I. INTRODUCTION
Since the U.S. Federal Communications Commission (FCC) approved the unlicensed use of ultra-wide-band (UWB) (range 3.1–10.6 GHz) for commercial purposes [1], extensive research and development efforts have been put into exploiting UWB technology for its potential applications in telecommunications. In this context, UWB bandpass filters have been investigated by several groups in academic and industrial research.
While the fabrication of multisection bandpass-coupled line filters is particularly easy in microstrip or stripline technologies, for bandwidths lower than 20% [Reference Chin, Lin and Kuo2], wider bandwidths' filters generally require very tightly coupled lines leading to high fabrication constraints. In [Reference Kuo and Shih3], a three-coupled-line microstrip structure was proposed early in 2001 to overcome this limitation. Recently, stepped impedance open stubs were implemented on this kind of structure to realize transmission zeros and to meet UWB mask requirements [Reference Singh, Basu and Wang4]. Besides, coupled resonators have sparked a great interest for improving filter's characteristics [Reference Ishika and Araki5–Reference Mondal, Mandal and Chakrabatry11]. Tight coupling in a microstrip to Coplanar Waveguide (CPW) transition has also been investigated. The use of broadside-coupled structures has received great attention providing a wide bandpass operation with a good trade-off in terms of insertion loss and group delay flatness [Reference Li, Kurita and Matsui12, Reference Kuo, Lin and Chen13]. Furthermore, structures based on short-circuited stubs have been carefully examined in order to design UWB filters [Reference Wong, Lin, Wang and Chen14, Reference Cai15].
This paper is focuses on the design of highly miniaturized UWB filter by using a semi-lumped approach, i.e., surface-mounted capacitors and transmission lines. The topology of the miniaturized filters is based on the approach developed in [Reference Hsu, Hsu and Kuo16], i.e., the combination of low-pass and high-pass filters. In [Reference Hsu, Hsu and Kuo16], a high-pass filter realized by shunt quarter-wave short-circuited stubs is embedded with a stepped-impedance low-pass filter. Note that a suspended stripline technology combining low loss with reduced size was also used to fabricate this composite filter [Reference Menzel, Tito and Zhu17]. Analytical techniques to synthesize an isolated cascade of high- and low-pass sections based on an iterative algorithm for both Butterworth and Chebychev cases were also reported in [Reference Gomez-Garcia and Alonso18].
In the work presented in this paper, the high degree of miniaturization is obtained by using the concept of capacitively loaded transmission lines [Reference Kaddour19]. The paper is organized as follows. First, a design method is carried out and validated by simulations in section II. Then, for a proof of concept, two filters with 3-dB fractional bandwidth of 142 and 150%, respectively, centered at 0.77 and 1 GHz are designed in section III. Measurement and simulation results are in very good agreement. The insertion loss is limited to less than 1 dB in the passband, and the maximum group delay variation is 1.6 ns. A filter based on the distributed approach developed in [Reference Hsu, Hsu and Kuo16] has been realized and measured for comparison. The size reduction reaches 85% for the semi-lumped filter and the shape factor is improved from 1.5:1 to 1.3:1. Furthermore, a spurious suppression technique using capacitively loaded stubs is introduced. Consequently, the first spurious frequency appears at more than eight times the center frequency when a 40 dB out-of-band attenuation is considered. Finally, in section IV a sensitivity study is carried out taking into account the fabrication constraints, the capacitors position, and tolerances, showing the robustness of the proposed approach.
II. DESIGN METHOD
Figure 1 shows the layout of the composite bandpass filter based on the combination of a low-pass and a high-pass filter as presented in [Reference Hsu, Hsu and Kuo16]. The high-pass filter, realized by shunt quarter-wave short-circuited stubs, is embedded with a stepped-impedance low-pass filter. The low characteristic impedance transmission lines sections, occupying the largest area of the device in Fig. 1, can be replaced by capacitively loaded transmission lines, in order to reduce the filter length, as demonstrated in [Reference Kaddour19]. In addition, two series capacitors can be added at the near and far ends of the filter to improve the rejection in the lower stopband. The equivalent electrical circuit of this semi-lumped bandpass filter is given in Fig. 2.
Fig. 1. Distributed bandpass filter layout.
