Analysis of asymmetric coupling lines and design of a Wilkinson power divider based on harmonic suppression network

Int. J. Electron. Commun. (AEÜ) 115 (2020) 153047

Contents lists available at ScienceDirect

International Journal of Electronics and Communications (AEÜ) journal homepage: www.elsevier.com/locate/aeue

Regular paper

Analysis of asymmetric coupling lines and design of a Wilkinson power divider based on harmonic suppression network Mohsen Hayati ⇑, Sepehr Zarghami Electrical Engineering Department, Faculty of Engineering, Razi University, Tagh-E-Bostan, Kermanshah 67149, Iran

a r t i c l e

i n f o

Article history: Received 30 May 2019 Accepted 21 December 2019

Keywords: Asymmetric coupling lines Harmonic suppression network Symmetric coupling lines Sharp roll-off Power divider

a b s t r a c t In this paper, symmetric (equal impedance lines) and asymmetric coupling lines (unequal impedance lines) are analyzed and investigated. From the research, it has been ascertained that the coupling effect in the equal impedance lines creates a new transmission zero. Also, the coupling effect in unequal impedance can control two created transmission zeros. The purpose of this work is to design a network for suppressing large numbers of harmonics with a large number of controlled transmission zeros. Therefore, a harmonic suppression network (HSN) is designed based on asymmetric coupling lines. Designed HSN generates a large number of transmission zeros with an acceptable stopband bandwidth. The proposed HSN has been replaced with two quarter-wavelength transformers in the conventional Wilkinson power divider. The number of suppressed harmonics by the HSN is greater than the number of suppressed harmonics by the quarter-wavelength, while the size of the HSN is much more compact. Also, a power divider is designed based on the proposed HSN. The designed power divider has a compact size and low insertion loss for S21 and S31 at 1.2 GHz. The number of suppressed harmonics is up to the 16 harmonic. The measured results show a frequency operation range from 0.7 to 1.26 GHz (109.6%) with a more than 10-dB return loss. The isolation in the entire operation range, agreeing well with the simulation results. Ó 2019 Elsevier GmbH. All rights reserved.

1. Introduction Microstrip transmission lines and microwave resonators can be coupled to create selective frequency structures utilized in microwave devices. Not only coupled microstrip transmission lines and resonators are used in filters, but also widely used in power dividers (PDs), couplers, transformers, and many other devices. The characteristics of coupled lines are examined in [1–8], where in [7] and [8] the asymmetric coupling lines have been studied extensively. In the RF/microwave community, Wilkinson power divider (WPD) is a well-known device used for dividing or combining signals. The basic function of a PD is to split a given input signal into two or more signals as needed by the system. Power dividers have different types, which can be categorized appropriately based on their output response. The symmetric coupling lines are used in the design of low-pass filters [9,10] and a band-pass filter [11], while the symmetric coupling effect is used to suppress unwanted harmonics and increase bandwidth. The asymmetric coupling lines or the coupled transmission lines with unequal impedance are

⇑ Corresponding author. E-mail address: [email protected] (M. Hayati). https://doi.org/10.1016/j.aeue.2019.153047 1434-8411/Ó 2019 Elsevier GmbH. All rights reserved.

used in the unequal PD designs [12–16]. Although the unequal divide of the signal needs to be precisely designed, compact size and harmonic suppression often are neglected. Harmonic suppression is an important parameter in the design of PDs. This parameter is considered in PDs based on narrow band bandpass filter [17–22] and neglected in other devices. In [17], two lowpass filters are employed to achieve a very wide stopband in the design of a bandpass WPD. Balanced-to-unbalanced filtering PD with compact size is proposed in [18], which in common-mode has a high suppression up to 7 GHz. Four H-shape resonators formed in ring-type coupling topology and the phase feature of the filtering structure formed by the electric coupling are used to design of compact, balanced filtering PDs [19]. Based on the presented model in [20], two-order, high-order, single-band, multiband, frequency-fixed, and frequency-tunable responses are available in the design of WPD. Although this model focused on the suppression of harmonics, it has avoided the reduction in the size and insertion losses. Although band-pass PDs [17–22] have a wide stopband bandwidth, their passband have a narrow, which result in less than 10% fractional band width (FBW). Another type of PDs is the dual-band bandpass PD, which has been studied in recent years [23–33]. Two filtering WPDs with

