1 Introduction

One of the widely used device in the modern wireless circuits and systems is Wilkinson power divider (WPD). Input signals are divided by WPDs into two or more signals [1,2,3] and used in many systems such as antenna arrays, power amplifiers, feeding networks. A conventional WPD, consists of two quarter wavelength (λ/4) lines and a 100 ohms isolation resistor between two lines.

Relatively large size and presence of unwanted harmonic in the frequency response are the main drawbacks of the conventional divider. So far, various methods are used to suppress unwanted harmonics and decrease the circuit size. In [4] by using a π type structure, which includes a capacitor between two lines, instead of quarter wavelength transmission line, 3rd harmonic of the power divider is suppressed; however, this design suffers from large size.

In [5], a divider with wide pass-band, using ring resonator is designed, which suppresses the unwanted harmonics. The return loss parameter at the operating frequency is not good. In [6], a simple power divider is presented by using microstrip open stubs, which suppresses 2nd to 6th harmonics. In [7] a compact WPD with anti-coupled line and capacitive load is reported. This divider has good harmonics suppression but, isolation parameter in this design is not very good.

Except using resonators [5] and coupling lines [7], some other methods such as the defected ground structure (DGS) [8], and photonic band gap (PCB) [9], are used to design compact WPD with harmonics suppression. The main drawback of these works is the complex fabrication process.

In this presented paper, a miniaturized WPD using low pass filter instead of large conventional quarter wavelength line is proposed. Furthermore, the proposed WPD has low insertion loss, wide harmonics suppression from 2nd harmonic to 8th and good isolation. In design procedure at first, a low pass filter using triangle-shaped resonators is described step by step. Then, the designed power divider by using the proposed low pass filter, has been presented.

2 Design Process

The structure of the conventional Wilkinson power divider (WPD) is depicted in Fig. 1. In the conventional divider structure an isolation resistor (R = 100Ω) and two quarter wavelength (λ/4) transmission lines with \(\sqrt {2 }\) Z0 impedance are used, which occupied relatively large size. In the proposed WPD, the relatively long λ/4 transmission lines, which used in conventional divider, are replaced by low pass filter structure.

Fig. 1
figure 1

The conventional Wilkinson power divider

Full size image

2.1 Resonator Design

The layout of the main resonator (triangular shape) is demonstrated in Fig. 2a. In the main resonator structure a high impedance line with short length and a triangle shaped resonator is connected to a high impedance transmission line. The dimensions of the designed resonator are as follows: L1 = 2.78 mm, W1 = 2.88 mm, L2 = 8.65 mm, W2 = 0.28 mm. The equivalent LC circuit of the main resonator is depicted in Fig. 2b. According to Eqs. (1) and (2) the low and high impedance transmission lines, are obtained as follows [10]:

Fig. 2
figure 2

The main resonator: a Layout, b LC equivalent circuit, c LC and EM simulation results

Full size image
$$l_{s} = \frac{1}{\omega } \times z_{s} \times \sin \left( {\frac{2\pi }{{\uplambda_{g} }}l} \right)$$
(1)
$$c_{s} = \frac{1}{\omega } \times \frac{1}{{z_{s} }} \times \tan \left( {\frac{\pi }{{\uplambda_{g} }}l} \right)$$
(2)

where \(z_{s}\) is the characteristic impedance of the applied transmission line, \(\uplambda_{g }\) is the guided wavelength at the cut-off frequency and \(l\) is the physical length of line.

Table 1 shows the optimized L-C parameters, which calculated by ADS software.

Table 1 The optimized L-C parameters of the main resonator
Full size table

S-Parameters simulation of the main resonator are depicted in Fig. 2c. Both of the EM and LC simulations responses are depicted. The agreement between curves are proved the validity of the equivalent LC circuit.

In order to improve the sharpness of transition-band and achieve wide harmonic suppression, two triangle shaped resonators are Inserted in both sides of the main resonator. The layout of the primary low pass filter is illustrated in Fig. 3a. The EM simulation results of the S-parameters for the primary low pass filter is illustrated in Fig. 3b. As seen in Fig. 3b, these three sections, are created three transmission zeroes.

