Millimeter-wave coplanar-waveguide parallel-coupled bandpass filters with lumped-element K-inverters

Millimeter-Wave Coplanar-Waveguide

Parallel-Coupled Bandpass Filters With Lumped-Element

K-Inverters

Yo-Shen Lin, Min-Shun Hsu, Chi-Hsueh Wang, and Chun Hsiung Chen

National Taiwan University, Taipei 106, Taiwan, +886-2-23635251-209 Abstract — Compact coplanar-waveguide (CPW)

bandpass filters are proposed, by introducing additional lumped inductor and capacitors to realize K-inverters in the conventional CPW parallel-coupled filter structure for achieving an equivalent to the quarter-wavelength resonator filters. As a result, the filter size may be reduced by about half. In addition, by introducing the cross-coupled effect, two transmission zeros at upper and lower stopbands may be created. Simple equivalent-circuit models are also established as effective design tools. Specifically, two CPW bandpass filters centered at about 40GHz with compact sizes and good selectivity are implemented and carefully examined.

I. INTRODUCTION

Coplanar waveguide (CPW) structure has gain substantial research interests due to the advantages such as lower dispersion and easier to integrate with solid-stated devices [1]. Various works on CPW bandpass filters were reported in the literature, and the parallel-coupled bandpass filters based on quarter-wavelength (O/4) coupled-line sections were widely used for their easy realization in planar circuits, wider range of realizable bandwidths, and simple synthesis procedure [2]. The edge-coupled CPW bandpass filter [3] was designed based on the symmetrical CPW coupled-line sections. The ribbon-of-brick-wall type CPW bandpass filter [4] based on the three-line CPW coupled-line structure may achieve larger amount of coupling thus wider bandwidth. Alternatively, shorted CPW coupled-line sections, or coupled-slots, may also be implemented in CPW bandpass filter design [5]. Compared to their microstrip counterpart, the CPW parallel-coupled bandpass filters have the advantage that the coupled-line impedances are mainly determined by the ratio of strip and slot widths. Therefore, the realizable impedance ranges of CPW coupled-line for a given substrate are larger, which is favorable for designing bandpass filters with wider ranges of 3-dB bandwidth.

In modern communication system applications, it is necessary to have filters with very good selectivity for better image or interference rejection. Therefore, improvements on achieving additional transmission zeros to the conventional CPW parallel-coupled bandpass filters were also reported. In [6], the capactively coupled gap and the O/4 open stubs were adopted for creating two transmission zeros. In [7], the CPW quasi-elliptic

bandpass filters based on stepped-impedance resonators may also achieve good selectivity and compact size.

In our previous works [8]-[10], novel parallel-coupled bandpass filters with additional lumped inductor as K-inverter and cross-coupling effect were proposed to achieve compact size and two transmission zeros. In this study, the 2nd-order filter structure in [8] is adopted for the design of a compact CPW bandpass filter at millimeter-wave frequencies. In addition, a novel 4th-order filter structure is also proposed for achieving better performance and more compact circuit size. Simple design formulas for the proposed filters may also be obtained based on the proposed equivalent-circuit models and the conventional filter synthesis technique.

II. FILTERSTRUCTURES

A. 2nd-order Filter

Shown in Fig. 1(a) is the layout of proposed CPW parallel-coupled bandpass filter of 2nd-order, with its equivalent-circuit model in Fig. 1(b). It is based on two cascaded coupled-line sections of electrical length T1 |

90o _{with an additional shunt inductance L in-between.}

Here the symmetrical CPW coupled-line structure is adopted in Fig. 1(a). The shunt inductor L is realized by a metal strip connected to the ground plane. The inductance value can be adjusted by varying the length and width of the metal strip. In order to suppress the unwanted odd CPW mode, bond-wires at suitable positions are also included. The capacitor Ccross in the

circuit model [Fig.1(b)] represents the gap-coupled capacitance between the open-ends of two adjacent coupled-line sections, which is used to provide a cross-coupled path such that two transmission zeros at the upper and lower stopbands may be created [8].

By noting that the signal through the cross-coupled path is substantially less than the one through the main path [8], the design of proposed filter can be simplified by first letting Ccross = 0 in Fig. 1(b). The

equivalent-circuit model of the filter in Fig. 1(a) can then be obtained as shown in Fig. 1(c). Here the symmetrical CPW coupled-line is modeled by a J-inverter along with two transmission lines of electrical length T1. The shunt

inductor L along with two transmission lines of length I1/2 are modeled by a K-inverter. Therefore, by letting

Ccross= 0 in Fig. 1(b), the equivalent-circuit model of the

resonator bandpass filter as shown in Fig. 1(c). As a result, the filter order is doubled with the additional inductor L compared to the conventional parallel-coupled filter [2]-[6].