2

M. Hayati, S. Zarghami / Int. J. Electron. Commun. (AEÜ) 115 (2020) 153047

miniature size and high selectivity are presented in [23]. Although in these PDs a multimode resonator is used to replace a k=4 transmission line, spurious harmonics have not been suppressed. In [24] and [25], two dual-band filtering PDs are presented based on loaded capacitors embedded in the resonators and modified stepped impedance resonators, respectively. The passbands of presented PDs of [24] and [25] can be independently controlled by tuning the loaded capacitors and the impedance ratio, respectively. In [26], an analytical design method has been studied for multiway arbitrary dual-band planar PDs. Two main advantages of this method are arbitrary power division and dual-band operations, and large area size is one of the disadvantages. To cover this defect, a design method of compact dual-band PDs is studied in [27]. The designed dual-band PD is based on the multisection coupled line, which reduces the size of the structure, but the rejection-band between the two passbands is not suitable, and the spurious harmonics have not suppressed. To cover the defect of rejection band between two passband, two PDs based on two p-shaped transmission lines series connected at two output ports in [28] and a simple structure with realistic impedance values, distributed design with reduced parasitic effect in [29] have been done. In [30], a method has been presented to design a dual-band unequal filtering power divider, which has outstanding property like arbitrary power division, arbitrary frequency ratio, arbitrary real terminated impedances, independently controllable bandwidth, and excellent isolation. Against these advantages, very large size and no harmonic suppression are the obvious defects of this design. However, designed PDs in [28–33] has a very large size and no particular idea for suppressing harmonics. One of the challenges in the design of the wideband or an ultrawideband PD is the increase of passband. In this way, the shortedend coupled lines and the open- and short-circuit slot lines are introduced in [34] to create wide pass-band. Also, in [35], the quasi-coupled lines, the open and shorted stubs added at the input and output ports are presented. A three coupled-line structure and a pair of half-wavelength open stubs [36] and looped coupled-line structures [37] are some important designs to challenge the creation of ultra-wideband PD. In the design of PDs, band-pass filters are commonly used based on the coupling lines. On the other hand, low-pass filters and resonators have been used to suppress harmonics. The WPD with compact size [38–40] based on low-pass filters are another type of PDs, which pay more attention to the suppression of harmonics and it can also have a wide bandwidth. Two 2:1 unequal wideband filtering unbalanced-to-balanced PD with an inherent impedance-transforming function has been presented in [41]. These PDs, which consists of four half-wavelength open circuit stubs and an asymmetric core block have disadvantages such as large size and no harmonic suppression. This paper is organized as follows: In Section 2, the performance of the conventional WPD is discussed. In Section 3, symmetric coupled microstrip lines and in Section 4, coupled microstrip lines with unequal impedances are analyzed and investigated. In these sections, formulas are derived to realize the coupling effects and their effect on the creation and adjustment the transmission zeros. In Section 5, HSN based on symmetrically coupled resonator is designed. Then, in Section 6, a design of WPD base on HSN is proposed. Finally, in Section 7, measurement and simulation results are discussed.

2. Conventional Wilkinson power divider The well-known WPD in Fig. 1(a) consists of two transmission lines (TL1 and TL2), which have a physical length l ¼ k0 =4 relative to the mid-band frequency of the divider (k0 is the guide wavelength). To prevent signal leakage from port 2 to port 3, the lumped

(a)

(b) Fig. 1. (a) Schematic diagram of 1.2 GHz WPD with quarter-wavelength lines and, (b) simulation s-parameters.

