Design Examples and Experiment Results

After achieving the core portion of the parallel-coupled filter, the cross couplings are then applied following the procedures described in [101].

5.4 Design Examples and Experiment Results

Several examples in this section will be implemented using microstrip line. The Rogers RO4003 substrate with a dielectric constant of 3.58 and thickness of 20 mils is chosen for implementations of the filters.

A. The trisection filters corresponding to Figs. 5.1(d) and (h)

The first two examples are two-order modified trisection filters and their coupling scheme is shown in Fig. 5.1(d). The transmission zero is located at Ω=3 for one filter and Ω=-5 for the other. The corresponding coupling matrices are shown in (5.13) and (5.15) respectively. The transformed matrices responses with a center frequency of 2.45 GHz and fractional bandwidth of 3% are shown in Fig. 5.3. From (5.22) and (5.23) the electrical parameters of the main coupling path can be obtained as Zoe1 = Zoe3 = 66.78 Ω, Zoo1 = Zoo3 = 40.25 Ω, Zoe2 = 53.89 Ω, and Zoo2 = 46.63 Ω

Fig. 5.3. Ideal performances calculated from the synthesized coupling matrices in (5.13) solid line, and (5.15) dotted line.

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Fig. 5.4 The layouts and the simulated and measured performances of the filters in Fig. 5.1(d). (a) Layout for the design with a transmission zero at Ω=3 (unit: mils). (b) Layout for the design with a transmission zero at Ω=-5 (unit: mils). (c) Simulated and measured results corresponding to Fig. 5.4(a). (d) Simulated and measured results corresponding to Fig. 5.4(b).

corresponding to (13), and Zoe1 = Zoe3 = 66.81 Ω, Zoo1 = Zoo3 = 40.25 Ω, Zoe2 = 54.10 Ω, and Zoo2 = 46.48 Ω corresponding to (5.15). The electrical lengths of the coupled-line sections are all 90^o at 2.45 GHz. Due to the very small frequency shifts caused by M11

and M22, there is almost no need to modify the length of the resonator. Then, follow [103] to add cross coupling paths. Figs. 5.4(a) and (b) show the physical dimensions of the filters. In Fig. 5.4(b), the electrical length of two identical delay lines is 360^o at center frequency for realizing the cross couplings MS2 and M1L. The full EM simulated results of the filter structures were performed to take all the EM effects into consideration by using a commercial electromagnetic simulator Sonnet [100]. The EM simulated and measured results of the two filters are shown in Fig. 5.4(c) and Fig.

5.4(d). In Fig. 5.4(d), there is an additional transmission zero at about 2.1 GHz due to

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Fig. 5.5. The proposed three-order CT filter. (a) Ideal real frequency responses. (b) Layout (unit: mils). (c) Simulated and measured results.

the unwanted cross coupling MSL. For the CT filter corresponding to Fig. 5.1(h), the calculated ideal bandpass responses with Ω=1.6 and -2, center frequency of 2.4 GHz, and fractional bandwidth of 5% are shown in Fig. 5.5(a). Then, taking the similar procedures as described above, and performing a full EM simulation to fine tune the

responses, the final layout is obtained as shown in Fig. 5.5(b). It should be emphasized that the J-inverter equivalent in Fig. 5.2(b) is only valid at center frequency. The more the asynchronous tuning is, the more discrepancy of the equivalent circuit will be. Here, the equivalent circuit model is still valid because the asynchronous tuning is small. The electrical length of the two identical delay lines is 360^o at the center frequency. Fig. 5.5(c) depicts the EM simulated and measured results. In Fig. 5.5(c), there are two additional transmission zeros at about 2.02 GHz and 2.98 GHz due to the unwanted cross coupling MSL.

B. The quadruplet filters corresponding to Figs. 5.1(e) and (f) and the modified canonical-form filter corresponding to Fig. 5.1(g)

For the quadruplet filter in Fig. 5.1(e), the ideal bandpass responses calculated from (5.19) with transmission zeros at Ω=±1.6, center frequency of 2.4 GHz, and fractional bandwidth of 5% are depicted in Fig. 5.6(a). The ideal bandpass responses excluding all cross coupling elements in (5.19) are also shown in Fig. 5.6(a). It can be obviously seen that adding the cross couplings in the proposed coupling scheme influence the in-band responses very little even for transmission zeros very close to the passband. Figs. 5.6(b) and 5.6(c) show the physical dimensions and the simulated and measured performances. In order to reveal the merit of the proposed filter, a quadruplet filter with coupling scheme in Fig. 5.1(c) with the same specification is designed, and its synthesized coupling matrix is in (5.18). The detail dimensions to achieve the specification are shown in Fig. 5.6(d). As can be seen in the layout that the gap used to realize the cross coupling MS3 in Fig. 5.1(c) is only 1 mil (0.025mm) which is far beyond the limit of standard printed circuit board process.

Similarly, the same concept of the filter in Fig. 5.1(e) can also be applied to the fourth-order quadruplet filter in Fig. 5.1(f). Again, two finite transmission zeros at

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Fig. 5.6. The proposed third-order quadruplet filter. (a) Two ideal frequency responses: one is to consider the matrix in (5.19) solid line and the other is to exclude all the cross-coupling elements in (5.19) dotted line. (b) Layout (unit: mils). (c) Simulated and measured performances. (d) Layout for realizing the coupling scheme in Fig. 5.1(c).

Ω=±1.3 are very close to the passband. The synthesized coupling matrix is shown in (5.20). The bandpass filter is designed with a center frequency of 2.4 GHz and fractional bandwidth of 7%. The ideal responses, physical dimensions, and the simulated and measured results are shown in Fig. 5.7.

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Fig. 5.7. The modified fourth-order quadruplet filter. (a) Ideal responses. (b) Layout (unit: mils). (c) Simulated and measured performances.

By introducing the source-load cross coupling as shown in Fig. 5.1(g), the canonical form response with two additional transmission zeros than the quadruplet on both sides of passband are created. In this example, two additional transmission zeros at Ω=±3 are chosen. The synthesized coupling matrix is shown in (5.21). The observation between the coupling matrices in (5.20) and (5.21) shows that it is no need to modify the main structure. The physical layout is shown in Fig. 5.7(b) that only modification is to add two extra delay lines to realize the coupling MSL. The ideal responses, physical dimensions, and the simulated and measured results are shown in Fig. 5.8. Due to the physical layout of the filter, a bond wire is needed to realize MSL.

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Fig. 5.8. The modified fourth-order quadruplet filter with source-load cross coupling.

(a) Layout (unit: mils). (b) Simulated and measured performances.

Chapter 6 Exact Synthesis of New High-Order Wideband Marchand