Fig. 2. Equivalent electrical circuit of the semi-lumped bandpass filter.
In the next two subsections, first the design steps are detailed for a classical design, and next a solution for improving the spurious suppression is proposed. To make the design more explicit, an example is treated by considering an UWB filter with 3-dB cut-off frequencies fixed to 0.5 and 2 GHz, i.e., a center frequency equal to 1 GHz on a logarithm scale, and a 150% relative bandwidth. In this paper, the center frequency f c of the bandpass filter is given by
where f L and f H are, respectively, the low and high 3 dB cut-off frequencies.
A) Design steps
The first step in the filter design procedure concerns the establishment of a rough initial estimation of the filter's parameters, by setting both low and high cut-off frequencies. To simplify the study, the series transmission lines' electrical length is supposed to be equal, i.e., θ = θ 1 = θ 2 = θ 3 = θ 4. Also, a perfect structure is considered with lossless transmission lines and ideal capacitors.
The high cut-off frequency f H of the UWB bandpass filter is defined by the low-pass filter. The low-pass filter elementary section is given in Fig. 3.
Fig. 3. Elementary section of the low-pass filter.
The study of the low-pass behavior of this structure has been carried out in [Reference Kaddour19]. The characteristic impedance Z 0 is generally fixed by the technology and results from a compromise between insertion loss and miniaturization. The relations for the loading capacitance C p and the transmission line electrical length θ defining the cut-off frequency f H are given in [Reference Kaddour19]. For a characteristic impedance equal to 120 Ω and assuming a 2 GHz high cut-off frequency, the developed equations lead to C p = 2.36 pF and θ = 29°.
Once the elementary low-pass section is dimensioned, the electrical length θ s of the short-circuited stubs has to be determined. θ s is obtained by a simple tuning carried out with Agilent ADS [20]. Considering our example, the 0.5 GHz low cut-off frequency is obtained for θ s = 23°.
At this point, rough initial values for C p, θ, and θ s are available. Using the parameters C p = 2.36 pF, θ = 29°, θs = 23°, the obtained cut-off frequencies are 0.5 and 1.92 GHz, respectively. Thus the simple design method described above is sufficient for a rough estimation of the filter's parameters. Note that the simulated filter suffers also from a poor matching in the passband with a return loss reaching only 9 dB around 1.6 GHz. However, the return loss will be improved in the second step of the design when the filter will be optimized.
For the second step consisting of a whole optimization of the complete filter, a microstrip technology is considered. A Rogers™ RO4003 substrate (with relative permittivity ɛ r = 3.38, substrate thickness h = 813 µm, and dielectric losses tan δ = 0.0027) has been considered. Also, T junctions, surface mounted capacitor's model, soldering pads, and via holes are taken into account. Only commercially available capacitors with discrete values are considered. Complete models taking into account the parasitic series elements with an inductance of 0.35 nH and a resistance of 0.25 Ω are used to obtain more accurate simulation responses. To maximize the degrees of freedom and obtain better results, the series transmission lines' electrical length and the capacitors' value are no more considered as equal.
The starting value for the series capacitors added in the near and far end of the UWB bandpass filter to improve the low stop-band rejection is fixed to 100 pF, leading to a small impedance compared to 50 Ω, keeping the low cut-off frequency unchanged. The transmission lines characteristic impedance has been set to 120 Ω, leading to a strip width W hi of 250 µm. Using the Agilent ADS [20], the 1 GHz filter is optimized, and the electrical lengths and capacitors values of the electrical circuit shown in Fig. 2 are obtained. Following the same guidelines, a semi-lumped filter centered at 0.77 GHz, with a 3-dB bandwidth of 142% is designed.
Table 1 lists the electrical lengths and capacitor's values obtained after optimization for the two UWB filters. Figure 4 gives the simulation results. For both filters, the return loss is better than 20 dB in the whole passband, and the insertion loss is limited to 0.2 dB at the center frequency. The shape factor, defined between −3 and −20 dB, equals 1.3:1 for both filters. Note that the improvement of the shape factor (in comparison with the distributed approach of [Reference Hsu, Hsu and Kuo16]) is not only due to the series capacitors. Sharp high-frequency slope is mainly due to the parasitic inductance of the shunt capacitors introducing transmission zeros near to the high cut-off frequency. The effect of the parasitic inductances will be discussed later. To investigate the out-of-band rejection, Fig. 5 gives the simulated |S21| parameter for the 0.77 GHz filter until 8 GHz. In the simulated response, spurious frequency occurs around 5 GHz, leading to an out-of-band rejection level of −40 dB to only 4.5 GHz, i.e., 4.5 times the center frequency. The study of the spurious origin is carried out in section II.B, where a simple original technique to reject theses spurious frequencies is suggested.