As illustrated in [8], the Ccross provides a cross-coupled

path along which the signal would cancel the one traveling along the main path of the filter at two frequencies, such that the overall filter response has two transmission zeros. Typical simulated responses of the filter structure in Fig. 1(b) are shown in Fig. 2. As Ccross

increases with reducing gap width, the two transmission zeros move toward the center frequency f0 at the expense

of decreasing insertion loss in the stopband.

B. 4th-order Filter

Shown in Fig. 3(a) is the layout of proposed 4th-order CPW parallel-coupled bandpass filter with lumped-element K-inverters. The corresponding circuit model is shown in Fig. 3(b). It is based on an extension of the 2nd-order filter in Fig. 1(b) with additional shunt capacitors C1 and transmission line sections introduced at

the input and output ports to realize K-inverters [11]. The small cross-coupling capacitance Ccross is again

introduced for generating two transmission zeros. Compared to the 4th-order parallel-coupled O/4 resonator filter in [10], the proposed filter has the advantage that the cross-coupled capacitance may now be easily achieved by the gap-coupled capacitance without having to bend the two coupled-line sections.

By first letting Ccross = 0 in Fig. 3(b), the

equivalent-circuit model of the filter in Fig. 3(a) can be obtained as shown in Fig. 3(d), which is equivalent to a 4th-order O/4 resonator filter when T1 - I2/2 = T2 - I1/2 = S/2. As a

result, the proposed filter may be simply designed based on the conventional filter synthesis techniques for O/4 resonator filters [12]. Given the desired center frequency, 3dB bandwidth, and reference impedance, one may determine the required values of J- and K-inverters in Fig. 3(d) through the conventional filter synthesis technique. The corresponding circuit parameters in Fig. 3(b) are then obtained from the J- and K-inverter values, with T1= S/2 + I2/2 and 'T = I1/2 - I2/2. The cross-coupled

element Ccross is included later and its value is chosen for

the desired locations of transmission zeros.

As shown in Fig. 3(a), an additional ground line is inserted between the parallel-coupled CPW to reduce the amount of coupling. Therefore, the gap between coupled-lines can be made smaller to avoid large power loss for narrowband designs as in [7]. The shunt inductor in the circuit model [Fig. 3(b)] is now realized by two shunt-connected metal strips to ground, which also connect the two ground planes and the center ground strip. As a Bond wire 2.1mm 0.5mm (a) L C_cross 1 T T1 (Z_0e, Z_0o) (Z_0e, Z_0o) (b) K J J 2 1 1 I T 2 1 1 I T 0 Z Z0 Z0 0 Z (c)

Fig. 1. 2nd-order CPW parallel-coupled filter with lumped-element K-inverter. (a) Layout, (b) circuit model, and (c) equivalent-circuit model to illustrate the equivalence between Fig. 1(a) and the 2nd-order O/4 resonator filter when Ccross = 0 and T1 - I1/2 = S/2. Frequency (GHz) -80 -60 -40 -20 0 10 20 30 40 50 60 70 C_cross=2.5 fF C_cross=1.0 fF C_cross=0.5 fF 21 |( dB) |S (a) 0 10 20 30 40 50 60 70

Upper stopband transmission zero Lower stopband transmission zero

C

(fF)

Frequency (GHz)

0 2 4 6 8 10

f₀

(b)

Fig. 2. (a) Simulated frequency responses of proposed 2nd-order parallel-coupled bandpass filter in Fig. 1(b) for different values of cross-coupled capacitance Ccross. (b) Simulated

relationship between the locations of transmission zeros and the values of Ccross. ( f0=38GHz, Z0e=72.22:, Z0o=38.89:,

result, compared to Fig. 1(a), no bond wires across the coupled-lines are required for this filter structure. The shunt capacitors C1 in Fig. 3(b) are realized by CPW

shunt open-stubs. The length and width of each open stub can be properly chosen for creating one additional transmission zero at the upper stopband when its length reaches a O/4.

Shown in Fig. 4 are the typical simulated frequency responses of proposed 4th-order filter structure in Fig. 3(b). Compared to Fig. 2, the filter selectivity is largely improved due to an increase in filter order. One may suitably choose the value of Ccross for the desired

level of selectivity and stopband rejection.

