Z_{o} and θ_{1} represent the characteristic impedance and the electrical length of the coupled line, respectively; while J is the admittance inverter. The admittance

Figure 1. Schematic and equivalent transmission line network of the proposed UWB BPF on microstrip line topology [15] .

Figure 2. (a) Schematic and (b) equivalent transmission line network of the first part of the proposed filter.

inverter J in ABCD matrix M_{c} can be replaced by the even and odd mode characteristic impedances (Z_{oe} & Z_{oo}) of the coupled line [18] :

$J{Z}_{o}+\frac{1}{J{Z}_{o}}=\frac{{Z}_{oe}+{Z}_{oo}}{{Z}_{oe}-{Z}_{oo}}$ (2)

$J{Z}_{o}^{2}=\frac{2}{{Z}_{oe}-{Z}_{oo}}$ (3)

Substituting by Equation (2), and Equation (3) into Equation (1); the ABCD matrix of the coupled line becomes:

${M}_{c}=\left[\begin{array}{cc}\frac{{Z}_{oe}+{Z}_{oo}}{{Z}_{oe}-{Z}_{oo}}\mathrm{cos}{\theta}_{1}& \frac{-j}{2}\left[\frac{4{Z}_{oe}{Z}_{oo}}{{Z}_{oe}-{Z}_{oo}}\frac{{\mathrm{cos}}^{2}{\theta}_{1}}{\mathrm{sin}{\theta}_{1}}-\left({Z}_{oe}-{Z}_{o0}\right)\mathrm{sin}{\theta}_{1}\right]\\ j\frac{2}{{Z}_{oe}-{Z}_{oo}}\mathrm{sin}{\theta}_{1}& \frac{{Z}_{oe}+{Z}_{oo}}{{Z}_{oe}-{Z}_{oo}}\mathrm{cos}{\theta}_{1}\end{array}\right]$ (4)

Z_{oe} and Z_{oo} can be calculated as in [2] .

2.1.2. High Impedance Line Analysis

The ABCD matrix of the high impedance line can be expressed as [18] :

${M}_{H}=\left[\begin{array}{cc}\mathrm{cos}{\beta}_{H}{l}_{H}& j{Z}_{H}\mathrm{sin}{\beta}_{H}{l}_{H}\\ \frac{j}{{Z}_{H}}\mathrm{sin}{\beta}_{H}{l}_{H}& \mathrm{cos}{\beta}_{H}{l}_{H}\end{array}\right]$ (5)

where Z_{H} is the highest line impedance, β_{H} is the propagation constant and l_{H} is the length of the high impedance line.

From Equation (4) & Equation (5), the ABCD matrix of the first part of the proposed filter is:

${M}_{1}={M}_{c}\times {M}_{H}$ (6)

Figure 3 shows the numerical results by using Mat-lab program version 2013 and simulated results by using CST MWS version 2014 of the input/output section. From Figure 3, it is clear that, both results are in good agreement.

2.2. Analysis of the Multi-Mode Resonator Section

The multi-mode resonator section can be considered as cascaded stepped impedance with high and low impedances as shown in Figure 4.

The ABCD matrix of the second part can be expressed as follows [18] :

${M}_{\text{I}}=\left[\begin{array}{cc}\mathrm{cos}{\beta}_{1}{l}_{1}& j{Z}_{1}\mathrm{sin}{\beta}_{1}{l}_{1}\\ \frac{j}{{Z}_{c1}}\mathrm{sin}{\beta}_{1}{l}_{1}& \mathrm{cos}{\beta}_{1}{l}_{1}\end{array}\right]$ (7)

${M}_{\text{II}}=\left[\begin{array}{cc}\mathrm{cos}{\beta}_{2}{l}_{2}& j{Z}_{1}\mathrm{sin}{\beta}_{2}{l}_{2}\\ \frac{j}{{Z}_{c2}}\mathrm{sin}{\beta}_{2}{l}_{2}& \mathrm{cos}{\beta}_{2}{l}_{2}\end{array}\right]$ (8)

${M}_{\text{III}}={M}_{\text{I}}$ (9)

${M}_{\text{IV}}={M}_{\text{II}}$ (10)

Figure 3. The numerical and simulated results for the input/output sections.

Figure 4. The multi-mode resonator section.