Fig. 4. Simulation response of the bandpass filters using parameters' values given in Table 1.
Fig. 5. Transmission zeros of the 0.77 GHz filter and the low-pass filters using capacitors values of 1.8 and 3.9 pF.
Table 1. Electrical lengths and capacitors' values of the proposed UWB semi-lumped bandpass filters.
B) Spurious analysis and improvement
Spurious frequencies are due to the capacitors's series parasitic inductance. This inductance is the sum of the intrinsic capacitor's, the soldering pads, and the via holes inductances. Considering the capacitor's model and the via hole's dimensions, its value L s can be estimated to 1.3 nH. Let us now propose a solution in order to reject these spurious frequencies.
Three transmission zeros are observed in the frequency response to 6 GHz in Fig. 5. So a possible solution to reject the spurious frequencies and to improve the rejection bandwidth could be to move the transmission zeros, either to push the 3.2 GHz transmission zero to higher frequencies, or to pull the 5.8 GHz transmission zero to lower frequencies. Therefore, the study of the origin of these transmission zeros has to be carried out first. Transmission zeros located at 2.2 and 3.2 GHz are due to the parasitic inductances, forming an LC shunt resonant circuit with the capacitors. To confirm the origin of these transmission zeros, the simulation of the low-pass sections of the filters has been carried out. Four cascaded elementary sections (see Fig. 3) have been considered, as in the filter topology given in Fig. 2. The 0.77 GHz filter has been considered, and the simulations have been carried out for the two capacitors equal to C p1 = 1.8 pF and C p2 = 3.9 pF (see Table 1), respectively.
Figure 5 shows also the simulation results for the two low-pass filters, compared to the UWB 0.77 GHz filter response. These results clearly show that transmission zeros occurring at 2.2 and 3.2 GHz are due to the LC shunt resonant circuits. The 2.2 GHz transmission zero is due to the resonant circuit formed by the 3.9 pF capacitor and the series parasitic inductance L s = 1.3 nH:
and the 3.2 GHz transmission zero can be related to C p1.
Hence there is no possibility of moving these two transmission zeros because the parasitic series inductance cannot be modified in order to obtain a lower value. The transmission zero appearing at 5.8 GHz is due to the short-circuited stub resonance that presents a 180° electrical length at 5.8 GHz. So a solution to pull this transmission zero to lower frequencies in order to interfere with the spurious response around 5 GHz, and improve the rejection bandwidth would be to increase the stubs electrical length at high frequency without modifying their behavior at low frequency because the low cut-off frequency is fixed by the stub's length. This can be achieved by using capacitively loaded stubs, leading to the whole UWB bandpass filter equivalent electrical circuit given in Fig. 6. A capacitively loaded stub will behave as an unloaded stub at low frequency because the capacitor's susceptance is high, so that the stub's behavior remains unchanged. When the frequency will increases, the loading capacitor becomes significant compared to the stub's transmission line distributed capacitor, and the wave velocity in the loaded stub decreases, leading to a lower resonant frequency for the stub.
Fig. 6. UWB filter equivalent electrical circuit with capacitively loaded stubs.
According to the transmission line theory, the input impedance of the short-circuited loaded stub is given by
where Z s′ and θ s′ are, respectively, the equivalent characteristic impedance and electrical length of the capacitively loaded stub. Z s′ can be easily calculated from the cascading matrix parameters, while θ s′ is extracted from the transmission parameter S 21
with
After optimization, the stub's loading capacitor value C sp has been fixed at 0.4 pF. The position of C sp is also of interest. The electrical lengths θ s1 and θ s2 have been fixed to 5° and 11°, respectively. The equivalent electrical length of both loaded (θ ′s) and unloaded (θ s) stubs are plotted in Fig. 7. While the unloaded stub electrical length increases proportionally vs. frequency, leading to a resonant frequency of about 5.6 GHz for a 180° electrical length, the loaded stub electrical length increases quickly with frequency, leading to a lower resonant frequency of 4.2 GHz. Thus, the transmission zero will be shifted from 5.8 to 4.2 GHz. In the lower band, the electrical length for both loaded and unloaded stubs are quite similar. So the low cut-off frequency remains quite unchanged.