For the conventional parallel-coupled filter of 4th-order [2]-[6], five cascaded O/4 coupled-line sections are required. On the other hand, for the proposed filter in Fig. 3(a), only two parallel-coupled line sections of approximately O/4 long are needed. Therefore, the size of proposed filter is about half that of the conventional ones of the same order.

III. RESULTS

A CPW bandpass filter for Fig. 1(a) is fabricated on an Al2O3 substrate (Hr= 9.9, thickness h = 0.381mm, tanG =

0.002). The center frequency f0is designed at 38.5 GHz.

The simulation is done by the full-wave simulation tool Ansoft Ensemble. The measured and simulated results are shown in Fig. 5. Good agreement between them is obtained except for some frequency shift. The measured

f0 is at 41 GHz, and the passband insertion loss is about

1.85 dB. Two transmission zeros are observed as expected, which greatly improve the filter selectivity.

The 4th-order CPW filter in Fig. 3(a) is also fabricated on the same Al2O3 substrate. The measured and

simulated results are shown in Fig. 6. The measured insertion loss is less than 2dB from 37 ~ 43 GHz. Two transmission zeros are observed at 32.5GHz and 47GHz. Compared to Fig. 5, better filter selectivity is obtained. Note that the length of the filter in Fig. 3(a) is only a little longer than 2/3O at f0, making it much smaller than the

conventional CPW parallel-coupled filters of the same order. Bond wire 2.5mm 0.93mm (a) C₁ 2 1 I T ' C₁ L₂ Z₀ C_cross 1 T (Z_0e, Z_0o) (Z_0e, Z_0o) 1 T 2 1 I T ' Z₀ Z₀ Z₀ (b) J12 Z0 Z0 J34 0 Z Z0 1 1 C jZ 1 T 2 L jZ 2 1 I 2 2 1 I T  2 I 1 1 C jZ T ' T1 2 T 2 2 1 I T  1 T 2 T 2 1 I T ' 1 T (c) 2 1 2 I T  0 Z Z0 Z0 0 Z 2 2 1 I T  K₂₃ J₁₂ J₃₄ K₄₅ K₀₁ 2 2 1 I T  2 1 2 I T  (d)

Fig. 3. Proposed 4th-order CPW parallel-coupled bandpass filter with lumped-element K-inverters. (a) Layout. (b) Circuit model. (c)-(d) Equivalent-circuit models to illustrate the equivalence between Fig. 3(a) and the 4th-order O/4 resonator filter when Ccross = 0 and T1 - I2/2 = T2 - I1/2 = S/2.

Frequency (GHz) -80 -60 -40 -20 0 10 20 30 40 50 60 70 C_cross=0.5 fF C_cross=1.0 fF C_cross=2.5 fF 21 |( d B ) |S (a) 20 30 40 50 60 0 1 2 3 4 5

C

(fF)

Frequency (GHz)

Upper stopband transmission zero Lower stopband transmission zero

f₀

(b)

Fig. 4. (a) Simulated frequency responses of proposed 4th-order parallel-coupled bandpass filter in Fig. 3(b) for different values of cross-coupled capacitance Ccross. (b) Simulated

relationship between the locations of transmission zeros and the values of Ccross. ( f0=38GHz, Z0e=57.48:, Z0o=44.27:,

Based on the proposed circuit models, the proposed filter structures may be simply extended to realize higher-order filters for better performance. One may also implement the proposed filters using the stepped-impedance resonators for further size reduction as in [7].

VI. CONCLUSION

In this study, two compact CPW parallel-coupled bandpass filters have been proposed and carefully examined. By introducing additional lumped-elements to realize K-inverters, along with the cross-coupled effect, the proposed bandpass filters may achieve about half the circuit area of conventional ones and two transmission zeros at upper and lower stopbands. Based on the proposed equivalent-circuit model and the conventional filter synthesis technique for O/4 resonator filter, the design equations can be simply obtained. The effectiveness of proposed filters for millimeter-wave applications is also demonstrated by measured results.

ACKNOWLEDGEMENT

This work was supported by the National Science Council of Taiwan under Grant NSC 93-2752-E-002-001-PAE and Grant NSC 93-2219-E-002-021.

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Fig. 5. Measured and simulated results for the CPW filter in Fig. 1(a). - 50 - 40 - 30 - 20 - 10 0

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Fig. 6. Measured and simulated results for the CPW filter in Fig. 3(a).