Design of a superconducting UWB bandpass filter with tunable notch band

By studying the principles of ultra-wideband (UWB) and band-stop, a novel band-pass filter with adjustable band-stop characteristics is proposed. The filter achieves 3.1-10.6 GHz UWB bandpass characteristics through an improved multi-mode resonator. An L-shape λ/2 notch resonator loaded with a 2-bit reconfigurable interdigital capacitor (IDC) array is coupled to the multiple-mode resonator and generates a tunable notch band to reject any undesired signal that may interfere with the UWB passband. By connecting the IDC to the ground or not, the capacitance of each IDC and the corresponding notch frequency can be adjusted. After design and optimization, the final size of the superconducting filter is 20.0 mm × 6.9 mm, and the test results and simulation results are highly consistent.


Introduction
Since 2002, when the U.S. FCC voted to allow the commercial use of the 3.1-10.6 GHz frequency band, ultra-wideband wireless communication technology has attracted considerable academic and industrial attention [1] .Compared to other communication systems, ultra-wideband wireless systems have many unique advantages, including higher data transmission speeds, low power consumption, and higher immunity to interference.To transmit and receive high-quality signals, as one of the key devices of ultra-wideband wireless systems, ultra-wideband filters with compact structure and superior performance have received more and more attention.Recently, various designs of UWB filters, including MMRs (multiple-mode resonators) [2] , cascaded bandstop and bandpass filters [3] , and electromagnetic bandgap structures [4] , have been reported.However, in some cases, some interfering signals (e.g., Bluetooth and wireless LAN signals around 5 GHz) happen to be within the transmission spectrum of the ultrawideband system, and this interference may cause some interference to the performance of the ultrawideband system.To solve this problem, the existing research work is to introduce a blocking band with a fixed center frequency within the original passband to suppress the unwanted interference signals [5][6] .The frequency of the external interference signal is not fixed because it depends on factors such as external power supply, other interfering devices, and electromagnetic radiation.Therefore, it is important to study tunable band-stop ultra-wideband filters from both academic and engineering perspectives.
HTS films are known to have significantly lower surface resistivity than conventional materials in the microwave region.High-performance HTS filters with low in-band insertion loss, high band-edge steepness, and high out-of-band rejection characteristics can be fabricated by using high-temperature superconducting materials [7] .In this paper, an ultra-wideband superconducting filter with a tunable notch is successfully realized by using a λ/2 L-type reconfigurable resonator loaded with a reconfigurable 2-bit IDC array coupled with a multimode resonator.

Conventional coupled resonators
Typical methods reported in the literature for introducing notch characteristics within the ultrawideband passband include coupled resonator, embedded open-circuit short-circuit line, and asymmetric input/output (I/O) coupling.The resistive band frequencies introduced by these methods are often constant and cannot effectively deal with the chaotic and complex electromagnetic interference problems in the outside world.The coupled resonator method introduces a resistive band with steeper band edges than the other methods (embedded open-circuit truncation method and asymmetric input/output coupling method).The basic principle is that when λ/2 resonators are coupled to a main transmission line, the response curves all produce a band resistance characteristic with a small bandwidth [8] .
The coupled resonator method uses an externally coupled λ/2 resonator to determine the center frequency of the resistive band, which can be adjusted by changing the electrical length of the resonator.Inspired by this, it is believed that if the frequency of the externally coupled resonator is freely changed, the center frequency of the resistive band can also be freely adjusted.Previous literature has reported various shapes of coupled resonators, such as U-shape, spiral shape, and ring shape [9] .However, the frequencies of most of these coupled resonators are constant and cannot be adjusted, and there are few reports on frequency-variable coupled resonators.

Theoretical computational analysis of L-shaped reconfigurable resonator
In this paper, an L-type λ/2 reconfigurable resonator is proposed, as shown in Figure 1, which consists of an L-type superconducting resonator main structure and an end-loaded 2-bit fork-finger capacitor array.The equivalent circuit diagram of this tunable resonator is shown in Figure 2, where C 1 , C 2 , and L are the C-L-C equivalent circuit elements of the superconducting resonator, C i1 and C i2 are the capacitance values of the two superconducting fork-finger capacitors, and C g1 and C g2 are the capacitance values between the two IDCs and the ground plane.We ignore the small differences between the two parts of the IDCs interacting up and down.We assume that they have the same capacitance value to ground and that the switch in Figure 1 is a lossless ideal switch.
where f 0 and C denote the resonance frequency and the equivalent lumped parameter capacitance of this resonator, and f and C denote their variation ranges, respectively.When the IDC array is in different ground states, the loaded capacitance value of this resonator is different, and thus the resonance frequency is also different.In Figure 1, we refer to the "closed" state of the resonator as State "1" and the "open" state of the resonator as State "0".Then, the reconfigurable resonator has four states, (00), ( 01), (10), and (11), which represent different configurations of the two switches.By adjusting the body length of the resonator and the structure of the IDC array, the desired bandwidth frequency and tuning range can be realized.