resistor R is connected between these ports. If the signal flows into port 1, it is split equally between ports 2 and 3. Fig. 1(b) shows simulation S-parameters of a WPD with quarter-wavelength lines. The scattering matrix of this PD as below [1]: pffiffi pffiffi 3 jð 22Þ jð 22Þ pffiffi 7 6 2 ½ S ¼ 6 0 0 7 5 4 jð 2 Þ pffiffi 0 0 jð 22Þ

2

0

ð1Þ

According to Fig. 1(b), WPD base on quarter-wavelength lines has very low insertion loss with the magnitude close together at the fundamental frequency. In other words, the signal flows into port 1 is evenly divided between two ports 2 and 3 with low insertion loss. As shown in Fig. 1(b), due to the creation of the pole at the fundamental frequency, appropriate port matching (S11, S22, and S33) and high return loss (RL) has been created in the passband. Also, very good isolation (S32) is created by this pole. As a result, for achieving a very good matching, high return loss, and proper isolation the creation and control of the pole are essential at the fundamental frequency. As shown in Fig. 1(b), it is clear that responses are repeated, alternately. This repetition means that all odd harmonics, can be divided with proper matching. One of the features of the PD design is suppression of the unwanted and spurious harmonics. Therefore, the passing of the odd harmonics (3f o ; 5f o ; 7f o ; etc:) is one of the disadvantages of the quarter-wavelength lines PDs. On the other hand, the quarter-wavelength lines occupy a large size.

3

M. Hayati, S. Zarghami / Int. J. Electron. Commun. (AEÜ) 115 (2020) 153047

3. Symmetric coupled microstrip lines

S= 0.1 mm

Fig. 2(a), shows a ‘‘coupled line” configuration consists of two transmission lines placed close and parallel to each other. Coupled lines are utilized extensively as a basic element for directional couplers, filters, and a variety of other useful circuits [4]. As shown in Fig. 2(a), the capacitors Cgd and Cga are the capacitive effects between the two microstrip lines with the dielectric of substrate and air, respectively. The capacitance Cf is the fringe capacitance, and Cp denotes the parallel plate capacitance between the strip and the ground plane [3]. The equations of these capacitors are given in [3]. For the coupling between two parallel lines, the electric field coupling can be used instead of the electromagnetic field. Electric field coupling is very similar to the gap coupling between microstrip lines [4]. Therefore, as shown in Fig. 2(b), the p-network model can be used for the coupling effect. The p-network is shown in Fig. 2(b) has the admittance matrix [3]:

½Y C  ¼ jxCg



Cg þ Cf

C g

C g

Cg þ Cf

½ABCD ¼ 4 ðY

Y 22 Y 21 Y 21

Y 11 Y 21

3

5¼

"

1

1 jxC g C g

0

1

ð4Þ

L1

Vi

R

CP

Cf

(a) Fig. 2. (a) Symmetric coupled microstrip lines, (b) coupling between coupled lines.

With coupling effect

L3

Cf

L1

Vo

(b) p-network representation of

L4 R Cg

C4

(b) Fig. 3. (a) The layout of the two rectangular-shaped resonators, (b) equivalent circuit of rectangular-shaped resonators.

where Co and Ce are the odd- and even-mode capacitances of the coupled line and can be obtained as follows:

 e 0:8  S mO CO r expðK O Þ ðpF=mÞ ¼ W W 9:6

ð5Þ

 e 0:9  S me Ce r expðK e Þ ðpF=mÞ ¼ 12 W W 9:6

ð6Þ

where S, W and er are the space between the lines, the width of the line and relative permittivity of the substrate, respectively. me , mo , K o and K e are variable and can be obtained as follows:

mO ¼

    W W  A2 A1 log h h

me ¼ A5 Cf

L4

C4

K O ¼ A3  A4 log Cg

Cgd

TZ2

(a)