${M}_{\text{V}}=\left[\begin{array}{cc}\mathrm{cos}{\beta}_{5}{l}_{5}& j{Z}_{5}\mathrm{sin}{\beta}_{5}{l}_{5}\\ \frac{j}{{Z}_{c5}}\mathrm{sin}{\beta}_{5}{l}_{5}& \mathrm{cos}{\beta}_{5}{l}_{5}\end{array}\right]$ (11)

${M}_{\text{VI}}={M}_{\text{II}}={M}_{\text{IV}}$ (12)

${M}_{\text{VII}}={M}_{\text{III}}={M}_{\text{I}}$ (13)

${M}_{\text{VIII}}={M}_{\text{II}}={M}_{\text{IV}}={M}_{\text{VI}}$ (14)

${M}_{\text{IX}}={M}_{\text{I}}={M}_{\text{III}}={M}_{\text{VII}}$ (15)

From Equation (7) to Equation (15), the ABCD matrix of the second part of the proposed filter is:

${M}_{2}={M}_{\text{I}}\times {M}_{\text{II}}\times \cdots \times {M}_{\text{IX}}$ (16)

The characteristic impedance and propagation constant of each section can be calculated as in [2] .

Figure 5 shows the numerical results by using Mat-lab program version 2013 and simulated results by using CST MWS version 2014 of the Multi-mode resonator section. From Figure 5, it is clear that, both results are in good agreement.

Therefore, from the above discussion, it is clear that the total ABCD matrix of the proposed filter can be expressed as:

$\left[\begin{array}{cc}A& B\\ C& D\end{array}\right]={M}_{1}\times {M}_{2}\times {M}_{1}$ (17)

The equations for computing the reflection and transmission coefficients from

Figure 5. The numerical and simulated results for the Multi-mode resonator section.

the previous set of ABCD-parameter values of the proposed filter can be written as follows [18] :

${S}_{11}=\frac{A+\frac{B}{{Z}_{0}}-c{Z}_{0}-D}{A+\frac{B}{{Z}_{0}}+c{Z}_{0}+D}$ (18)

${S}_{21}=\frac{2}{A+\frac{B}{{Z}_{0}}+c{Z}_{0}+D}$ (19)

Figure 6 shows the numerical results by using Mat-lab program and simulated results by using CST MWS of the proposed filter. Regarding S_{11}, there is frequency shift about 0.6 GHz between the numerical and simulated results in the first resonant frequency. This may be attributed to the different method of analysis used in the CST and Mat-lab program, while this shift decreases with the second and third resonant frequency as illustrated in Figure 6. The S_{21} shows very good agreement between the simulated and the numerical results especially in the band of operation from 3.1 GHz to 11.6 GHz. Finally, from Figure 6, one can observe that both results are in good agreement.

3. Filter Design

The proposed filter is designed based on the example described in Ref. [19] but with a new contribution which is the controllable tunable bandwidth. This will be achieved by modifying the length of the outer open circuited stubs using diode switching matrix tools (instead of using PIN diodes). In this work, the proposed UWB-BPF consists of two parts, EBG-embedded MMR and interdigital coupled lines. The MMR is formed by connected series of open circuited stubs coupled with high impedance microstrip lines in center.

Three shapes of the proposed filter are presented, the first one is UWB BPF with MMR formed by three open circuited stubs mutually coupled with two high impedance microstrip lines in center, the second one is MMR formed by five open circuited stubs mutually coupled with four high impedance microstrip lines in center, and third one as same as the second one but with different length of each open circuited stubs.

Figure 6. The numerical and simulated results of the proposed filter.

3.1. First Proposed Filter Design

The first proposed design with its optimized dimensions is shown in Figure 7. The overall dimension of the proposed filter is 14.0 mm × 10.1 mm. The filter operating bandwidth will be controlled by adjusting the length of the outer open circuited stubs (W_{L}). As W_{L} increases the bandwidth of the filter decreases as shown in Table 1. The length W_{L} is modified by using diodes switching matrix equipment where the character D refers to the diode and the different diodes states are described as follow:

1) When all the eight diodes (D_{1}, D_{2}, D_{3}, D_{4}, D_{5}, D_{6}, D_{7}, and D_{8}) are in off state, the length W_{L} will be equal to 4.9 mm, so the bandwidth of the filter will be 7.9 GHz with band extends from 3.5 GHz to 11.4 GHz.

2) When D_{1}, D_{2}, D_{3}, and D_{4} are in on state; while D_{5}, D_{6}, D_{7}, and D_{8} are in off state, the length W_{L} will be equal to 7.5 mm, so the bandwidth of the filter will be 4 GHz with band extends from 3.5 GHz to 7.5 GHz.

3) When all diodes (D_{1}, D_{2}, D_{3}, D_{4}, D_{5}, D_{6}, D_{7}, and D_{8}) are on, the length W_{L} will be equal to 10.1 mm, so the bandwidth of the filter will be 2.4 GHz with band extends from 3.5 GHz to 5.9 GHz.

From the above discussion, the length W_{L} can be modified to control the filter operating bandwidth. The above cases are summarized in Table 1.