Fig. 3
figure 3

Primary low pass filter: a Layout, b EM simulation results

Full size image

Finally, in order to have better results and also reduce the circuit size of the primary filter, the long lines of symmetrical resonators have been bended. So the layout of the proposed lowpass filter and the EM simulations results of the filter are illustrated in Fig. 4a, b, respectively. The dimensions of the proposed filter are as fallow: L3 = 3.63 mm, L4 = 1.4 mm, L5 = 0.72 mm, L6 = 1.89 mm and W3 = 1.5 mm, W4 = 0.1 mm. As shown in Fig. 4b, the proposed triangle-shaped low pass filter creates three transmission zeroes in 4 GHz, 12.6 GHz and 15.5 GHz frequencies.

Fig. 4
figure 4

Proposed low-pass filter: a Layout, b EM simulation results

Full size image

2.2 Power Divider Design

By inserting two proposed LPFs symmetrically instead of quarter wavelength lines in conventional power divider, a compact WPD is proposed as illustrated in Fig. 5. In this structure the 100 Ω isolation resistor is used.

Fig. 5
figure 5

The layout of the proposed compact WPD

Full size image

3 Simulated and Measured Results

The proposed WPD is fabricated on the Rogers4003c substrate with a dielectric constant of 3.38, thickness of 20 mil and loss tangent of 0.0022. The overall dimension of the fabricated device is 8.3 mm × 8.95 mm (0.09 λg × 0.097 λg), where λg is the guided wavelength of the center frequency (2 GHz). The proposed divider has about 56% size reduction compared to the conventional 2 GHz WPD, which shown in Fig. 6. The fabricated image of the designed WPD is illustrated in Fig. 7.

Fig. 6
figure 6

The layout of the conventional WPD at 2 GHz

Full size image
Fig. 7
figure 7

The fabricated image of the proposed divider

Full size image

Figure 8 shows the measured and simulated S-parameters of the proposed WPD. According to the Fig. 8a, b, the experimental results show that at the operating frequency of 2 GHz the input (S11) and output (S22 = S33) return losses are better than 20 dB. From the measurement results in Fig. 8c could be observed that, the insertion loss at the 2 GHz frequency is less than 0.1 dB (S12 = S13 = 3 \(\pm\) 0.1). As seen in Fig. 8d the output ports isolation (S23) parameter is better than 26 dB.

Fig. 8
figure 8

EM simulation and experimental scattering parameters results: a the input return loss b the output return loss c the insertion loss d the isolation response

Full size image

As seen in Fig. 8a, from Eq. (3) 59% fractional bandwidth (1.44–2.66 GHz) was observed from measured results by considering |S11| greater than 15 dB.

Moreover, as seen in Fig. 8c the proposed divider features a wide range of harmonics suppression from 2nd up to 9th harmonic (4–18 GHz) with better than 20 dB attenuation level.

A performance comparison among some reported works and the proposed WPD are listed in Table 2. The results show that the proposed divider has very good specifications compare to others works.

Table 2 A comparison among some reported works and the proposed WPD
Full size table
$$FBW \, \left( \% \right) = \frac{{f_{2} - f_{1} }}{{0.5\left( {f_{1} + f_{2} } \right)}} \times 100$$
(3)

4 Conclusion

In this paper, a compact Wilkinson power divider (WPD) with ultra wide stop band (4–18 GHz) and low insertion loss with 2 GHz operating frequency is designed and fabricated. By using a low pass filter based on triangle-shaped resonators instead of quarter wavelength lines of a conventional divider, not only the unwanted harmonics from 2nd to 9th are suppressed, but also the size of the divider is reduced over 56% compared with the conventional divider. Moreover the proposed WPD has 59% fractional bandwidth (1.44–2.66 GHz). Good agreement are observed among simulation and experimental results.