1 Introduction

Dividers and filters are important key devices in the modern microwave systems and circuits [1,2,3,4,5,6]. Modern communication circuits require harmonic suppressed and compact circuits to reduce cost and circuit area [7, 8]. The typical WPD has relatively large area and also could not suppress spurious harmonics [9]. In past decade, lots of works are being contributed to suppress unwanted harmonics and reduce circuit area.

In [2, 3] and [10] harmonic suppression and miniaturization are achieved using open ended stubs. This is a simple method, but single stub could not be effective. The single stub can only reduce a few harmonics and also achieve small size reduction. In [11,12,13], the photonic band gap (PBG) and defected ground structure (DGS) are applied for harmonic suppression and size miniaturization. These solutions provide relatively considerable harmonic suppression and size reduction, but these methods increase the complexity of circuit. Component in these methods should be suspended from ground plane and etch pattern on ground plane are required, which is undesirable [1].

In [14, 15] resonators and filters are applied to achieve size miniaturization and suppression of the spurious harmonics. This method usually applied to suppress high order harmonics. In these works, 2nd and 3rd harmonics which have more destructive effects are not suppressed.

In this article, a miniaturized and harmonic suppressed WPD using low pass filter and open-ended stubs is proposed. Two LPFs are applied together to eliminate unwanted harmonics. Moreover, three open stubs at the proposed structure ports are used to improve the divider specifications. The proposed WPD suppresses 2nd up to 30th harmonics.

2 Proposed Wilkinson power divider (WPD) design process

The block diagram of the typical WPD and presented divider are illustrated in Figs. 1 and 2, respectively. The conventional WPD is build up of two branch lines and an isolation resistor (2Z0) between two output ports. The branch lines have characteristic impedance of √2Z0 and ninety degree electrical length (λ/4).

Fig. 1
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The schematic diagram of the Conventional WPD

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Fig. 2
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The block diagram of the proposed WPD

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In the proposed WPD structure, three open stubs are added at each port and two LPFs are inserted at each branch lines of the conventional WPD. The 2nd harmonic in the proposed WPD is suppressed by applied open-ended stub at port one. Also, symmetric open-ended stubs at port 2 and port 3 are used to improve output return losses (S22 and S33) and output ports isolation (S32) parameters. Moreover, two same LPFs symmetrically applied in the branch line to suppress high order harmonics (3rd–30th).

2.1 The applied low pass filter

In the designed WPD, 3rd–30th harmonics of the WPD are suppressed by two similar applied LPFs based on [16]. The layout of the applied LPF is shown in Fig. 3. The applied LPF dimensions are as follows: w1 = 1.5, w2 = 3.1, w3 = 3.0, w4 = 0.1, w5 = 0.1, wt = 14.7, l1 = 3.0, l2 = 3.3, l3 = 4.9, l4 = 9.8, l5 = 9.8, l6 = 2.5, l7 = 7.3, lt = 28.5 and g1 = 0.2 (all dimensions are in mm).

Fig. 3
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The layout and EM simulation results of the applied LPF

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The electromagnetic (EM) simulation frequency response of the LPF is also depicted in Fig. 3. The result shows that, the − 3 dB cut off frequency of the LPF is 1.5 GHz. Also, insertion loss of 0.1 dB and ultra wide stopband bandwidth of about 28.4 GHz (1.6 GHz up to 30 GHz) with attenuation level of more than 20 dB are obtained for the LPF. The circuit size of the applied low pass filter is 0.1 λg × 0.19 λg (14.7 mm × 28.47 mm).

2.2 Primitive power divider design

The primitive power divider is consisting of three open ended stubs, as depicted in Fig. 4. One open stub is inserted at input port to eliminate the 2nd harmonic. Two similar open stubs are added at port 2 and port 3, to improve output return losses (S22 and S33) and output ports isolation (S32) parameters.

Fig. 4
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The layout of the primitive divider

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Applying an open stub in the divider can suppress one harmonic corresponding to its electrical length. In order to suppress the nth harmonic, value of π/2n should be considered for the electrical length of inserted open stub [1]. Since the divider works at 1 GHz and the applied LPF suppresses from 1.68 GHz up to 44 GHz, the 2nd harmonics should be suppressed by open stub. Therefore, the electrical length of the utilized open-ended stub at input port is equal to π/4. The EM simulation result of the primitive WPD using ADS (advanced design system) software is depicted in Fig. 5. According to the results, the primitive design of WPD works correctly at 1 GHz. But, one harmonic is only suppressed in this design. The inserted open sub at input port suppresses the 2nd harmonic with good attenuation level. The two open stubs at output ports results in the good specifications of the WPD, such as output ports isolation and output port return losses.

Fig. 5
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The S-parameters EM simulation results of the primitive power divider

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2.3 The proposed WPD design process

In the proposed WPD, two LPFs and three open-ended stubs are applied to decrease circuit dimensions and suppress spurious harmonics. The layout of the designed WPD is illustrated in Fig. 6. RT/Duroid 5880 substrate is used to simulate and fabricate the proposed divider. The total size of the fabricated WPD is 34.6 mm × 31.2 mm (0.14 λg × 0.13 λg).

Fig. 6
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The layout of the designed WPD

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3 Results of the proposed WPD

Frequency responses of the proposed WPD are depicted in Fig. 7(a), (b). The S11 and S21 parameters are shown in Fig. 7(a). The results show that, 53 dB input return loss and 0.1 dB insertion loss are achieved at the operating frequency of 1 GHz. The S22 and S23 parameters are shown in Fig. 7(b). The output ports isolation and output return loss values are better than 48 dB and 45 dB, respectively, at operating frequency of 1 GHz.

Fig. 7
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a The measurement and EM simulation results of the S11 and S21 parameters of proposed WPD. b The measurement and EM simulation results of the S22 and S32 parameters of proposed WPD

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In order to have better consideration on harmonics suppression, wideband review of the S11 and S21 parameters are shown in Fig. 8. According to this figure, the designed WPD eliminates the 2nd–30th harmonics with high levels of attenuation. The proposed design can achieve more than 30 dB suppression level in the stopband.

Fig. 8
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Wideband review of the measurement and EM simulation results of the S11 and S21 parameters and fabricated photograph of the proposed WPD

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A comparison between recently works with harmonics suppression is summarized in Table 1. As the comparison result shows, the designed WPD has the widest harmonics rejections band. Moreover, the proposed divider features the best specifications compared to the reported works at operating frequency. As results show, the designed WPD has the minimum insertion loss, best output ports isolation and best matching ports compared to the reported works in Table 1.

Table 1 The comparison between the designed WPD and some reported works
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4 Conclusions

A harmonics suppressed power divider using LPFs and open-stubs is presented in this paper. The inserted open-ended stub at input port eliminates the 2nd harmonic and inserted LPFs reject the 3rd up to 30th harmonics. The proposed power divider is designed, simulated and fabricated. According to the obtained results of the presented power divider, the measurement results verify the simulation results.