4 Wideband Bandpass Filters with Wide Upper Stopband Using Stepped-
4.2 bandpass filter by cascading two stepped-impedance 180 0 hybrid couplers with
(a)
(b)
Fig. 4-7. Schematics of the proposed wideband filters (a) Basic structure (b) Modified structure .
Although the bandpass filter shown in Fig. 4-1 exhibits wide bandwidth, it still has the spurious problem. Now, consider the two-section hybrid ring shown in Fig. 4-7(a) and its S-parameters at the center frequency are
22 0
11 = S =
S
43 0
21 = S =
S
2 2 2 1 2 2 2 1 42
31 S (Y Y )/Y Y
S = =− − +
) /(
2 1 2 12 22
32
41 S YY Y Y
S =− = + . (4-6) When Y1=Y2, the signal excited at port 1 is equally divided between 3’ and 4’ and no power reaches 2’. The signal arriving at 3’ and 4’ are out of phase. Then, the signal at 3’ is equally divided between 3” and 4” and the signal arriving at 3” and 4” are out of phase. The signal at 4’ is equally divided between 3” and 4” and the signal arriving at 3” and 4” are in phase. Therefore, all of the power excited at port 1 will be delivered to port 4 and no power reaches port 3 and port 2 (corresponding to a 0-dB coupler).
This means that a bandpass response can be obtained by cascading two 3-dB 180o hybrid rings.
Fig. 4-8. Characteristic impedances Z1, Z3, and bandwidth versus return loss for the equal-ripple response bandpass filter shown in Fig. 4-7(b).
Fig. 4-9. Simulated results of the proposed wideband filter (a) Basic structure (b) Modified structure.
Here, to increase the order and the bandwidth of the proposed filter, a 900 transmission line of impedance Z3 can be added between two 180o hybrids as shown in Fig.4-7(b). With the design method described in section 3.1, the bandwidth of this filter corresponding to specific return losses can be obtained. Fig. 4-8 shows the plot of characteristic impedances of Z1, Z3, and bandwidth versus return loss for the bandpass filter shown in Fig. 4-7(b).
The simulated results of the filters in Fig. 4-7(a) and 4-7(b) with 15-dB return loss are depicted in Fig. 4-9 that they correspond to third (Z1=Z2=53.31Ω) and fourth (Z1=Z2=58.65Ω and Z3=41.16Ω) order filter respectively. Although wide passband can be easily achieved, the first spurious passband at 3f0 results in poor upper stopband performance. In chapter 2, the frequency of the first spurious response of the 180o hybrid ring can be moved using the stepped-impedance structure by adjusting its structural parameters. Thus, by applying the stepped-impedance structure to Fig.
4-7(b), a wideband filter with broad upper stopband characteristics can be obtained.
The design procedures are summarized as follow:
Step 1) Specify the required return loss and obtain the corresponding circuit parameters in Fig. 4-7(b). This can be easily obtained from Fig. 4-8. (15dB-
return loss, Z1=Z2=58.65Ω and Z3=41.16Ω in this design)
Step 2) Employ the stepped-impedance structure to each line section in Fig. 4-7(b).
For a given θΗ and θL, parameters (ZH and ZL) of the stepped-impedance circuit equivalent to a quarter-wave transmission line of the specific impedance can be calculated by using (2-3)-(2-5). These are the initial parameters of the bandpass filter.
Step 3) Fine-tune the circuit parameters to optimize the circuit performance.
The optimized circuit parameters are shown in Table 4.1.
Following the above-described design steps, the circuit parameters of the proposed bandpass filter can be obtained. However, the realization of a wideband 1800 phase inverter on microstrip circuits would be a problem. This can be solved by using a λ/4 short-ended coupled line with the VIP structure. Therefore, the ideal 1800 phase inverter and crossovers, shown in Fig. 4-7, are implemented by a λ/4 short-ended coupled line with the VIP structure. Then, we employ stepped-impedance structure to the λ/4 short-ended VIP coupler. To simplify this design, the short-ended stepped-impedance VIP coupler is approximately equivalent to a balanced stepped-impedance transmission line with 180o of twist (physically 180o of twist equivalent to an ideal 180o phase inverter). This equivalence is valid as long as the even- to odd-mode impedance ratio is large. The characteristic impedance of each balanced line section approximately equals to 2Z0eZ0o/(Z0e-Z0o). Its physical length can be determined by the effective odd-mode dielectric constant because the signal going through it is mainly odd-mode. Fine tuning the length of each VIP line section to fit the insertion phase of other three step impedance lines at the center frequency may be required. Both the main circuit and the VIP couplers are implemented on a RO4003 substrate with thickness (hv and hs) of 20-mil and dielectric constant (εr1 and εr2) of 3.38. The filter is designed to operate at the center frequency of 2 GHz.
