# A wideband differential bandpass filter based on T-shaped stubs and single ring resonator.

1. INTRODUCTIONBalanced circuits are essential in building a modern communication system. Recently, under the trend of system-on-chip, it requires the integration of RF and analog circuits onto the digital baseband processor, thus the problem of interference and crosstalk from substrate coupling between components is getting more and more serious. For balanced circuits, differential filters with the advantages of high immunity to the environmental noises, good dynamic range, and low electromagnetic interference (EMI) are extremely important. These filters should be able to produce the desired differential-mode frequency responses and reduce the common-mode signal interference at the same time, which is essential in increasing the signal-to-noise-ratio (SNR) in the receiver and improving the efficiency of the dipole antenna in the transmitter. In recent years, lots of structures have been demonstrated for differential bandpass filter (BPF) design, which are fabricated with single band, dual bands, wide band and improved common-mode suppression characteristics [1-14]. In [1], a novel ultra -wideband (UWB) differential filter is presented based on double-sided parallel-strip lines. In [2,3], differential-mode UWB BPFs are fabricated with multiple stages branch-line. Theory and applications by means of complementary split ring resonators are discussed in [4, 5] for common-mode suppression in microstrip differential lines while both microstrip and defected ground structures (DGS) are utilized in [6,7]. In [8,9], many kinds of coupled structures are used for balanced filters applications. In [10,11], balanced coupled-resonator BPFs with common-mode suppression and stopband extension are constructed based on stepped-impedance resonators and in [12, 13], various types of full differential bandpass filters are designed and fabricated. In [14], a new technique for realizing a fully differential filter using an operational amplifier (op amp) without common-mode feedback (CMFB) is presented.

In this letter, a wideband differential bandpass filter (BPF) with differential mode passband and common mode suppression is proposed and implemented on microstrip lines for wideband application. The initial BPF is similar to a single ring resonator with two unequal feed lines which have 180[degrees] separation and its improved one is formed by loading the T-shaped stubs on the ring for better performances. This structure is very simple, compact and easy for construct without any coupling structure. With the adoption of the 180[degrees] swap structure, the proposed filter presents a perfect electric conductor wall under common mode excitation and a perfect magnetic conductor wall under differential mode excitation along the symmetric line of the ring resonator. Thus, differential wideband BPF and common mode suppression can be obtained. The improved one is formed by loading the T-shaped stubs on the ring for better performances. Finally, a microstrip differential wideband BPF is designed, simulated, fabricated, and measured. The presented differential BPF has a 3dB fractional bandwidth (FBW) of 38% for the differential mode and the common mode suppression is greater than 17 dB. Good agreement between simulations and measurements is obtained.

2. ANALYSIS AND DESIGN

As depicted in Fig. 1, a wideband differential BPF with pairs of unequal feed lines, single ring resonator and T-shaped stubs is proposed. These unequal feed lines have 180[degrees] phase separation, which can be utilized to realize conversion between differential-mode and common-mode. If the input ports (ports 1 and 1') are excited by differential-mode signals, the out-of-phase signals will be converted to in-phase signals when they pass through the 180[degrees] swap structure, then a virtual open appears at the symmetrical line T-T' and a wideband BPF is constructed. Similarly, a virtual short appears at T-T' when in-phase signals of ports 1 and 1' are converted to out-of-phase and signals will be reflected to realize common-mode suppression. Then, the circuit schemes of common-mode and differential-mode can be obtained as shown in Fig. 2.

Figure 2 shows the equivalent half circuits of common-and differential-mode of the differential BPF. For the common-mode circuit in Fig. 2(a), signals will be reflected at the center short circuit point and common-mode suppression is obtained. As for the differential-mode circuit as shown in Fig. 2(b), it can be analyzed in even-odd-mode theory. T-shaped stubs have been loaded in some other circuits to improve the performances [15-21]. The presented T-shaped can be used in microstrip circuits to crate dual controllable transmission zeros for sharper skirt and some other better performances.

The transmission-line model of the differential-mode is shown in Fig. 3 [22], in which Fig. 3(a) presents its odd-mode circuit and (b) represents its even-mode circuit. For conventional denotation, the characteristic impedances of the stubs are [Z.sub.1], [Z.sub.2], and [Z.sub.3] while their electric lengths are [[theta].sub.1], [[theta]'.sub.1], [[theta].sub.2], and [[theta].sub.3], respectively.

For the odd-mode circuit in Fig. 3(a), the odd-mode input admittance [Y.sub.odd] can be expressed as

[Y.sub.odd] = -J[Y.sub.1] cot([theta] + [theta]') (1)

If [Y.sub.odd] = 0, we can drive the resonance condition to determine the odd-mode resonant frequency. Fig. 4 plots the odd-mode resonant frequencies versus [[theta].sub.x] + [[theta]'.sub.x]. Obviously, one transmission pole [f.sub.0] is located at [[theta].sub.x] + [[theta]'.sub.x] = 90 deg.