ð3Þ

Cga

CP

TZ

#

1 1 C  C 2 o 4 e

Cf

Without coupling effect

TZ1

The ABCD matrix of gap capacitor is useful to the analysis of coupled transmission line based on impedance and electrical length. Fig. 3(a), shows two similar rectangular-shaped resonators, which are in close to each other. Due to the similarity of two resonators, they have a common transmission zero at TZ = 4.3 GHz. However, if the gap between these two resonators is reduced, the coupling effect is created between them. The coupling effect is caused by electromagnetic field between two transmission lines placed by parallel to each other. According to Fig. 3(b), coupling effect create two new transmission zeros (TZ1 and TZ2). TZ1 is less than old TZ and TZ2 is greater than TZ. In other words, the coupling effect has reduced the capacitor effect of a resonator (TZ2) and increased the capacitor effect of another resonator (TZ1). Hence, for two resonators with unequal impedances, coupling effect increases the resonator capacitor effect, that its transmission zero is at low frequencies. More to be explained about this topic in the next section. Using the p-network model, an LC equivalent circuit can be proposed for resonators of Fig. 3(a), which is depicted in Fig. 3(b). The capacitance Cg represents the electric field across the gap and can be defined as [3]:

Cg ¼

Output

ð2Þ

1 Y 21

11 Y 22 Y 12 Y 21 Þ

Input



where the xC g is equivalent to a transmission zero generated by the gap capacitor. If the effect of capacitor Cf is to be ignored, then the following formula [3] can be used to write the ABCD matrix for the gap capacitor:

2

W= 3.9 mm

K e ¼ A6

 0:12 W h

  W h

ð7Þ

ð8Þ ð9Þ ð10Þ

where A1 ¼ 0:619, A2 ¼ 0:3853, A3 ¼ 4:26, A4 ¼ 1:453, A5 ¼ 0:8675,A6 ¼ 2:043. The value of the gap capacitor (Cg) is calculated using the (4) to (10) formulas. According to substrate RT/Duroid 5880 with relative permittivity er ¼ 2:2, a thickness of

4

M. Hayati, S. Zarghami / Int. J. Electron. Commun. (AEÜ) 115 (2020) 153047

h = 0.787 mm, S = 0.1 mm and W = 3.9 mm, me , mo , K e and K o are obtained 0.87, 0.22, 1.21 and 3.25. So:

 0:9   2:2 0:1  103 C e ðpFÞ ¼ 3:9  103  12  9:6 3:9  103

!0:87

 exp ð1:21Þ ¼ 0:0017 Next:

!   2:20:8 0:1  103 0:22 3 C O ðpFÞ ¼ 3:9  10  9:6 3:9  103 ð12Þ

Finally:

C g ¼ 0:5ð0:0138Þ  0:25ð0:0017Þ ¼ 0:0065 pF

0

Þ are tic functions (Accurate and simple expressions for the ratio Kðk KðkÞ 0

ð11Þ

 exp ð3:25Þ ¼ 0:0138

0

Þ where eo ¼ 8:85  1012 F  m1 and Kðk is the ratio of the ellipKðkÞ

ð13Þ

available in [8]). Using Eqs. (14)–(18), the capacitance C g can be calculated accurately. Fig. 5(a) illustrates the layout of designed coupled resonators with unequal impedance as an asymmetrically coupled resonator (ACR). This structure composed of a low-impedance rectangularshaped resonator with short base line (LIRSR) and a highimpedance rectangular-shaped resonator (HIRSR) with the long base line, near each other. The simulation S-parameters of each designed resonator without coupling effect and both resonator with the coupling effect, are shown in Fig. 5(b). As shown in this figure, a rectangular-shaped resonator with the short base line has a transmission zero (TZx) at 6.5 GHz. Also, a rectangularshaped resonator with the long base line has a transmission zero

4. Coupled microstrip lines with unequal impedances Fig. 4, shows the coupled transmission line with unequal impedance with total capacitance into air and dielectric capacitances. When the impedance of the lines is not equal, the capacitors Cgd, Cga, Cf, and Cp values are changed. On the other hand, each line has a separate transmission zero, and two microstrip lines with unequal impedances produce two transmission zeros away from each other. But it does not mean that the coupling between the two lines does not effect. For simplicity, we ignore the effects of Cf and CP capacitors. Then, we calculate the coupling capacitance 0