Based on the above-described method, the characteristic impedances and effective dielectric constants for even- and odd-modes of the VIP coupler can be obtained by the 3-D EM simulator (Ansoft HFSS) as given in Table 4-2. Fig. 4-10 indicates the geometry of the fabricated filter. The 3-D structure and photograph of the proposed wideband filter is shown in Fig.4-11 where port 2 and port 3 are the input and output port, respectively. Both port 1 and port 4 are isolated ports and are terminated with a
50-Ω load.
TABLE 4-1
Parameters of the stepped-impedance bandpass filter ZH
(Ω)
ZL
(Ω)
θH
(Degree)
θL
(Degree)
λ/4, Z=58.65Ω 97 29 30 19.5
λ/4, Z=41.16Ω 84 23 22.3 20
TABLE4-2
Computed results by HFSS (f0=2 GHz) Z
(Ω)
H (mil)
W (mil)
εre εro Z0e
(Ω)
Z0o
(Ω)
59.0 70 21.5 1.28 2.87 348.0 27.2
50.8 70 25.9 1.26 2.91 336.0 23.5
(a)
(b)
Fig. 4-10. Geometry of the fabricated filter (a) Main circuit section. W1=101 mil, W2=12 mil, W3=135 mil, W4=17 mil, S=82 mil, L1=158 mil, L2=283 mil, L3=200 mil, L4=195 mil, L5=201 mil (b) VIP stepped-impedance coupler. Wv1=133 mil, Wv2=29 mil, Lv1=184 mil, Lv2=296 mil.
Fig. 4-12 shows the simulated and measured results of the proposed filter and the measured insertion loss is approximately 0.4dB. Note that the simulated results of the proposed filter are simulated with the computed parameters in Table 4-2 by the circuit simulator (AWR Microwave Office). The measured 10-dB return loss bandwidth is from 0.95 to 2.8 GHz (92.5%). The stopband rejection is better than -20dB from 3.3 to 6.8 GHz. The measured bandwidth is a little narrower than the simulated responses and the experimental stopband rejection is a little worse than the simulated results.
This may be caused by the junction effect (especially junctions at microstrip and VIP coupler) and circuit fabricating imperfections.
(a)
(b)
Fig. 4-11. (a) 3-D structure of the proposed wideband filter with the stepped-impedance structure (b)Photograph of the fabricated filter
Fig. 4-12. Measured and simulated results of the proposed wideband filter with the stepped-impedance structure.
4-3 Bandpass filter by cascading two stepped-impedance 1800 hybrid couplers with two unit elements
(a)
(b)
Fig. 4-13. Schematics of the proposed wideband bandpass filters with no crossover (a) Basic structure (b) Modified structure.
In the previous sections, crossovers are required to realize these bandpass filter.
However, these crossovers will cause the serious parasitic problem at higher operating frequencies. Now, consider the schematic shown in Fig. 4-13(a). If the transmission line is long enough (larger than one quarter wavelength), two hybrid rings can be connected without crossover. Therefore, two hybrid rings are cascaded with two unit elements as shown in Fig. 4-13(b). Fig. 4-14 shows characteristic impedances Z1, Z3, and bandwidth versus return loss for the equal-ripple response bandpass filter shown in Fig. 4-13(b) with Z1=Z2 and Z3=Z4.
Following the design steps mentioned in the section 4-2, this type of the wideband bandpass filter with stepped-impedance structure can be easily designed. By increase the high/low impedance ratio of the stepped-impedance structure, the filter exhibits not only the higher first spurious passband but also smaller size. The optimized circuit parameters are listed in table 4-3. Extremely high impedance and low impedance can be realized using CPS and interdigital CPS. Besides, the wideband phase inverter can be readily implemented by using hybrid CPS/interdigital CPS structure, as mentioned in chapter 2. Therefore, hybrid CPS/interdigital CPS structure is one of the most suitable structures to implement this proposed bandpass filter.
Fig. 4-14. Characteristic impedances Z1, Z3, and bandwidth versus return loss for the equal-ripple response bandpass filter shown in Fig. 4-13(b).