Design of ultra-wideband superconducting filters with tunable band-stop characteristics
Based on an L-type λ/2 reconfigurable resonator, an ultra-wideband filter with tunable band-stop characteristics is designed by the coupled resonator method.The filter utilizes a multimode resonator with a U-shaped topology to achieve an ultra-wideband passband with appropriate external cross-finger coupling.
Figure 3 shows the topology of the final realized ultra-wideband filter with a tunable bandstop.The filter consists of an ultra-wideband bandpass filter and an L-type λ/2 resonator coupled with a 2-bit IDC array.The ultra-wideband bandpass filter is designed based on the U-shaped multimode resonator, the L-type λ/2 resonator is coupled to the middle part of the multimode resonator, and the coupling strength is controlled by varying the distance g 1 between them.).One end of this L-shaped reconfigurable resonator is loaded with a 2-bit IDC array, which is used to change the frequency of this resonator to produce a tunable resistive band within the ultrawideband passband.When a λ/2 resonator is coupled to a primary transmission line, a narrow-bandwidth resistive band characteristic is produced.As shown in Figure 2, a λ/2 L-type resonator is coupled to the center portion of the multimode resonator at a distance of g 1 .The center frequency of the resistive band is determined by the L-type resonator, i.e., the wavelength of the L-type resonator is equal to the half electrical length corresponding to the center frequency of the resistive band.The suppression regime of the resistive band is determined by the coupling spacing g 1 .The smaller the spacing is, the stronger the coupling is, and the higher the resistive band suppression is.The magnitude of the capacitance of each loaded fork finger capacitor can be varied by grounding the IDC with a solder wire (labeled as State "1") or without grounding it with a spot solder wire (labeled as State "0"), as shown in Figure 3 (b).Therefore, by selecting whether the solder wire is grounded or not, the resonant frequency of the L-type resonator can be controlled to change the center frequency of the stop band, thus realizing the design of an ultra-wideband filter with tunable bandstop characteristics.In practice, we use two spot weld lines for grounding to ensure the stability of grounding.
The simulation characteristics of the filter shown in Figure 3 (a) were completed through the electromagnetic field simulation software Sonnet.In the simulation process, the "ground" simulation is to simulate the actual machined AlSi spot welding wire connection by connecting the IDC to the metal box wall by using a microstrip wire with a width of 0.02 mm.Optimized by software, the final filter size selection is L 1 = 1.16 mm, W 1 = 0.86 mm, L 2 = 3.08 mm, W 2 = 0.38 mm, L 3 = 4.60 mm, g 1 = 0.16 mm, W 4 = 0.16 mm, L 4 = 2.00 mm, L 5 = 0.60 mm, W 5 = 0.04 mm, and g 2 = 0.04 mm.For the convenience of spot welding, the length L 6 and width W 6 of the microstrip block used for spot welding ground at the outer end of the IDC are 0.36 mm and 0.33 mm, respectively.The circuit size of the tunable band-stop wideband filter (excluding the feeder) is 15.1 mm × 4.8 mm, approximately 0.91 λ g × 0.29 λ g , where λ g is the waveguide wavelength of the 50 Ω impedance microstrip line corresponding to the center frequency of the filter.
The simulation performance of the filter under different ground states is shown in Figure 4, and the specific parameters are shown in Table 1.The passband of UWB ranges from 3.2 GHz to 10.4 GHz, and the 3-dB relative bandwidth is 105.9%.The center frequency of the stopband is adjustable from 6.00 GHz to 6.90 GHz.In all ground states, the 3-dB bandwidth of the stopband is less than 4% and its rejection is greater than 20 dB, showing high selectivity and high rejection performance.In addition, by changing the structure of the loaded IDC array, more tunable states and a wider tuning range can be achieved.Over most of the passband, the reflection coefficient is higher than 15 dB.

Filter fabrication and test results
The filter was fabricated on a 20.0 mm × 6.9 mm MgO substrate.The substrate has a dielectric constant of 9.8 and a thickness of 0.5 mm, which is coated on both sides with the superconducting film of YBCO with a thickness of 600 nm and has a surface resistance in the µΩ range.One side of the superconducting film is processed into a filter circuit by etching and other processes, and the other side is used for the overall ground layup.Finally, the ultra-wideband superconducting filter is placed in a metal shielding box for encapsulation.11).The filter state was tuned by disusing or using the bonding wires.Using a Network Analyzer (Agilent N5230C Vector), performances of the proposed filter in various states were measured at 55 K (the input power is set to -25 dBm), as shown in Figure 4 (b) and Table 1.The experimental performances with no tuning are highly consistent with the simulation results.The measured 3-dB passband had a range of 3.3-10.4GHz and its fractional bandwidth was 102.2%.The notch band shifted from 6.02 to 7.01 GHz within the UWB passband.It exhibits a high selectivity (<4% 3-dB bandwidth) and a high rejection rate (greater than 22 dB) in all four states.Its return loss exceeded 15 dB in most cases.The differences between measured results and simulated results can be attributed to fabrication errors.

