Size and Harmonic Reduced Wilkinson Balun Using Parallel Coupled Line with Open Stub

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  • ABSTRACT

    In this paper, a size-reduced Wilkinson balun with wide harmonic-suppressed band is presented. An accurate analysis of the parallel coupled line with an open stub (PCL-OS) is carried out. The PCL-OS 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 (PCL-OS) , Wilkinson Size Reduction , Balun

  • I. INTRODUCTION

    The parallel coupled line with an open stub (PCL-OS) 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 PCL-OS demonstrates excellent performances, including its low pass filter with wideband rejection characteristics and sharp skirt response as well as its structural compactness. The equivalent T-network and equivalent LUC block are represented in Fig. 1(b) and (c). The analysis of this PCL-OS was also attempted in [2,4,5].

    However the derived analytical equations for the PCL-OS 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 two-port 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 even-odd mode analysis of the structure is also reported [3], which is limited in the transmission zeros with a quarter-wavelength for a bandstop filter design. When we design a microwave component that contains the PCL-OS 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 [68]. The balun consists of two 3λ/4 and λ/4 transmission lines with a λ/2 line with Z0 and a resistor with 2Z0. 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 even-odd mode analysis to the whole PCL-OS 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 PCL-OS

    To analyze the PCL-OS 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],

    image
    image
    image
    image

    where θP, Z0e, and Z0o are the electrical length, even- and oddmode impedances of the parallel coupled line, respectively.

    The open-stub section is modeled as an equivalent capacitor, Cs as shown in Fig. 3(b).

    image

    where ω is the angular frequency, and θs is the electrical length of the open-stub.

    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.

    image
    image

    Using (3a)–(3b) and the well-known port reduction procedure the four-port impedance matrix, (1a)–(1d), can be converted into a two-port impedance matrix, (4a)–(4b).

    image
    image

    where,

    To design the three-stage low pass filter in Fig. 1(b) with a given specification of ripple and cutoff frequency fc, we can determine the L and C values from the standard low pass filter design procedure [9]. The impedance matrix of T-type low pass filter can be derived as

    image
    image

    where ω0 is the center angular frequency of the LUC’s calculation and design.

    By equating (4) to (5), we can calculate the exact equivalent capacitance, CS, for the PCL-OS with the characteristics of the low pass prototype filter, as follows.

    image

    where D = ω0CZ0e, E = ω0CZ0o

    Now, we can decide the other structural parameters for the PCL-OS 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 PCL-OS from [1] and [9], as follows.

    image
    image
    image
    image

    where ZI and βℓ are the image parameters of the parallel coupled line.

    Meanwhile, the designed PCL-OS with low pass filter characteristics can be used to design various devices that have λ/4 transmission-line blocks or λ/4-LUCs. The λ/4-LUC 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 T-network in Fig. 1(b) with the T-type equivalent circuit for a transmission line in Fig. 4.

    image
    image

    where θI-LUC is the image electrical length and ZI-LUC is the image impedance. From (2) and (4), the impedance matrix of the PCL-OS or the LUC can be derived as (9).

    image
    image

    where

    To compare the exactness of derived (4a)–(4b) with those previously reported, (1) of [2] or ZT of [5], arbitrary parameter values for a PCL-OS in Table 1 are used to calculate and simulate the Z-parameters, 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 Z-parameter 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 fn of the LUC is located at the frequency of |S21| = 0.

    From the relation [8] between the impedance and scattering matrices, S21 can be obtained as (10)

    image

    Then, the notch frequency fn can be decided by (Z21 = 0) or (Z21≠∞ and Z11 = ∞).

    The notch frequency fn is independently controlled without changing the low pass filter parameters defined above. The open stub has two parameters, ZS and θS, and, hence CS and fn can be determined independently. The various fn examples according to the decreasing ZS with constant CS 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 CPW-Wilkinson 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 S21, S31, and isolation. The LUC’s cutoff frequency fc must be carefully determined considering the operating frequency band and spurious rejection of the balun. A recommended value is f0 = fc +BW/2, where BW is the bandwidth of the balun. For a small pass-band ripple as in Fig. 6, the choice of f0 = fc gives also good result.

    The LUC is designed using the following procedure:

    We designed a T-type Chebyshev low pass filter with a cutoff of 2.45 GHz and a ripple of 0.01 dB. By using the obtained L, and C of the low pass filter, we calculated the LUC parameters shown in Table 2 using the above LUC design procedure for f0 = 2.45 GHz. For good harmonic suppression, we chose three different fn values of the LUCs.

    The power division, impedance matching, and isolation properties in a pass-band around 2.45 GHz are as good as a conventional Wilkinson balun. The thickness and relative dielectric constant of the WINUS ISO640-338 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 CPW-Wilkinson 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 f0 (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 pass-band. 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 PCL-OS 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 pass-band 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.

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  • [Fig. 1.] (a) The structure of the parallel coupled line with an open stub (PCL-OS). (b) The equivalent T-network and (c) equivalent low pass filter unit cell (LUC) block.
    (a) The structure of the parallel coupled line with an open stub (PCL-OS). (b) The equivalent T-network 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.
    (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).
    (a) Parallel coupled line. (b) Equivalent circuit for Fig. 1(a).
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  • [Fig. 4.] A transmission line and its T-type equivalent circuit.
    A transmission line and its T-type equivalent circuit.
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  • [Table 1.] Arbitrary parameter values for comparison of the parallel coupled line with an open stub (PCL-OS) design equations
    Arbitrary parameter values for comparison of the parallel coupled line with an open stub (PCL-OS) design equations
  • [Fig. 5.] Impedance parameter comparison for ADS, proposed (4a)?(4b), and equations in [2] and [5]. (a) Z11, (b) Z21.
    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.
    Notch frequencies according to the decreasing ZS, with constant CS.
  • [Table 2.] Parameter values of the LUCs for the balun design
    Parameter values of the LUCs for the balun design
  • [Fig. 7.] The comparison of the proposed Wilkinson balun and the conventional Wilkinson balun.
    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.
    Measured and simulated frequency responses: (a) S21 and S31, (b) S11 and S32.
  • [Fig. 9.] Measurement results of the conventional Wilkinson balun.
    Measurement results of the conventional Wilkinson balun.
  • [Fig. 10.] Comparisons of the output phase differences.
    Comparisons of the output phase differences.