Fig. 7. Comparison of the electrical length of the capacitively loaded stub (C sp = 0.4 pF) and the unloaded stub.
Figure 8 compares |S 21| of the 0.77 GHz filter with both loaded (C sp = 0.4 pF) and unloaded stubs. Whereas the filter response remains unchanged in the passband, the loading capacitor effect appears for higher frequencies. When the capacitively loaded stubs are used, the third transmission zero which was located at 5.8 GHz occurs now at 4 GHz, while the first two transmission zeros due to LC resonance remain fixed. Consequently, the high-frequency rejection band, defined below an attenuation of −40 dB, is enlarged to about 6.5 GHz, i.e., more than eight times the filter's center frequency of 0.77 GHz.
Fig. 8. Simulated insertion loss for the 0.77 GHz filter with loaded and unloaded stubs.
III. UWB FILTERS REALIZATION AND MEASUREMENTS
In this section, the two UWB filters with a 3-dB bandwidth of 142 and 150% centered, respectively, at 0.77 and 1 GHz are realized and measured. The circuit layout is given in Fig. 9. A distributed UWB filter based on the basic topology [Reference Hsu, Hsu and Kuo16] was also fabricated for a 3-dB bandwidth from 0.5 to 2 GHz (same as the 1 GHz filter) in order to compare size and electrical characteristics of both topologies.
Fig. 9. Semi-lumped UWB bandpass filter layout.
Surface-mounted capacitors with a 0402 case (0.5 mm × 1 mm) have been used. The filter's length is 3.7 cm for the 0.77 GHz filter and 2.9 cm for the 1 GHz filter.
A) Comparison of the semi-lumped and distributed filters
The photograph of both filters centered at 1 GHz is given in Fig. 10. Geometric dimensions of the distributed filter are L 1= 2.26, L 2 = 4.49, L 3 = 5.6, L 4 = 0.55, L 5 = 6.03, L 6 = 8.97, L stub = 13.8, Whi = 0.25, and W stub = 0.26, all in mm, leading to a total length of 5 cm. Thanks to the semi-lumped technology, the filter length is reduced of 43%.
Fig. 10. Photograph of distributed and semi-lumped UWB bandpass filters centered at 1 GHz.
First, the measurement and simulation results of the semi-lumped filter alone are given in Fig. 11, in order to validate the design method. A good agreement is observed in the filter passband. A wideband of 1.5 GHz is achieved leading to the expected bandwidth of 150%. The measured return and insertion loss are found to be higher than 17 dB and lower than 0.3 dB over the passband, respectively. As illustrated in Fig. 11, insertion loss increases quickly near to the low cut-off frequency, while the filter transmission parameter near to the high cut-off frequency is flatter. The first spurious response appears around 5.4 GHz. A slight shift of about 600 MHz is observed between simulations and measurements. This shift is probably due to the capacitor's model that is not sufficiently accurate at high frequencies. The measured rejection band, if a minimum 40-dB attenuation is considered, extends to about 4.9 GHz, i.e., 4.9 times the center frequency. In addition, the group delay, plotted in Fig. 12 is smaller than 2 ns as predicted by simulations, and the group delay variation is lower than 1.4 ns.
Fig. 11. Comparison between the simulation and measurement results of the 1 GHz filter.
Fig. 12. Comparison between the simulated and measured group delay of the 1 GHz filter.
Next, Fig. 13 gives the comparison between the measurement results to 3 GHz, for both filters realized in semi-lumped and distributed technologies. Return loss and bandwidth are the same for the two topologies. The flatness is better in the low-frequency part of the passband for the semi-lumped filter where it is better in the high-frequency part for the distributed filter. The shape factor, defined between −3 and −20 dB, is improved from 1.5:1 to 1.3:1 for the semi-lumped technology.
