*A wideband bandstop filter (WBSF) with extended upper passband consists of a modified transmission line ring with one embedded capacitor. Interference between two signal paths produces three adjustable transmission zeros used to create a wide, controllable stopband. Use of the embedded capacitor prevents the stopband from repeating at odd multiples of the fundamental stopband center frequency, resulting in a much wider upper passband. The circuit is simple, very compact and easy to fabricate. A prototype WBSF has a 20 dB rejection bandwidth of 90.7 percent at a center frequency of 1.2 GHz.*

Microwave bandstop filters (BSF) are widely used in wireless communication and RF circuits for their effective suppression of spurious while allowing desired signals to pass. Compact WBSFs with high skirt selectivity are in demand for many communication and radar systems. Conventional BSFs using a shunt open circuited stub and coupled-line are generally large and narrowband.^{1}

Several BSF configurations in planar technology with rejection and a wide stopband have recently been reported. Li, et al.^{2} and Hsieh and Wang^{3} describe WBSFs that combine quarter-wavelength lines with coupled-line sections of the same electrical length. WBSFs are also achieved by connecting two quarter-wavelength coupled-line sections, one with a short circuit and the other with an open circuit.^{4}

The signal interference technique has been used to design WBSFs with good skirt selectivity.^{5-7} The structure is made up of two parallel transmission lines with different electrical lengths and characteristics. By successfully placing the transmission zeros near the stopband edges, signal interference techniques enable sharp rejection with high skirt selectivity. In addition, the performance of these filters can be improved with additional lines. For example, Kanti, et al.^{8} use a parallel-coupled transmission line section to improve BSF performance with five transmission zeros in the stopband. Similarly, the use of an open-ended coupled-line significantly enhances the 20 dB rejection bandwidth.^{9,10} Furthermore, ultra-wide bandwidth and sharp rejection can be balanced with two-section open stubs.^{11} Despite attractive stopband characteristics, the bandwidth of the upper passband in these filters is generally narrow; worse, the bandwidth of the upper passband decreases largely as the bandwidth of the stopband increases.

In this article, we describe a novel WBSF that improves the stopband and broadens the upper passband. The structure includes two bilateral transmission lines and one embedded capacitor to reduce signal interference. This generates three adjustable transmission zeros in the controllable stopband for sharp rejection and expands the upper passband tremendously compared to the similar structures,^{7-11} through the use of the embedded capacitor.

**CONFIGURATION**

The modified transmission line model (see ** Figure 1**) can be decomposed into two parallel sections. One is the upper transmission line having a characteristic admittance Y

_{1}and electrical length θ

_{1}; the other is the cascaded structure consisting of two bilateral transmission lines with characteristic admittance Y

_{2}, electrical length θ

_{2}and one embedded capacitor.

Considering the entire structure to be lossless, the overall Y matrix is

If θ_{1} = π when f = f, then _{ }=+∞ at frequency f_{1}.

For the lower section, at frequency,

Obviously, there is a series resonance for the lower section when f = f_{2}. For this design, f_{2} is always set lower than f_{1} to generate three transmission zeros. Then the total parallel Y matrix of the structure can be expressed as

The BSF creates transmission zeros at the frequencies where |S_{21}| = 0, and the relationship between the admittance matrices and scattering matrices can be given by

The condition for production of the transmission zeros can be simplified by setting =0, which yields the relationship

The relevant graph of Equation 5 is shown in ** Figure 2**. The solid line and dashed line represent and -, respectively, and the intersection points in the curves reveal the approximate locations of the stopband transmission zeros.

As shown in Figure 2, the first transmission zero positioned at f_{z1} is generated at the lower side of f1 since f_{2} < f_{1} is satisfied in this design. Another two transmission zeros f_{z2} and f_{z3} are provided between f_{1} and 2f_{1} when.

With the choice of appropriate parameters, the structure produces three transmission zeros for a BSF response.

Note that the transmission zero distribution in this design is not inherently symmetrical about the central transmission zero, while the transmission zero distributions of almost all the previous reported WBSFs are symmetrical. In fact, by tuning C or Y_{1}, different transmission zero distributions can provide either symmetric or asymmetric BSF responses. The asymmetric bandstop filter response can also eliminate the restriction of a fixed central transmission zero, resulting in better adjustability and flexibility compared with the previous reported WBSFs.

As shown in ** Figure 3a** and the above analysis, for given upper and lower transmission line parameters, the transmission zero distribution can be adjusted effectively by changing C. With increasing C, f

_{2}decreases, moving the first transmission zero lower. Meanwhile, the dashed line (- ) becomes sharper, pushing the second transmission zero higher and drawing the third transmission zero lower. Accordingly, the transmission zero separation between f

_{z1}and f

_{z2}increases while the transmission zero separation between f

_{z2}and f

_{z3}decreases with increasing C. As shown in

**, different BSF responses with different transmission zero distributions can be obtained by changing C.**

*Figure 3b*The characteristic admittance of the upper transmission line is also an important factor in adjusting the transmission zero distribution. As indicated in ** Figure 4a**, when increasing the upper transmission line’s characteristic admittance Y

_{1}, becomes sharper, pushing the first and the second transmission zeros higher and drawing the third transmission zero lower. Accordingly, the transmission zero separation between f

_{z1}and f

_{z2}changes slightly while the transmission zero separation between f

_{z2}and f

_{z3}becomes smaller with increased Y1. Therefore, as shown in

**, different bandstop filtering responses with different transmission zero distributions can be achieved by altering Y**

*Figure 4b*_{1}.

