W-band sharp-rejection bandpass filter with notch cavities

Chen Zhenhua Xu Jinping

(State Key Laboratory of Millimeter Waves， Southeast University， Nanjing 210096， China)

E-plane waveguide filters have been widely used at millimeter-wave frequencies for realizing low insertion loss，low cost and mass producible microwave configurations［1-4］.While used in electronic systems operating at higher millimeter-wave frequencies，the functional modules ofthe systems are usually assembled with waveguide interfaces，so these kinds of filters are easy to be integrated with other components without any further transition structures.

In a heterodyne receiver system，isolation between the radio frequency(RF)and the local oscillator(LO)is critical to the sensitivity and dynamic range of the receiver.High-isolation performance is usually realized by a filter with a high stopband suppression level.Furthermore，many multi-channel or diplexer applications require filters with sharp cut-off characteristics.To increase the steep attenuation slope，positioning transmission zero close to the cut-off frequency is more convenient than increasing the order of the filter，which will increase the size and insertion losses.In Ref.［5］， a folded cross-coupling configuration is adopted to produce transmission zeros and the out-of-band rejection performance can be locally improved by selectively positioning transmission zeros.In Ref.［6］， a 3-order E-plane filter compatible with the split-block housing E-plane topology is proposed to produce sharp higher frequency roll-off by implementing a transmission zero.However， these involved structures are metal-insert E-plane filters which are difficult to machine precisely at W-band(75 to 110 GHz).

Although E-plane fin-line filters have higher machining precision than the metal-insert type，they are still difficult to suppress the frequency points which are very close to the passband［7］.To achieve better sharp-rejection performance， higher order fin-line filters are required， which will bring more loss and an unrealistic metal strip width.In this paper，we present a low-order E-plane fin-line filter with sharp-rejection characteristics，in which the transmission zeros are introduced by high-Qnotch cavities cascaded with the fin-line structure.By properly choosing the dimensions of the resonators and optimizing the coupling between the cavities and the fin-line structure，the suppression level at the unwanted frequency points near the passband can be greatly improved without disturbing the passband performance.The measured results present good sharp-rejection characteristics while maintaining low cost and simple structure.

1 Notch Mechanism and Coupling Effects between Fin-Line Filter and Notch Cavity

As required by a specific application， a 93.9 GHz center frequency， a 1 GHz passband bandwidth， a less than 3 dB passband insertion loss and a more than 75 dB suppression from 91.6 GHz to 91.8 GHz are specified for the filter design.

The proposed filter is composed of a 5-order E-plane fin-line filter and high-Qnotch cavities.The notch mechanism and the coupling effects between the fin-line filter and the single-notch cavity are investigated.The final prototype filter is fabricated with double-notch cavities，which will be demonstrated in section 2.

The design approach of the conventional fin-line filter proposed by Konishi［8］is relatively mature and adopted in our filter design.The fin-line structure is realized with a standard WR10 waveguide(a=2.54 mm，b=1.27 mm)and a 5-mil-thick RT/Rogers 5880 substrate(εr=2.2).Its layout and dimensions are summarized in Fig.1 and Tab.1， respectively.

Tab.1 Dimension of the fin-line structure mm

The notch characteristic is introduced by a high-Qcavity resonator［9］， which is shaped by two-side step E-plane extensions of a standard rectangular waveguide.The extension section is designed as a dual mode cavity，which supports the first and the second distinct electromagnetic modes of propagation.The dual mode cavity has a cut-off frequency less than the operating frequencyf0for the second mode，while the WR10 waveguide has a cut-off frequency greater thanf0for the second mode.Its partial view is depicted in Fig.2.

Fig.2 Partial view of the single-notch cavity

As the incident wave in the form of the fundamental mode TE10propagates into the extension section，a part of this mode will be converted into the second higher mode TE11(Here， the simplest case is considered， so the degenerate mode of TE11and the other higher order modes are not explained in detail).Upon reaching the other end of the dual mode cavity，most of the energy in the second mode will be reflected back through the dual mode section，while a small portion will be reconverted into the field pattern of the first mode.By adjusting the parameters of the dual mode section，it may be made resonant atf0in the second mode，and that portion of the second mode atf0which is reconverted into the first mode will be precisely equal in amplitude and oppositely phased to that portion of the wave energy atf0which has remained in the form of the first mode.Thus， transmission atf0in the first mode is nullified.It is noteworthy that the conversion from TE11to TE10will not occur while the extension is symmetric， i.e.，w1=w2.This can be concluded from the Fourier transform of the incident wave in the form of TE10that，the second mode TE11will not exist in the expansion equation when the extension section is symmetric， therefore， the coupling between the first mode and the second mode is absent.

Fig.3 gives the variations of notch frequency(frequency corresponding to maximum reflection)vs.different combinations ofw1andw2.It can be found that notch frequency decreases asw1+w2increases，and the singular points exist whenw1=w2，which is due to the absence of coupling.