Fig. 13. Comparison between the measured responses to 3 GHz, for both UWB bandpass filters centered at 1 GHz, realized in distributed and semi-lumped technologies.
Thus it can be concluded that the semi-lumped technology leads to a significant miniaturization without scarifying to the electrical performances in the passband.
Figure 14 gives the DC to 12 GHz measurements results for both |S 21| and |S 11|. In the distributed approach, spurious responses appear only above 10 GHz, compared to 4.9 GHz for the semi-lumped approach. A semi-lumped filter with improved stopband rejection is presented in section III.C.
Fig. 14. Comparison between the measured responses to 12 GHz, for both UWB bandpass filters centered at 1 GHz, realized in distributed and semi-lumped technologies.
The measured 0.77 GHz filter also provides a good agreement between simulations and measurements with a relative bandwidth of 142%. The realized filter exhibits interesting electrical performances with low losses lower than 0.2 dB and good matching in the passband (18 dB).
B) Improved miniaturized semi-lumped filter
Now that the concept of the semi-lumped approach has been experimentally validated, the aim is to reduce the whole filter surface. A simple solution consists in bending the stubs. Note that this could not be achieved efficiently with the distributed technology because of the large areas occupied by the low characteristic impedance sections.
This technique has been applied to the 0.77 GHz filter. The filter has been optimized with the bended stubs in order to take into account the parasitics introduced with the bends, in particular the capacitive behavior.
Figure 15 gives the layout of the bended stub's filter. The photograph of the two filters (with and without bended stubs) is shown in Fig. 16. The miniaturization improvement with bended stubs reaches 75% (in term of surface) compared to the semi-lumped filter with straight stubs. Compared to the distributed approach, the miniaturization with bended stubs reaches 92%.
Fig. 15. Layout of the bended stub's filter with all dimensions, in mm.
Fig. 16. Photograph of the semi-lumped 0.77 GHz filter (a) without bended stubs and (b) with bended stubs.
The measurement results are given in Fig. 17 for comparison between both semi-lumped filters with straight and bended stubs. With bended stubs, the low 3-dB cut-off frequency is shifted to 0.45 GHz while the high cut-off frequency remains unchanged. In addition, return loss is slightly degraded (15 dB instead of 18 dB for straight stubs). The same bandstop behavior is observed for both filters with a 40-dB rejection band to 4.2 GHz.
Fig. 17. Comparison between the measured frequency responses to 5 GHz, for both semi-lumped filters with straight and bended stubs.
C) Spurious response improvement
As explained in section II.B, capacitively loaded stubs can be used in order to improve the filter rejection. This technique is applied to the 0.77 GHz filter. Figure 18 shows the photograph of the filter with capacitively loaded stubs. Measurements of both filters with loaded and unloaded stubs are compared in Fig. 19. With the introduction of capacitively loaded stubs, the first spurious peak is shifted from about 4.5 to 6.7 GHz. The measured rejection band (a minimum of 40-dB attenuation is still considered) extends to about 6 GHz when capacitively stubs are used, i.e., more than eight times the center frequency, showing a significant improvement. Although the distributed filter rejection remains greater, these results validate the capacitively loaded stub's technique.
Fig. 18. Photograph of the semi-lumped filter A, designed for spurious response improvement with capacitively loaded stubs.
Fig. 19. Comparison between measured frequency responses, for both UWB filters centered at 0.77 GHz with loaded and unloaded stubs.
IV. SENSITIVITY STUDY
A sensitivity study has been carried out by means of a Monte Carlo analysis in order to define the accuracy constraints to be applied to the dimensions and capacitor's values by considering the return loss and the cut-off frequencies. For this purpose, the frequency response of the 1 GHz filter is studied.
A) Sensitivity vs. transmission lines length
A ±10 µm precision is considered for the realization of the microstrip transmission lines. This corresponds to the accuracy given by the prototyping machine manufacturer [21]. With the Monte Carlo analysis results, we can conclude that the sensitivity vs. the transmission lines length can be neglected. This result was expected because the ±10 µm condition only represents ±0.005% of the wavelength at the centre frequency.
B) Sensitivity vs. transmission lines width
The Monte Carlo analysis has been carried out assuming ±10 µm variation on the transmission lines width. Similar conclusions as for the lines length can be obtained: the sensitivity vs. the transmission lines width is negligible. Only the return loss is slightly degraded. Here also, this result was expected as the characteristic impedance vary only by ±1 Ω around its nominal value of 120 Ω.