**FABRICATION AND MEASUREMENTS**

A prototype WBSF having a 20 dB fractional bandwidth (FBW) of 90.7 percent at f_{c} = 1.2 GHz was fabricated on a 0.5 mm substrate with a relative dielectric constant of 2.65 and loss tangent 0.02. The physical dimensions and photograph are shown in ** Figure 5**. The optimized parameters are w

_{0}= 2.4 mm, l

_{0}= 10.4 mm, w

_{1}= 0.32 mm, l

_{1}= 38.2 mm, l

_{2}= 4.7 mm, w

_{50}=1.35 mm, l

_{50}= 19.8 mm and C = 4.3 pF (achieved using MURATA 1.6 mm × 0.8 mm patch capacitors). Ansoft HFSS was used for simulation, and the Keysight 8510C vector network analyzer was used for the corresponding measurements.

** Figure 6** shows good agreement between simulation and measurement. Measured transmission zero locations are at 0.71 GHz (with a suppression of 42.9 dB), 1.25 GHz (with a suppression of 40.2 dB) and 1.73 GHz (with a suppression of 29.9 dB), respectively. The measured 20 dB attenuation band is from 0.65 to 1.8 GHz, forming a wide attenuation bandwidth and a high FBW of 95.8 percent. Measured passband insertion loss, including connector loss, is less than 1 dB up to 0.50 GHz, increasing slightly in the upper band. The loss is less than 2 dB from 1.87 to 2.58 GHz and 3.45 to 5 GHz, and it is less than 3 dB for the entire upper passband. Attenuation rates at the passband to stopband transition knees are 171.3 dB/GHz (measured attenuation of 5 and 29.5 dB at 0.55 and 0.69 GHz, respectively) and 163.3 dB/GHz (measured attenuation of 5 and 29.5 dB at 1.90 and 1.75 GHz, respectively) on the lower and upper side of the stopband.

Without the feed line, the WBSF occupies a compact size of 41 mm × 15.2 mm, corresponding to 0.022λ_{g}^{2} (0.243λ_{g} × 0.09λ_{g}), where λ_{g} is the guide wavelength of a 50 Ω transmission line at the center frequency of 1.2 GHz.

A comparison of this filter with other reported WBSFs is provided in ** Table 1**. It exhibits a wider stopband, sharper rejection level and wider upper passband. Additionally, its size is much smaller.

**CONCLUSION**

A novel compact WBSF with extended upper passband is realized by using the signal interference technique and one embedded capacitor. The distributions of the three transmission zeros can be easily and flexibility adjusted by changing the value of the embedded capacitor and the circuit characteristic admittance to obtain the desired performance. Moreover, the WBSF exhibits sharp rejection in the stopband. The circuit size is only 0.022 λ_{g}^{2} making it suitable for applications where small size is important. Design equations, curves and theoretical analyses are provided. The theoretical predictions are verified through measurement of a prototype WBSF with a 20 dB FBW of 90.7 percent centered at 1.2 GHz.

**ACKNOWLEDGMENT**

This work was supported by the program for Zhejiang leading team of science and technology innovation (2011R50004), the National Natural Science Foundation of China under grants (61101052) and 521 talent project of Zhejiang Sci-Tech University.

**References**

- D. M. Pozar,
*Microwave Engineering*, 3^{rd}Edition, Wiley, N.Y., 2005. - R. Li, D. I. Kim and C. M. Choi, “Compact Structure with Three Attenuation Poles for Improving Stopband Characteristics,”
*IEEE Microwave and Wireless Components Letters*, Vol. 16, No. 12, December 2006, pp. 663–665. - M. Y. Hsieh and S. M. Wang, “Compact and Wideband Microstrip Bandstop Filter,”
*IEEE Microwave and Wireless Components Letters*, Vol. 15, No. 7, July 2005, pp. 472–474. - M. K. Mandal, K. Divyabramham and S. Sanyal, “Compact, Wideband Bandstop Filters with Sharp Rejection Characteristic,”
*IEEE Microwave and Wireless Components Letters*, Vol. 18, No. 10, October 2008, pp. 665–667. - M. K. Mandal and P. Mondal, “Design of Sharp-Rejection, Compact, Wideband Bandstop Filters,”
*IET Microwaves, Antennas & Propagation*, Vol. 2, No. 4, June 2008, pp. 389–393. - M. K. Mandal, K. Divyabramham and S. Sanyal, “Design of Compact, Wide-Band Bandstop Filters with Sharp Rejection Characteristics,”
*Microwave and Optical Technology Letters*, Vol. 50, No. 5, May 2008, pp. 1244–1248. - K. Divyabramham, M. K. Mandal and S. Sanyal, “Sharp-Rejection Wideband Bandstop Filters,”
*IEEE Microwave and Wireless Components Letters*, Vol. 18, No. 10, October 2008, pp. 662–664. - M. K. Mandal, K. Divyabramham and V. K. Velidi, “Compact Wideband Bandstop Filter With Five Transmission Zeros,”
*IEEE Microwave and Wireless Components Letters*, Vol. 22, No. 1, January 2012, pp. 4–6. - M. K. Mandal, V. K. Velidi, S. Sanyal and A. Bhattacharya, “Design of Ultra-Wideband Bandstop Filter with Three Transmission Zeros,”
*IEEE Microwave and Optical Technology Letters*, Vol. 50, No. 11, November 2008, pp. 2955–2957. - V. K. Velidi, A. B. Guntupalli and S. Sanyal, “Sharp-Rejection Ultra-Wide Bandstop Filters,”
*IEEE Microwave and Wireless Components Letters*, Vol. 19, No. 8, August 2009, pp. 503–505. - M. A. Sanchez-Soriano, G. Torregrosa-Penalva and E. Bronchalo, “Compact, Wideband Bandstop Filter with Four Transmission Zeros,”
*IEEE Microwave and Wireless Components Letters*, Vol. 20, No. 6, June 2010, pp. 313–315.