For the even-mode equivalent circuit of the differential-mode half circuit shown in Fig. 3(b), the even-mode input admittance [Y.sub.even] is written as

[Y.sub.even] = [Y.sub.1] [Y.sub.L] + j[Y.sub.1] tan ([[theta].sub.1] + [[theta]'.sub.1] / [Y.sub.1] + j[Y.sub.L] tan ([[theta].sub.1] + [[theta]'.sub.1])

where

[Y.sub.L] = j[Y.sub.2] [Y.sub.3] + [Y.sub.2] tan [[theta]sub.2] cot [[theta].sub.3] / [Y.sub.3] tan [[theta].sub.2] - [y.sub.2] cot [[theta].sub.3] (3)

If [Y.sub.even] = 0, the even-mode resonant frequencies can be determined. Thus, another two resonant frequencies [f.sub.1] and [f.sub.2] of even-mode can be obtained as

[[theta].sub.1] = arctan ([square root of ([Y.sub.1] - [Y.sub.2] + [Y.sub.3]/[Y.sub.1])]) (4a)

[[theta].sub.e2] = -arctan ([square root of ([Y.sub.1] - [Y.sub.2] + [Y.sub.3]/[Y.sub.1])]) (4b)

Figure 5 plots the even-mode input admittance versus [[theta].sub.x] + [[theta]'.sub.x]. Obviously, two transmission poles [f.sub.1] and [f.sub.2] are located at the sides of [f.sub.0].

The even-mode resonant frequencies spectrum versus [Z.sub.L]/[Z.sub.1] is shown in Fig. 6. The two transmission poles [f.sub.1] and [f.sub.2] can be adjusted by changing the characteristic impedance [Z.sub.L] ([Z.sub.2] and [Z.sub.3]), thus the FBW of this filter can be controlled within a wide range.

To verify our discussion, a differential wideband filter is fabricated and measured. The configuration of the proposed differential wideband BPF is shown in Fig. 1. The filter is manufactured on RT/Duroid Rogers 4003 substrate with a relative permittivity of 3.38 and loss tangent of 0.0027, with a height of 0.508 mm. The photograph of the fabricated differential wideband BPF is shown in Fig. 7.

3. RESULTS AND DISCUSSION

Based on the above discussions and the theoretical analysis in Section 2, the final parameters for the differential filter with unequal feed lines are [Z.sub.0] = 50[omega], [Z.sub.1] = 80[omega], [Z.sub.2] = 110[omega], and [Z.sub.3] = 80[omega]. The final structure parameters for the differential wideband BPF are [w.sub.1] = 3.1 mm, [w.sub.2] = 0.5 mm, [w.sub.3] = 0.5 mm, [w.sub.4] = 1.0 mm, [l.sub.1] = 6.8 mm, [l.sub.2] = 3.2 mm, [l.sub.3] = 3.5 mm, [l.sub.4] = 6.3 mm, and [l.sub.5] = 4.0 mm.

To provide a simple figure-of-merit for characterizing the implement differential filter, the common-mode rejection ratio (CMRR) can be defined by

CMRR = 20 log [absolute value of [S.sup.dd.sub.21]] / [absolute value of [S.sup.cc.sub.21]] (5)

The value of the CMRR may be used to quantitatively discuss the degree of resemblance between the implemented differential filter.

The simulated and measured results of [S.sup.cc.sub.21], [S.sup.dd.sub.21], [S.sup.cc.sub.11], and [S.sup.dd.sub.11] for the proposed wideband differential BPF are shown in Figs. 8(a) and (b). Meanwhile, the CMRR provides an important figure -of-merit for a meaningful characterization of differential filters. Fig. 8(c) shows the simulated and measured responses of CMRR for the implemented differential filter based on unequal feed lines, T-shaped stubs and single ring resonator. Specifically, the filter has a maximum CMRR of more than 45 dB at the center frequency of the filter with all CMRR values above 17 dB between the 3-dB passband. The simulated results and measured results agree well with each other.

To clarify the proposed wideband differential BPF design, the design procedure can be summarized as follows:

1) The common mode suppression can be obtained easily using this filter structure due to the equivalent half circuit of common-mode equivalent half circuit as shown in Fig. 2(a).

2) The center frequency of differential mode can be determined by the electrical length of the ring resonator and the loaded T-shaped stubs, as analyzed in Equation (1).

3) Varied characteristic impedances of [Z.sub.1], [Z.sub.2], and [Z.sub.3] can be used to control the bandwidth of differential mode for the proposed wideband differential BPF, as shown in Fig. 6 and Equation (4).

4) The final dimensions can be obtained by using some microwave simulators although the open ends and cross sections will affect the practical electrical lengths of the resonator.

4. CONCLUSION

A wideband differential bandpass filter (BPF) with differential mode passband and common mode suppression is proposed and implemented on microstrip lines for wideband application. With the help of loaded T-shaped stubs, the performances of the filter are improved rather than the initial BPF which is similar to a single ring resonator with two unequal feed lines which have 180[degrees] separation. The presented differential BPF has a 3-dB fractional bandwidth (FBW) of 38% for the differential mode and larger than 17 dB common mode suppression. Good agreement between simulated and measured results is obtained. This simple, compact, and low cost structure will be very useful for differential communication systems.

ACKNOWLEDGMENT

The authors would like to express their great appreciate to editors and reviews for their valuable comments and suggestions.

Received 15 March 2013, Accepted 3 May 2013, Scheduled 8 May 2013

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Hui Wang *, Wei Kang, Guo Yang, and Wen Wu

Ministerial Key Laboratory of JGMT, Nanjing University of Science and Technology, Nanjing 210094, China

* Corresponding author: Hui Wang (wh5300@sina.com).

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Author: | Wang, Hui; Kang, Wei; Yang, Guo; Wu, Wen |
---|---|

Publication: | Progress In Electromagnetics Research Letters |

Article Type: | Abstract |

Geographic Code: | 1USA |

Date: | May 1, 2013 |

Words: | 2503 |

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