6.8

HIRSR

2.9

0.1 1.8

6.4 3.9

LIRSR

0

C g . The coupling capacitance C g consists of capacitances for the 0

4.7

0.1 2.2

0

field in the air (C ga ) and a dielectric substrate (C gd ) [8]: 0

0

0

C g ¼ C gd þ C ga

ð14Þ

8.4

(a)

0

0

C gd

Kðk Þ ¼ eo er KðkÞ

1

1.8

where the value of these capacitors can be calculated by the following formulas [8]:

Simulation S21 (LIRSR)

ACR

ð15Þ

(HIRSR)

0

0

C ga ¼ eo

Kðk Þ KðkÞ

ð16Þ

where

1 þ ws1 þ ws2 ð1 þ ws1 Þð1 þ ws2 Þ

ð17Þ

TZACR2 TZACR1

and,

qffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0 2 k ¼ 1k

TZy

TZx

ð18Þ

(b) Z 3, θ3

Cg

TL2

Z 1, θ1 TL1

MSub2

Z 4, θ4 TL4

TL3

Z 1, θ1

Z 2, θ2 Z1, 4(θ1)

TL1

2

k ¼

Z 1, θ1 TL1

TL1

MSub1 (c)

Fig. 4. Coupled microstrip lines with unequal impedances.

Fig. 5. (a) the layout of designed coupled resonators with unequal impedance (all dimensions in mm), (b) S21 Simulation of LIRSR, HIRSR and ACR, (c) the equivalent circuit based on line impedance.

5

M. Hayati, S. Zarghami / Int. J. Electron. Commun. (AEÜ) 115 (2020) 153047

(TZy) at 3.2 GHz and combine these two resonators ACR have two transmission zeros (TZACR1, 2) at 2.8 and 7.4 GHz. TZACR1, 2 are the same zeros of transmission TZx and TZy, which are separated by the coupling effect. As described in the previous section, the coupling effect separates the two transmission zeros, and by increasing the coupling effect, the zeros are more separated. The coupled resonators with unequal impedances, not only creates two new transmission zeros but also create an acceptable stopband to suppress unwanted harmonics. On the other hand, this structure has a pole in the passband, which is controlled by the rectangularshaped resonator with the long base line. To obtain the S-parameters of this structure, the equivalent circuit shown in Fig. 5(c) has been proposed. The equivalent circuit is based on impedance line and gap capacitor and divided into three main sections. The total matrix of the structure is computed by multiplying of the ABCD matrix of all sections. The ABCD matrix of the proposed ACR (MACR), is obtained to calculate the S21 and S11 parameters by equations bellow [3]:

S21 ¼

f Cg ¼

S11 ¼

2 A þ ZBo þ CZ o þ D

ð19Þ

" M Z2 ¼

Y 22 Y 21

1 Y 21

ðY 11 Y 22 Y 12 Y 21 Þ Y 21

Y 11 Y 21

#

In the following, by Eq. (26), the ABCD matrix of Section 2 can be obtained. Using the total structure matrix (Eq. (22)), S21 can be approximated by Eq. (19). Since the asymmetric coupled lines do not have an equivalent circuit; the analysis can be placed on the transmission zero frequency generated by the gap capacitor (fCg). In the same vein, the obtained equation S21 equal to zero, and a function for fCg is obtained in (27). According to this function, fCg versus Z3, Z4, h1, h2, h3 and h4 has been plotted in Fig. 6. To investigate the effect of fCg, the value of the obtained zero from the asymmetric coupling effect fCg = 5.1 GHz is considered. This zero is selected between the two value of transmission zeros derived from HIRSR and LIRSR. Herein, the Z3 value is equal to the maximum impedance line (180 X), Z2 = Z1/2, Z3 and Z4 values are considered near the minimum impedance line. As shown in Fig. 6(a), Z3 and Z4 values are obtained for coupled microstrip lines with unequal impedances. The values of h1, h2, h3 and h4 are obtained at fCg = 5.1GHz from Fig. 6(b). Consequently, an ACR is designed using the formulas in this section and Fig. 6, which is shown in Fig. 5(a).