C) Sensitivity versus capacitor's precision
A ±2.5% variation is considered for the capacitors, corresponding to the manufacturer's precision. The return loss is slightly degraded to −18 dB in the worst case. The low cut-off frequency is not sensitive. The principal effect leads to the high cut-off frequency that is changed by 3.5% in the worst case. These results show that the precision on the lumped capacitors value has to be in regard with the precision expected on the high cut-off frequency.
D) Sensitivity vs. capacitor's quality factor
Figure 20 depicts the UWB filter response for several values of the capacitors quality factor calculated at 1 GHz (Q = 50, 100, 200, and 400). It is obvious that when the quality factor decreases, insertion loss in the passband increases leading to the degradation of the filter's performances. In our case, the capacitor's quality factor is near to 400, leading to a 0.2 dB insertion loss as obtained in the measurement results.
Fig. 20. The UWB bandpass filter response for several values of the capacitor's quality factor calculated at 1 GHz (Q = 50, 100, 200, and 400).
V. CONCLUSION
In this paper, a miniaturized semi-lumped UWB bandpass filter is proposed. It is based on a topology published by another research group in 2005 [Reference Hsu, Hsu and Kuo16], consisting of the combination of a low-pass and a high-pass filter realized using transmission lines.
The hypothesis of replacing the low characteristic impedance transmission lines by capacitively loaded transmission lines and the introduction of series capacitors at near and far end have shown a great improvement in terms of size reduction and sharpener rejection, without scarifying to the electrical performances. The synthesis method of the bandpass filter has been developed and validated by simulations. Two UWB filters centered at 0.77 and 1 GHz have been designed and fabricated. Simulated and measured results have shown a good agreement in terms of return loss (better than 18 dB) and insertion loss (lower than 0.3 dB). The selectivity has been improved compared to the classical distributed topology [Reference Hsu, Hsu and Kuo16], with a shape factor of 1.3:1 instead of 1.5:1. A miniaturization better than 85% has been achieved. However, the distributed filter high-frequency stopband remains greater with a first spurious frequency at 11 times the center frequency. Thus, a spurious suppression technique, using capacitively loaded stubs, has been carried out and has demonstrated its efficiency to eliminate spurious responses until more than eight times the center frequency. A sensitivity study demonstrated that the precision of the capacitors value is the most critical element affecting the return loss and the cut-off frequencies. A miniaturized filter with bended loaded stubs is under realization, in order to improve both the filter rejection and the miniaturization.
Darine Kaddour was born in Mechmech, Lebanon, on February 1982. She received the B.S. degree in Physics from the Lebanese University, Faculty of Sciences, Tripoli, Lebanon, in 2003, and the M.S. degree in “optics, optoeletronics, and microwaves” from the “Institut National Polytechnique de Grenoble” (INPG), Grenoble, France, in 2004. She joined the Institute of Microelectronics Electromagnetism and Photonic (IMEP) and received a Ph.D. degree from the University of Joseph Fourier in July 2007. Her main research interest concerns microwave passive filters.
Jean-DanielArnould was born in Chevreuse, France, on July 8, 1974. He received the M.Sc. degree in electronics engineering from the “Ecole Nationale Supérieure d'Electronique et de Radioélectricité” of Grenoble (ENSERG), France, in 1999 and a Ph.D. degree in optical and radio-frequency engineering from INPG, France, in 2002. Since 2002, he has been an Assistant Professor at ENSERG, where his research includes microwave photonics, semiconductor physics, and microelectronic component characterization and modeling.
Philippe Ferrari was born in France in 1966. He received a B.Sc. degree in electrical engineering in 1988 and a Ph. D. degree from the “Institut National Polytechnique de Grenoble” (INPG), France, in 1992. Later, he joined the laboratory of microwaves and characterization of the University of Savoy, France, as an Assistant Professor in electrical engineering. Since September 2004, he is an Associate Professor at the University Joseph Fourier, France, and he continues his research at the Institute of Microelectronics Electromagnetism and Photonic (IMEP) at INPG. His main research interest is the conception and realization of tunable and miniaturized microwave devices.