This wideband bandpass filter is fabricated on an Al2O3 alumina substrate with 15-mil thickness (h) and a dielectric constant (εr) of 9.8. This filter is designed to operate at the center frequency of 2 GHz. Using the CPS design curves provided in section 2.3, the CPS parameters can be obtained as shown in Table 4-4. The layout of the proposed wideband bandpass filter is shown in Fig. 4-15. Fig. 4-16 shows layouts of discontinuities for the proposed wideband bandpass filter. The simulated results of the proposed filter are simulated with the computed parameters in Table 4-3 by using the circuit simulator as shown in Fig. 4-17. It is should be noted that the bandwidth of the stepped-impedance bandpass filter is a little narrower than that of the quarter- wavelength structure. Fig. 4-17 also shows the simulated results of the proposed filter with discontinuity effects. It can be observed from Fig. 4-17 that the discontinuity junctions whose parasitic effects alter the frequencies of harmonics. The EM simulated results and measured results of the proposed filter are shown in Fig. 4-18.
The measured insertion loss is approximately 1.2dB. The measured return loss is better than 10-dB is from about 1 to 3 GHz (100%). The stopband rejection is better than -30dB up to 17.7 GHz. In Fig.4-18, the simulated first spurious passband is
around 8.3GHz. However, due to CPS losses the spike-like spurious responses around these frequencies are not found in the measurement. Fig. 4-19 shows a photograph of the fabricated bandpass filter and the overall size is 950 mil × 642 mil.
TABLE 4-3
Parameters of the stepped-impedance bandpass filter ZH
(Ω)
ZL
(Ω)
θH
(Degree)
θL
(Degree)
λ/4, Z=61.40Ω 184 22 17.4 14.8
λ/4, Z=53.23Ω 184 22 15.4 16.8
TABLE 4-4
CPS and interdigital CPS parameters of the stepped-impedance bandpass filter Line width
W (mil)
Gap width S (mil)
(Ω)Z
Interdigital CPS (N=3) 4 1.6 22
CPS 4 24 184
D
A E
B
C
Fig. 4-15. Layout of the fabricated stepped-impedance wideband bandpass filter.
(a)
(b) (c)
(d) (e)
Fig. 4-16. Layouts of discontinuities (a) Discontinuity A (b) Discontinuity B (c) Discontinuity C (d) Discontinuity D (e) Discontinuity E.
Fig. 4-17. Simulated results of the proposed stepped-impedance wideband bandpass filter by using the circuit simulator.
Fig. 4-18. EM simulated results and measured results of the proposed bandpass filter.
Fig. 4-19. Photograph of the fabricated stepped-impedance wideband bandpass filter.
Chapter 5 Conclusion
In this dissertation, several novel 1800 hybrid couplers have been proposed and implemented with microstrip and uniplanar structure. Then, on the basis of these 1800 hybrid couplers, a new class of wideband bandpass filters is presented.
The 1800 hybrid ring coupler using a novel interdigital CPS phase inverter has been designed and fabricated to exhibit size reduction and wideband performance.
Extremely low/high impedances can be obtained by using CPS/interdigital CPS. With design equations for the stepped-impedance and design curves for CPS/interdigital CPS, the proposed hybrid ring coupler can be readily designed. This hybrid provides good amplitude and phase characteristic and good isolation over a wide bandwidth due to the phase inverter being independent of frequency. This circuit shows about 87% size reduction compared to the conventional 3/2λ CPS hybrid ring.
Based on the reconfigured the ideal single-section hybrid ring, the wideband two-section hybrid rings with Chebyshev characteristics have been developed for bandwidth enhancement, size reduction, and high power-division ratios. In addition, the two-section hybrid ring by cascading of two single-section unit with a unit element at each I/O port is presented for further bandwidth improvement. The short-ended VIP coupler has been successfully used to approach an ideal
single-section unit. It also provides a good crossover for realization of the circuit.
Thus, the wideband multi-section hybrid rings using the VIP coupler are suitable for microstrip implementation.
By cascading two 1800 hybrid rings with one or two pairs of 900 transmission lines, a stepped-impedance wideband bandpass filter has been designed and fabricated to exhibit wide passband and broad stopband performance simultaneously. In addition, the bandwidth can be further enhanced by cascading more sections of 900 transmission lines between two rat-race hybrid couplers or at each I/O port of the rat-race hybrid coupler in the proposed structure. All the measured results show good agreements with the simulated responses. With provided design equations, design curves and design procedures for all above-mentioned circuit, these circuits can be designed systematically.
In the future work, the performance of the proposed wideband bandpass filter can be improved with transmission zeros for the both upper and lower cutoff selectivity enhancement.
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