Size and Harmonic Reduced Wilkinson Balun Using Parallel Coupled Line with Open Stub
 Author: Lee WonKyun, Hwang HeeYong
 Organization: Department of Electrical and Electronic Engineering, Kangwon National University, Chuncheon, Korea.; Department of Electrical and Electronic Engineering, Kangwon National University, Chuncheon, Korea.
 Publish: Journal of electromagnetic engineering and science Volume 14, Issue4, p387~392, Dec 2014

ABSTRACT
In this paper, a sizereduced Wilkinson balun with wide harmonicsuppressed band is presented. An accurate analysis of the parallel coupled line with an open stub (PCLOS) is carried out. The PCLOS structure shows excellent low pass filter and harmonicsuppression characteristics, which is useful for designing a low pass filter unit cell (LUC) with a reduced size. The designed Wilkinson balun at a 2.45 GHz center frequency not only shows an excellent harmonic suppression including the 5th harmonics up to 14 GHz over 15 dB, but it also has an area reduced to 48% of the conventional one.

KEYWORD
Harmonic Suppression , Low Pass Filter Unit Cell (LUC) , Parallel Coupled Line with an Open Stub (PCLOS) , Wilkinson Size Reduction , Balun

I. INTRODUCTION
The parallel coupled line with an open stub (PCLOS) in Fig. 1(a) has been reported and widely adopted as a building block or low pass filter unit cell (LUC) in designing a compact low pass filter [1], compact wideband bandstop filters [2,3], an harmonic and size reduced ring hybrid [4], and a compact and harmonic suppressed Wilkinson power divider [5]. The PCLOS demonstrates excellent performances, including its low pass filter with wideband rejection characteristics and sharp skirt response as well as its structural compactness. The equivalent Tnetwork and equivalent LUC block are represented in Fig. 1(b) and (c). The analysis of this PCLOS was also attempted in [2,4,5].
However the derived analytical equations for the PCLOS are approximated as an undefined floating port of the coupled line, which is connected to the open stub, is used as if a defined port in the analysis of the serially connected twoport networks in Fig. 2 of [2], Fig. 3 of [4], and Fig. 1 of [5]. The equivalent capacitance C in Fig. 1 was treated as a simple summation of the equivalent capacitance of the parallel coupled line (CP in [2,4,5]) and the equivalent capacitance of the open stub (CS). An evenodd mode analysis of the structure is also reported [3], which is limited in the transmission zeros with a quarterwavelength for a bandstop filter design. When we design a microwave component that contains the PCLOS or LUC using the previous equivalent equations, we have to perform repetitive iteration processes to obtain exact or desired characteristics.
Meanwhile, a simple coplanar waveguide (CPW) balun having the structure of a Wilkinson divider has been recently proposed [6–8]. The balun consists of two 3λ/4 and λ/4 transmission lines with a λ/2 line with Z_{0} and a resistor with 2Z_{0}. Hence, it has serious drawbacks in its size and unwanted harmonics for low frequency applications. The microstrip version of the Wilkinson balun is shown in Fig. 2(a).
In this research, we first derived the exact design equations for the LUC by applying the full evenodd mode analysis to the whole PCLOS structure.
Second, to demonstrate the validity of the analysis we applied the design equations for the LUC to designing a size and harmonic reduced microstrip Wilkinson balun as shown in Fig. 2(b).
II. ANALYSIS OF PCLOS
To analyze the PCLOS structure we assumed that the structure is lossless and the discontinuity effect between the parallel coupled line and the open stub is negligible.
The characteristics of a parallel coupled line as shown in Fig. 3(a) can be expressed as an impedance matrix as follows [9],
where
θ_{P}, Z_{0e} , andZ_{0o} are the electrical length, even and oddmode impedances of the parallel coupled line, respectively.The openstub section is modeled as an equivalent capacitor,
C_{s} as shown in Fig. 3(b).where
ω is the angular frequency, andθ_{s} is the electrical length of the openstub.The relations between the node voltages and the branch currents around the connection point in Fig. 3(b) are given as (3a) and (3b) by Kirchhoff’s law.
Using (3a)–(3b) and the wellknown port reduction procedure the fourport impedance matrix, (1a)–(1d), can be converted into a twoport impedance matrix, (4a)–(4b).
where,
To design the threestage low pass filter in Fig. 1(b) with a given specification of ripple and cutoff frequency
f_{c} , we can determine theL andC values from the standard low pass filter design procedure [9]. The impedance matrix of Ttype low pass filter can be derived aswhere
ω _{0} is the center angular frequency of the LUC’s calculation and design.By equating (4) to (5), we can calculate the exact equivalent capacitance,
C_{S} , for the PCLOS with the characteristics of the low pass prototype filter, as follows.where
D =ω _{0}CZ _{0e},E =ω _{0}CZ _{0o}Now, we can decide the other structural parameters for the PCLOS in Fig. 1(a), which performs the response for the desired low pass filter in Fig. 1(b), using the equivalent parameters for coupled line part of the PCLOS from [1] and [9], as follows.
where
Z_{I} andβℓ are the image parameters of the parallel coupled line.Meanwhile, the designed PCLOS with low pass filter characteristics can be used to design various devices that have λ/4 transmissionline blocks or λ/4LUCs. The λ/4LUC is defined as an equivalent λ/4 line consisting of an LUC and two short transmission lines.