Figure 8 shows the simulated results of the proposed filter with different lengths of the outer open circuited stubs (W_{L}) by using readymade software package (CST MWS version 2014). It is clear that the 3dB bandwidth of the bandpass filter varies according to W_{L}, and thus there are three tuned bands with the three different lengths (W_{L}).

3.2. The Second Proposed Filter Design

The second proposed design has five open circuited stubs mutually connected with four high impedance microstrip lines in middle as given in Figure 9. The overall dimension of the proposed filter is the same as the overall dimension of the first proposed filter (14.0 mm × 10.1 mm) and the design procedure of the second proposed filter is the same as in first shape, but the passband starts from 3.1 GHz instead of 3.5 GHz and so the bandwidth is changed also. These differences

Table 1. The S parameters against (W_{L}) for the first proposed filter.

Figure 7. The proposed UWB BPF with three O.C. stubs and two high impedance microstrip lines (all dimensions in mm).

Figure 8. The simulated lS_{11}l and lS_{21}l using CST software package for different W_{L} lengths, (a) W_{L} = 4.9 mm; (b) W_{L} = 7.5 mm; (c) W_{L} = 10.1 mm; and (d) lS_{11}l for all values of W_{L}.

are given in Table 2. Figure 10 shows the simulated results of the second proposed filter design, there are three bands with different lengths of the outer open circuited stubs (W_{L} = 4.9, 7.5, 10.1 mm) by using CST. It should be noted that

Table 2. The S parameters against (W_{L}) for the second proposed filter.

Figure 9. The proposed UWB BPF with five O.C. stubs and four high impedance microstrip lines (all dimensions in mm).

Figure 10. The simulated lS_{11}l and lS_{21}l using CST software package for different W_{L} lengths, (a) W_{L} = 4.9 mm; (b) W_{L} = 7.5 mm; (c) W_{L} = 10.1 mm; and (d) lS_{11}l for all values of W_{L}.

the roll off of the second filter in the passband is better than the first one, and the bandwidth increased to 8.5 GHz instead of 7.9 GHz as shown in Table 2. Also the first resonance of the second filter occurs at 5 GHz instead of 6.9 GHz for the first filter as in Figure 11, so the performance of the second filter is better than the first one especially for the case of W_{L} = 4.9 mm.

3.3. The Modification of the Second Proposed Filter

From the second proposed filter performance, it is noticed that the selectivity and the out of band rejection are bad, so it has been modified to improve them. An optimization procedure was carried out and the length L_{3} was changed from 5 mm to 4 mm, L_{2} changed from 4.9 mm to 3.6 mm, and L_{1} remains the same as shown in Figure 12.

The design procedure of the modified filter is the same as in the second proposed filter. Figure 13 shows the simulated results of the modified filter design, there are three bands with different lengths of the outer open circuited stubs (W_{L} = 4.9, 7.5, 10.1 mm) by using CST.

It should be noticed that the selectivity is improved and the out of band rejection has become better (S_{21} improved by more than 20 dB from 11.6 to 14 GHz) for the case of W_{L} = 4.9 mm as in Figure 14, and as in Table 3.

Our proposed designed filter is compared with similar filters as given in Table 4, where we noticed that the proposed filters are distinguished from the other published filters due to smaller size and larger bandwidth. The proposed design achieves total area reduction of more than 50% compared with [21] , 70% compared with [22] , and 54% compared with [23] . It also provides a wider operating bandwidth, achieving a 10.6% increase in bandwidth compared with [20] [23] , 18.6% compared with [21] , and 1.2% compared with [22] .

4. Fabrication and Measurements

The designed filters are fabricated using thin film technology and photolithographic technique on Rogers RO3006 (lossy) substrate with (ε_{r} = 6.15, h = 1.52 mm, and tan δ = 0.002). The photos for the fabricated filters are shown in Figure 15. The connecting wires are soldered to the circuit, and then connecting the diode switch matrix tool (that replaces the PIN diode switch). The filters are

Figure 11. The simulated lS_{11}l and lS_{21}l using CST software package for the first and the second filters.

Figure 12. The modified UWB BPF with five O.C. stubs and four high impedance microstrip lines (all dimensions in mm).

Figure 13. The simulated lS_{11}l and lS_{21}l for the modification of the second proposed filter design using CST software package for different W_{L} lengths. (a) W_{L} = 4.9 mm; (b) W_{L} = 7.5 mm; (c) W_{L} = 10.1 mm; and (d) lS_{11}l for all W_{L}.

Figure 14. The simulated lS_{11}l and lS_{21}l using CST software package for the three shapes of filters.

Table 3. The S parameters against (W_{L}) for the modified proposed filter.

Table 4. Comparison of the proposed filter with published UWB Bandpass filters.

