency: 12 GHz, A1 = 19.05 mm, A2 = 9.5 mm.

Fig. 10. Convergence characteristics of |S11| by N. Parameter: A2, frequency: 12 GHz, A1 = 19.05 mm, L = 2.3 mm.

Fig. 11. Convergence characteristics of |S21| by NR. Frequency: 10 GHz, A1 = 19.05 mm, A2 = 9.5 mm, L = 2.3 mm, R = 2.5 mm.

Fig. 12. Equivalent circuit of diplexer.

4. Design of Diplexer Using Broadband

Filters

A design is presented for a diplexer made of two iris-coupled waveguide bandpass filters with different frequency bands joined by a waveguide H-plane T-junction. The equivalent circuit of the diplexer is shown in Fig. 12. The methods of analysis used for the design and characteristic calculation of the diplexer and its relationship to the regions of application are shown in Fig. 13. For filter 1 in the figure, the broadband design method presented in Section 3.2 is applied. The relationship between the iris susceptance and the physical dimensions in filters 1 and 2 is derived by the mode matching method. The rounded corners of the iris due to manufacturing limitations are accurately analyzed by the mode matching method combined with the staircasing approximation. The design and characteristic calculation of the H-plane T-junction are carried out by the boundary element method [10, 11]. A highly accurate

Fig. 13. Relation between calculation tools for analysis and applied region in diplexer.

65

Fig. 14. Photograph of fabricated diplexer.

characteristic calculation is carried out for the diplexer by combining the mode matching method and the boundary element method [12] so that the dimensions of the diplexer are optimized.

5. Experimental Results

According to the design procedure shown in Section 4, a diplexer using Chebyshev bandpass filters with 11 and 4 resonators in the Ku band was fabricated. For the 11-stage filter, the broadband design method described in Section 3.2 is applied so that the passband is widened. A photograph of the tested diplexer is shown in Fig. 14. The insertion and return loss characteristics are shown in Fig. 15, where the solid line indicates the measured values and the dotted lines indicate the calculated results. The computed frequency

Fig. 15. Frequency characteristics of fabricated diplexer.

characteristics agree very well with the measured data. The VSWR of the test diplexer is less than 1.24 and the isolation between the ports is more than 53 dB at passband sizes of 32 and 7% relative to the wavelength regions.

6. Conclusions

For the iris-coupled waveguide bandpass filter with a Chebyshev function as its transfer function, ideal reflection zero frequencies are specified. A broadband design procedure based on correction of the iris susceptance by optimization was presented. By using this method, a Ku band waveguide diplexer with passband bandwidths of 32 and 7% relative to the wavelength was realized and the effectiveness of the present design method was demonstrated. The computed values and the measured results were found to agree well, so that the validity of the method is confirmed.

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