The image parameters of the LUC in Fig. 1(c) can be obtained as (8), equating the Tnetwork in Fig. 1(b) with the Ttype equivalent circuit for a transmission line in Fig. 4.
where
θ_{ILUC} is the image electrical length andZ_{ILUC} is the image impedance. From (2) and (4), the impedance matrix of the PCLOS or the LUC can be derived as (9).where
To compare the exactness of derived (4a)–(4b) with those previously reported, (1) of [2] or
Z_{T} of [5], arbitrary parameter values for a PCLOS in Table 1 are used to calculate and simulate the Zparameters, and the graphical results are depicted in Fig. 5. Here, the real parts of the impedance parameters are zero for all frequencies and hence do not appear in the figure. The Zparameter values calculated by the ADS simulator are exactly the same as those by (4a)–(4b) above, while the equations of [2] and [5] provide approximated values.The transmission zero frequency of notch frequency
f_{n} of the LUC is located at the frequency of S _{21} = 0.From the relation [8] between the impedance and scattering matrices,
S _{21} can be obtained as (10)Then, the notch frequency
f_{n} can be decided by (Z_{21} = 0) or (Z_{21}≠∞ and Z_{11} = ∞).The notch frequency
f_{n} is independently controlled without changing the low pass filter parameters defined above. The open stub has two parameters,Z_{S} andθ_{S} , and, henceC_{S} andf_{n} can be determined independently. The variousf_{n} examples according to the decreasingZ_{S} with constantC_{S} are depicted in Fig. 6.III. MICROSTRIP WILKINSON BALUN DESIGN
Using the LUC design equations, we designed and fabricated a size and harmonics reduced microstrip Wilkinson balun operating at 2.45 GHz. Fig. 2(b) shows the layout of the proposed Wilkinson balun compared to the CPWWilkinson balun [6] of Fig. 2(a). Here, the transmission line sections of the Wilkinson balun are replaced by three LUCs. The LUC 1, 2, and 3 are good for harmonic reduction in
S _{21},S _{31}, and isolation. The LUC’s cutoff frequencyf_{c} must be carefully determined considering the operating frequency band and spurious rejection of the balun. A recommended value isf_{0} =f_{c} +BW/2, where BW is the bandwidth of the balun. For a small passband ripple as in Fig. 6, the choice off_{0} =f_{c} gives also good result.The LUC is designed using the following procedure:
We designed a Ttype Chebyshev low pass filter with a cutoff of 2.45 GHz and a ripple of 0.01 dB. By using the obtained
L , andC of the low pass filter, we calculated the LUC parameters shown in Table 2 using the above LUC design procedure forf_{0} = 2.45 GHz. For good harmonic suppression, we chose three differentf_{n} values of the LUCs.The power division, impedance matching, and isolation properties in a passband around 2.45 GHz are as good as a conventional Wilkinson balun. The thickness and relative dielectric constant of the WINUS ISO640338 substrate used for the simulation and experiment is 0.762 mm and 3.38, respectively. Fig. 7 shows photographs of the proposed and a microstrip version of the conventional CPWWilkinson balun [6], which have the center frequency of 2.45 GHz. The area of the proposed microstrip Wilkinson balun is reduced to 48% of the conventional one. The simulated and measured amplitude results are shown in Fig. 8. They agree well with each other on the viewpoints of the power division, the matching, the isolation and the harmonic suppression properties. The measured insertion losses in
f_{0} (including SMA connectors) are 0.308 dB and 0.307 dB at the two output ports, port 2 and port 3. Furthermore, the harmonics and isolation of the proposed Wilkinson balun are suppressed below 15 dB up to 14 GHz. However, the measured result of the conventional Wilkinson baluns in Fig. 9 shows that the spurious harmonics are repeated in the whole frequency band above the passband. Fig. 10 shows the simulated and measured output phase differences of the proposed balun and those of the conventional one. They agreed well with each other.IV. CONCLUSIONS
The exact analysis of the PCLOS and an application of the Wilkinson balun are presented. The designed microstrip Wilkinson balun shows a significantly reduced size and a harmonicsuppressed property simultaneously, without degradation of the passband performances.
The proposed design equations and the LUC design procedure could be helpful in designing various microwave devices needing size reduction and harmonic suppression, simultaneously.

[Fig. 1.] (a) The structure of the parallel coupled line with an open stub (PCLOS). (b) The equivalent Tnetwork and (c) equivalent low pass filter unit cell (LUC) block.

[Fig. 2.] (a) The microstrip version of [6, 7] and (b) the proposed microstrip Wilkinson balun.

[Fig. 3.] (a) Parallel coupled line. (b) Equivalent circuit for Fig. 1(a).

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[Fig. 4.] A transmission line and its Ttype equivalent circuit.

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[Table 1.] Arbitrary parameter values for comparison of the parallel coupled line with an open stub (PCLOS) design equations

[Fig. 5.] Impedance parameter comparison for ADS, proposed (4a)？(4b), and equations in [2] and [5]. (a) Z11, (b) Z21.

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[Fig. 6.] Notch frequencies according to the decreasing ZS, with constant CS.

[Table 2.] Parameter values of the LUCs for the balun design

[Fig. 7.] The comparison of the proposed Wilkinson balun and the conventional Wilkinson balun.

[Fig. 8.] Measured and simulated frequency responses: (a) S21 and S31, (b) S11 and S32.

[Fig. 9.] Measurement results of the conventional Wilkinson balun.

[Fig. 10.] Comparisons of the output phase differences.