Figure 15. Photos for the fabricated filters, (a) First shape; (b) Second shape; (c) Third shape.

measured using the vector network analyzer (N9928A FieldFox Handheld Microwave Vector Network Analyzer, 26.5 GHz.).

Figures 16-18 show the measured and simulated results of the three structures. The measured results are consistent with the simulated ones. The measured 3dB passband of the first proposed filter is between 3.5 to 11.4 GHz in the 1st band, while in the second and third proposed filter is from 3.1 GHz to 11.6 GHz, from 3.5 to 7.5 GHz in the 2nd band of the first filter, while in the second and third filter from 3.1 GHz to 7.8 GHz, and from 3.5 to 5.9 GHz in the 3rd band of the first filter, while in the second and third filter from 3.1 GHz to 5.8 GHz. All filters have compact sizes with dimensions 14.0 mm × 10.1 mm.

Figure 18(a) shows the measured and simulated lS_{11}l and lS_{21}l of the modified filter with five open circuit stubs with frequency range from 1 GHz to 20 GHz at W_{L} = 4.9 mm. It should be noted that the frequency range is extented up to 20

Figure 16. The simulated and measured lS_{11}l and lS_{21}l for the first filter shape for different W_{L} lengths (a) W_{L} = 4.9 mm; (b) W_{L} = 7.5 mm; and (c) W_{L} = 10.1 mm.

Figure 17. The simulated and measured lS_{11}l and lS_{21}l for the second filter shape for different W_{L} lengths (a) W_{L} = 4.9 mm; (b) W_{L} = 7.5 mm; and (c) W_{L} = 10.1 mm.

GHz in order to show that the out of band rejection has been improved due to the modifications that were carried out in the lengths of the open circuit stubs. HFSS software package was also used as another simulation tool to validate and verify the obtained performance of the proposed filters. Figure 19 shows the group delay variations for the three shapes of the proposed filters simulated by

Figure 18. The simulated and measured lS_{11}l and lS_{21}l for the modification of the second proposed filter for different W_{L} lengths (a) W_{L} = 4.9 mm (with frequency range from 1 GHz to 20 GHz); (b) W_{L} = 4.9 mm; (c) W_{L} = 7.5 mm and (d) W_{L} = 10.1 mm.

Figure 19. The group delay for the three shapes of the proposed filter.

the CST MWS software. It should be noted that the maximum variation of group delay within 1 - 14 GHz is 0.4 ns for the modified filter, while the maximum variation of group delay for second proposed filter is 4.35 ns, and for the first proposed filter is 7.68 ns. As can be noted that the reported values for the modified proposed filter is lower than the other two proprosed filters and indicates a very low distortion that can be happened for the modified filter.

From the above figures, one can notice that:

1) There is a difference between the first, second, and third shape of the proposed filter in the frequency band and the center frequency as shown in Table 5, as well as differences in group delay and roll off behavior.

Table 5. Comparison between the three shapes of the proposed filters.

2) The insertion loss within the pass band of the two shapes is the same.

3) The fabrication of the second and third shapes is more difficult than the first shape.

4) The slope of the insertion loss of the third shape is sharper than the first and second shape.

5. Conclusion

Reconfigurable Ultra-Wideband Bandpass Filters with EBG Embedded Multi-Mode Resonator have been designed, simulated, and fabricated. Two packages of software were used, namely CST MWS 2014 and 3D EM commercial software HFSS version 13.0 to design and simulate the filters. The simulated and measured results are comparable. The measured results were characterized using a N9928A FieldFox Handheld Microwave Vector Network Analyzer, 26.5 GHz. Small size and three different frequency bands add some advantages to these filters. By adjusting the length of the outer open circuit stubs, the center frequency and the 3 dB frequency band can be easily adjusted. The final size of these filters is 14.0 mm × 10.1 mm, which is suitable for modern ultra-wide band wireless communication systems. According to The FCC regulations, the proposed filters in all their structures satisfy the definitions of the UWB filters whether according to the first definition of FCC which is 3.1 - 10.6 GHz bandwidth requirements or according the second definition which is 500 MHz bandwidth requirements. So, the proposed filter can be used in communication systems with UWB application [24] .

Cite this paper

Ouf, E. , Mohra, A. , Abdallah, E. and Elhennawy, H. (2018) A Reconfigurable UWB Bandpass Filters with Embedded Multi-Mode Resonators.*Open Journal of Antennas and Propagation*, **6**, 43-59. doi: 10.4236/ojapr.2018.63005.

Ouf, E. , Mohra, A. , Abdallah, E. and Elhennawy, H. (2018) A Reconfigurable UWB Bandpass Filters with Embedded Multi-Mode Resonators.

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