Conclusion
This paper presents and demonstrates the design, fabrication, and test process and results of an ultra-wideband high-temperature superconducting filter with tunable stopband characteristics.The tunable stopband is realized by coupling a λ/2 L-type resonator loaded with a reconfigurable 2-bit IDC array at one end of the UWB filter.Test results show excellent filter performance with high selectivity (3 dB bandwidth less than 4%) and high rejection ratio (more than 22 dB) for the tunable stopband.

Figure 2 .
Figure 2. Equivalent circuit diagram.It is assumed that the inductance of this L-type reconfigurable resonator remains unchanged at different grounding states, and the frequency tuning range can be expressed as follows:

Figure 3 .
Figure 3. (a) The proposed UWB BPF (not to scale); (b) Using bonding wires to connect the IDC array to the ground (State 1) or disusing them (State 0).One end of this L-shaped reconfigurable resonator is loaded with a 2-bit IDC array, which is used to change the frequency of this resonator to produce a tunable resistive band within the ultrawideband passband.When a λ/2 resonator is coupled to a primary transmission line, a narrow-bandwidth resistive band characteristic is produced.As shown in Figure2, a λ/2 L-type resonator is coupled to the center portion of the multimode resonator at a distance of g 1 .The center frequency of the resistive band is determined by the L-type resonator, i.e., the wavelength of the L-type resonator is equal to the half electrical length corresponding to the center frequency of the resistive band.The suppression regime of the resistive band is determined by the coupling spacing g 1 .The smaller the spacing is, the stronger the coupling is, and the higher the resistive band suppression is.The magnitude of the capacitance of each loaded fork finger capacitor can be varied by grounding the IDC with a solder wire (labeled as State "1") or without grounding it with a spot solder wire (labeled as State "0"), as shown in Figure3 (b).Therefore, by selecting whether the solder wire is grounded or not, the resonant frequency of the L-type resonator can be controlled to change the center frequency of the stop band, thus realizing the design of an ultra-wideband filter with tunable bandstop characteristics.In practice, we use two spot weld lines for grounding to ensure the stability of grounding.The simulation characteristics of the filter shown in Figure3(a) were completed through the electromagnetic field simulation software Sonnet.In the simulation process, the "ground" simulation

Figure 4 .
Figure 4. Frequency responses of the proposed UWB BPF in four states.Table 1. Simulated and measured responses of the proposed filter in four states.

Figure 5 .
Figure 5. Photograph of the fabricated UWB BPF in State (11).Figure5depicts the fabricated UWB BPF in State (11).The filter state was tuned by disusing or using the bonding wires.Using a Network Analyzer (Agilent N5230C Vector), performances of the proposed filter in various states were measured at 55 K (the input power is set to -25 dBm), as shown in Figure4(b) and Table1.The experimental performances with no tuning are highly consistent with the simulation results.The measured 3-dB passband had a range of 3.3-10.4GHz and its fractional bandwidth was 102.2%.The notch band shifted from 6.02 to 7.01 GHz within the UWB passband.It exhibits a high selectivity (<4% 3-dB bandwidth) and a high rejection rate (greater than 22 dB) in all four states.Its return loss exceeded 15 dB in most cases.The differences between measured results and simulated results can be attributed to fabrication errors.

Figure 5
Figure 5. Photograph of the fabricated UWB BPF in State (11).Figure5depicts the fabricated UWB BPF in State (11).The filter state was tuned by disusing or using the bonding wires.Using a Network Analyzer (Agilent N5230C Vector), performances of the proposed filter in various states were measured at 55 K (the input power is set to -25 dBm), as shown in Figure4(b) and Table1.The experimental performances with no tuning are highly consistent with the simulation results.The measured 3-dB passband had a range of 3.3-10.4GHz and its fractional bandwidth was 102.2%.The notch band shifted from 6.02 to 7.01 GHz within the UWB passband.It exhibits a high selectivity (<4% 3-dB bandwidth) and a high rejection rate (greater than 22 dB) in all four states.Its return loss exceeded 15 dB in most cases.The differences between measured results and simulated results can be attributed to fabrication errors.

Table 1 .
Simulated and measured responses of the proposed filter in four states.