диафрагмированные волноводные фильтры / 54444bb5-66c9-4cc2-881f-2c8c2062538b

Design of waveguide bandpass filter based on nonresonating ‘T’ junctions

Q.F. Zhang and Y.L. Lu

A design method for waveguide bandpass filters based on nonresonating ‘T’ junctions is presented. The wideband characteristics of the nonresonating waveguide ‘T’ junction are fully considered in the design method. As a design example, a four-pole waveguide bandpass filter with about 6% fractional bandwidth has been designed and fabricated. The measured results agree well with the calculated results and it shows good in-band equal ripple performance and sharp rejection performance.

Introduction: Elliptic filters are designed according to three slightly different approaches. Cross-coupled resonator filters [1] are well known as the first approach, in which the generation of the real transmission zeros (TZs) often requires coupling coefficients of mixed signs. The second approach, known as the extracted pole technique [2], was a breakthrough allowing individual control of the TZs. However, the extracted pole technique has its drawbacks in that the assumed constant phase shifts in the main line are not readily realised or even adequately approximated except for narrowband applications. Recently some flexibility has been added with the concept of nonresonating nodes (NRNs) [3, 4]. The phase shifts in the main line of the filter are eliminated and replaced by constant reactance to reduce the effect of dispersion. In waveguide filter applications, the nonresonating nodes are usually realised by H-plane or E-plane ‘T’ junctions. However, the ‘T’ junction cannot be regarded as a purely series or parallel node in a wide frequency band. Therefore, the dispersion effect of the ‘T’ junction should be considered in the design of wideband waveguide filters. This Letter explores the application of the NRNs technique to the design of waveguide filters in a wider frequency band. The wideband characteristics of the ‘T’ junction are fully considered in the design.

Fig. 1 Routing diagram of four-pole filter, and realisation of resonator using ‘T’ junction

a Routing diagram

b Realisation of resonator

a b

Fig. 2 Equivalent circuit of waveguide ‘T’ junctions

a Exact form

b Reduced form

Filter design: Fig. 1a shows the routing diagram of a four-pole canonical filter. For simplicity, we assume it is symmetrical and has two symmetrical second-order TZs in the response. We combine every nonresonating node and its adjacent resonating node as one resonator, which is realised by an E-plane ‘T’ junction combined with an impedance inverter and a transmission line, as shown in Fig. 1b. The equivalent circuit of the E-plane waveguide ‘T’ junction is shown in Fig. 2a [5]. If the reference planes of port 1 and port 2 are chosen properly, the two parallel immittances at port 1 and port 2 are close to zero and can be neglected. Therefore, we can get the reduced form of the equivalent circuit as shown in Fig. 2b. The components in the equivalent circuit are calculated from the admittance matrix of the three-port ‘T’

junction and they are all considered as frequency-dependent components. The normalised series impedance of the resonator, as shown on the left side of Fig. 1b can be expressed as

where mi,i+1 is the coupling coefficient between the resonating node and the nonresonating node, xi is the series reactance of the nonresonating node, and xi+1 is the TZ. The normalised series impedance of the realised structure on the right side of Fig. 1b can be expressed as

where Z0 is the characteristic impedance of the waveguide. So the mapping function for the transformation as shown in Fig. 1b can be expressed as

zi(−1) = Zi(v2)

where v0, v1 and v2 are the central angular frequency, upper edge angular frequency and lower edge angular frequency, respectively. A slit-coupled waveguide ‘T’ junction as shown in Fig. 3a is employed and an efficient mode-matching program is employed to calculate the admittance matrix of the waveguide ‘T’ junction. By changing the slit parameters, the admittance of the ‘T’ junction can be adjusted to satisfy the mapping equations (1)–(4) and then the required K parameter and transmission line can be calculated. The configuration of the whole resonator is shown in Fig. 3b.

a b

Fig. 3 Configuration of ‘T’ junction and resonator

a Slit-coupled waveguide ‘T’ junction b Whole resonator

Design example: The series reactance of all the nodes and coupling coefficients between the nodes for the lowpass prototype filter is calcu-

lated as: x1 ¼ x7 ¼ 1.205, x2 ¼ x8 ¼ 2, x3 ¼ x5 ¼ 22.522, x4 ¼ x6 ¼ 22, mS,1 ¼ mL,7 ¼ 1.043, m1,2 ¼ m7,8 ¼ 1.71, m3,4 ¼ m5,6 ¼ 1.829. The waveguide bandpass filter is designed in X-band and Fig. 4

shows the configuration of the four-pole canonical waveguide bandpass filter. Fig. 5 shows the measured results and calculated results using a mode-matching program. It is noted that the measured results agree well with the calculated results and show good in-band equal ripple performance and sharp rejection performance. The fractional bandwidth is more than 6%, which is not a narrowband filter in most cases. It is also interesting to find that there are two TZs in the upper frequency band. This is due to the mutual coupling between the second and third resonators at their resonant frequency (TZ).

Fig. 4 Configuration and fabricated photo of waveguide filter

frequency, GHz

Fig. 5 Calculated and measured scattering parameters of designed filter

Conclusion: A design method for waveguide bandpass filters based on the nonresonating ‘T’ junctions is presented. As a design example, a four-pole waveguide bandpass filter with about 6% fractional bandwidth has been designed and fabricated. The measured results agree well with the calculated results and show good in-band equal ripple performance and sharp rejection performance.

# The Institution of Engineering and Technology 2010

15 March 2010

doi: 10.1049/el.2010.0697

Q.F. Zhang and Y.L. Lu (School of Electrical and Electronics Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore)

E-mail: e070022@ntu.edu.sg

References

1 Atia, A., and Williams, A.E.: ‘New type of waveguide bandpass filters for satellite transponders’, COMSAT Tech. Rev., 1971, 1, (1), pp. 21–43

2 Rhodes, J.D., and Cameron, R.J.: ‘General extracted pole synthesis technique with application to low-loss TE011-mode filters’, IEEE Trans. Microw. Theory Tech., 1980, 28, pp. 1018–1028

3Amari, S., and Rosenberg, U.: ‘Synthesis and design novel in-line filters with one or two real transmission zeros’, IEEE Trans. Microw. Theory Tech., 2004, 52, (5), pp. 1464–1478

4 Amari, S., and Rosenberg, U.: ‘A third order in-line pseudoelliptic filter with a transmission zero extracted at its center’, IEEE MTT-S Int. Microw. Symp. Dig., June 2004, pp. 459–462

5 Marcuvitz, N.: ‘Waveguide handbook’ (IEE, London, UK, 1986)