ðZ 2 cosh1 cosh2  Z 1 sinh1 sinh2 ÞðZ 3 Cosh3 Cosh4  Z 4 sinh3 sinh4 Þ    11 Z cosh2 Z 3 cosh3ðZ 1 cosh4 sinh1 þ Z 4 cosh1 sinh4Þ þ sinh3 Z 3 2 cosh1 cosh4  Z 1 Z 4 sinh1 sinh4 þ B B 2 CC   AA 2p@Cg @ 2 sinh2 Z 1 Z 3 sinh1 ðZ 3 cosh4 sinh3 þ Z 4 cosh3 sinh4 Þ þ Z 2 cosh1 ðZ 3 cosh3 cosh4  Z 4 sinh3 sinh4 Þ 0

0

A þ ZBo  CZ o  D

ð20Þ

A þ ZBo þ CZ o þ D

The ABCD matrix of gap capacitance (Mg) is calculated using (3). The ABCD matrix (MTLi) of transmission lines can be given as:

"

MTLi ¼

coshi

jZ i sinhi

j Z1 sinhi

coshi

i

#

; i ¼ 1; 2; 3; 4

ð21Þ

The ABCD matrix of ACR can be derived as:

M ACR ¼ MTL1  Msection2  M TL1

ð22Þ

The ABCD matrix MTL1, which contains of only one TL, can be obtained easily by Eq. (21). Section 2 consists of two subsections, which ABCD matrix of each subsection are named as MSub1 and MSub2. MSub1 consists of the TL1, and its ABCD matrix can be obtained by Eq. (21). MSub2 is obtained as:

M sub1 ¼ M TL2  M TL3  M g  MTL4  MTL1

ð23Þ

After obtaining MSub1 and MSub2, Y-matrix (YSub1 and YSub2) can be obtained from the ABCD matrixes, according to the following formula:

" Y subi ¼

D B 1 B

ð26Þ

ðADBCÞ B A B

# ; i ¼ 1; 2

ð24Þ

where A, B, C and D are the ABCD matrix parameters. The Y-matrix of Section 2 (YSection2) can be given as:

Y section2 ¼ Y sub1 þ Y sub2

ð25Þ

Then, the M sectionII can be obtained from Y sectionII using the following equation:

ð27Þ

5. Harmonic suppression network An ideal HSN, with a simple and compact structure, generates a large number of transmission zeros and a relatively reasonable stopband bandwidth. To suppress disturbing harmonics, HSNs can be used to design of low-pass filters, power dividers and couplers. On the other hand, the ACR structure has two transmission zeros. The first zero is set to suppress primary harmonics and the second zero is set to increase stopband bandwidth. But to suppress more harmonics, more transmission zeros are needed. To overcome this problem, we use two ACR structures in series connection, in which case another coupling effect is created between two ACR. The secondary coupling effect converts two transmission zeros to four transmission zeros. In other words, the secondary coupling effect converts each transmission zero of the ACR structure to two new transmission zeros. Therefore, to design an HNS, two ACRs can be used in series. Fig. 7(a) shows the layout of proposed HSN, where S21 simulations of ACR and HSN are illustrated in Fig. 7(b). Four generated transmission zeros and relative stopband are specified in Fig. 7 (b). TZ1 and TZ2 are to suppress the second and third harmonics, and TZ3 and TZ4 are to extend stopband. The equivalent circuit based on impedance line and secondary coupling effect (Cg2) be expressed as Fig. 7(c). As shown in Fig. 7(d), for suppressing at frequency of 4.2 GHz, Cg2 can be eliminated by increasing the distance between the two series ACRs. In this case, although the suppression improves at frequencies such as 4.2 or 10.9 GHz, the number of transmission zeros are decreased. According to the equivalent circuit, to obtain S-parameters, the calculation of the ABCD matrix of the whole structure is necessary. At first, the series elements are computed:

6

M. Hayati, S. Zarghami / Int. J. Electron. Commun. (AEÜ) 115 (2020) 153047

Fig. 6. (a) fCg versus Z3 and Z4, (b) fCg versus h1, h2, h3 and h4.