Fig.3 Variations of notch frequency vs.different w1and w2

The initial values of the notch cavity are chosen as follows:L=2.15 mm，w1=0.5 mm，w2=0.75 mm.Thus，the resonant frequencyfrof the second mode TE11is 91.7 GHz， and the unloaded quality factorQof the notch cavity is 3 750.When the high-Qnotch cavity is cascaded with the fin-line structure，which implies that the cavity is loaded，its quality factorQbecomes a loaded quality factorQL，and it can be estimated by

whereQfin-lineis the quality factor of the fin-line filter structure.The distance between the cavity and the fin-line structure is defined asd.At higher millimeter-wave frequencies，discontinuities between the fin-line filter and the notch cavity are significant，which may have great effects on the filter performance.Therefore， the interaction between the notch cavity and the fin-line filter is investigated to avoid performance degradation.

As shown in Fig.4，QLand the notch frequency change slightly with the increase ind.This means that the notch frequency is relatively independent of the coupling between the cavity and the fin-line filter.It is mainly determined by the dimensions of the notch cavity.In addition，QLdecreases greatly compared to the unloadedQ，and this may decrease the suppression at the notch frequency to some degree.Fig.5 shows the insertion loss over the passband and the suppression at the notch frequency(91.7 GHz)for differentd.It can be found that both inband and out-of-band performance have a great relationship with the valued.In order to maintain the whole structure compact，dshould be as small as possible， but too small adwill lead to serious higher order modes interaction， which will decrease the filter performance.

Fig.4 Loaded quality factor and notch frequency for different distances between notch cavity and fin-line structure

Fig.5 Maximum insertion loss in passband and suppression at notch frequency for different distances between notch cavity and fin-line structure

An optimization is implemented to achieve the technical requirements of the filter and the compact structure size simultaneously，andd=2 mm is chosen for the subsequent design.

Based on the above analysis，a conventional five-order fin-line bandpass filter integrated with a single notch cavity is simulated with Ansys HFSS.Its structure is depicted in Fig.1.Fig.6 shows the comparison of the simulated results of two filters:the conventional E-plane fin-line filter and the proposed filter with a single-notch cavity.It is clearly shown that a notch point is introduced by the proposed single-notch filter， and the suppression at 91.7 GHz and the sharp-rejection performance are greatly improved compared with the conventional filter without disturbing the passband performance.

Fig.6 Comparison results of two type filters

2 Design of Band-Pass Filter with Dual Notch Cavities

As depicted in Fig.6， the notch bandwidth is relatively narrow due to the inherent attributes of the notch cavity，and the frequency offset is sensitive to the machining precision of the notch cavity at W-band.This can be clearly observed from Fig.3.Therefore， sufficient surplus of the notch bandwidth should be reserved to prevent that the desired notch frequency 91.7 GHz deviates out of the notch band.So another notch cavity is added to the former single-notch filter to introduce another notch point and broaden the notch bandwidth.Fig.7 shows a partial view of the proposed double-notch filter.

Fig.7 Partial view of the double-notch filter

These two notch points are designed to deviate properly in order to further extend the notch bandwidth.Instead of cascading the two cavities directly，they are arranged at the input end and output end of the E-plane fin-line filter，respectively.This arrangement can avoid the appearance of spurious Bragg resonances which may occur when the two notch cavities are cascaded directly［10］.

The expansion width of the second notch cavity is the same as that of the first one.The lengths of the two cavitiesL1andL2are adjusted to produce two separated notch frequency points to obtain the desired notch bandwidth.Fig.8 shows the suppression performance of the doublenotch filter for differentL2.L1is fixed to 2.1 mm， so its associated notch frequency is about 91.9 GHz.AsL2becomes larger，the corresponding notch frequency decreases gradually，and the two notch points will overlap whenL1=L2=2.1 mm.The greater the difference betweenL1andL2， the broader the notch bandwidth.All the dimension parameters are summarized in Tab.2.

Fig.8 Simulated suppression of the notch band for different values of L2(L1=2.15 mm)

Tab.2 Dimension of the double-notch cavity mm

3 Experimental Results

The above mentioned double-notch filter has been fabricated and measured. Fig.9 shows the fabricated waveguide block of the bandpass filter.The 5-order finline filter is inserted along the E-plane of the waveguide block，and the two notch cavities are shaped by the E-plane extension of a standard WR10 waveguide.

Fig.9 Fabricated W-band bandpass filter

Measured results depicted in Fig.10 are obtained by a frequency extended Agilent N5254A vector network analyzer(VNA).The minimum measured insertion loss in the passband is 2.6 dB and the return loss is greater than 10 dB from 93.5 to 94.5 GHz.The suppression at 91.7 GHz is more than 85 dB.It can be found that there is some difference between the measured and the simulated suppression near 91.7 GHz.This is partly introduced by the limited dynamic range of the VNA operating in this frequency band and the misalignment of assembly.

Fig.10 Measured and simulated S-parameters of double-notch filter.(a)S-parameters across 90 to 100 GHz;(b)Detailed information of the insertion loss

4 Conclusion

A W-band E-plane waveguide filter employing a conventional fin-line filter structure integrated with two E-plane extended notch cavities is proposed.Taking advantage of the double-mode resonant characteristics of the cavity resonators，the presented filter achieves good sharp-rejection without disturbing the passband performance，and the suppression bandwidth is extended with two separated notch cavities to ensure the desired notch frequencies to be located within the notch band.

A prototype of the filter is designed and tested.Measured results show that the insertion loss is 2.6 dB with about a 1.1%fractional bandwidth at 93.9 GHz， and the suppression achieves 85 dB at 91.7 GHz， which is only 2.2 GHz lower than the center frequency.

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