M x ¼ M 4  M5  M Cg1

ð28Þ

My ¼ M6  M7

ð29Þ

According to Fig. 7(c), the MN1 section consists of Mx, My and MTL2. The ABCD matrix of this section is calculated by the equation bellow [3]:

2 M N1 ¼ 4

1 þ ZZ2y Z2

1 Zy

þ Z1x þ ZyZ:Z2 x 1 þ ZZ2y

ð30Þ

Since the structure is symmetric, the Cg2 and the TL3 are parallel. So, their admittance matrix will be summed up:

ð31Þ

where Y C g2 and Y TL3 can be obtained from Eqs. (3), (21) and (24). Next, the Y N2 matrix is converted to the MN2 matrix using the Eq. (26). Consequently, the equivalent circuit is simplified as shown in Fig. 7(d), and the total ABCD matrix of the structure (Mtot ) can be derived as:

Mtot ¼ M TL1  M N1  M N2  M N1  M TL1

3 5

Y N2 ¼ Y Cg2 þ Y TL3

ð32Þ

The input impedance of the structure (Z in Þ can be calculated from the formula:

Z in ¼

Z o Atot þ Btot Z o C tot þ Dtot

ð33Þ

7

M. Hayati, S. Zarghami / Int. J. Electron. Commun. (AEÜ) 115 (2020) 153047

Fig. 7. (a) the layout of HSN (all dimensions in mm) (b) S21 Simulation of ACR and HSN, (c) the equivalent circuit of HSN based on line impedance, (d) S21 Simulation HSN with and without Cg2, (e) the equivalent circuit simplified.

where Atot , Btot , C tot and Dtot are Mtot matrix parameters.

coefficient Cin at input port 1 equivalent to the parameter S11 of the proposed power divider, S11 can be then expressed as:

6. Design Wilkinson power divider base on HSN

S11 ¼ Cin ¼

So far, the design of ACR and the series of the two ACR structures has been investigated. Now, the design of the WPD with the proposed HSN structure has several steps as follows:

where Cin is the reflection coefficient at the input port 1, Z o ¼ R=2 ¼ 50 ohm and Z ein is input impedance on the left side of Fig. 8(c). To calculate the Z ein , the impedances step by step can be formulated as:

- ACR design: design of an asymmetric coupled resonator and adjust the pole of this structure for the fundamental frequency of the power divider. - Adjustment of the first transmission zero of the ACR structure between the second and third harmonics. - Adjustment of the second transmission zero of the ACR structure between the sixth and seventh harmonics. - Connect the two series of ACR structures with the secondary coupling effect to create four transmission zeros. - Power divider design with ACR structure and 100-ohm resistor. The layout and fabricated power divider based on the mentioned ideas is shown in Fig. 8(a) and (b), respectively. The equivalent circuit of the proposed WPD is depicted in Fig. 8(c). Moreover, the even- and odd-mode equivalent circuits to analysis proposed WPD can be expressed as Fig. 8(d). With the derived reflection

Z ein ¼ Z N  so,

S11 ¼

Z ein  2Z o Z ein þ 2Z o

ð34Þ

Z o þ jZ N tan hN Z N þ jZ o tan hN

ð35Þ

   Z N 2  2Z o 2 Z N 2 þ 2Z o 2 tan2 hN  3Z N 2 Z o 2 2

9Z N 2 Z o 2  ðZ N 2 þ 2Z o 2 Þ tan2 hN j

2Z N Z o ðZ N 2  2Z o 2 Þ tan hN 2

9Z N 2 Z o 2  ðZ N 2 þ 2Z o 2 Þ tan2 hN

ð36Þ

Also, the following formula can be used to calculate S23:

S23 ¼

Ceout  Coout 2

ð37Þ

8

M. Hayati, S. Zarghami / Int. J. Electron. Commun. (AEÜ) 115 (2020) 153047

(a)

(b)

(c)

ZN1, θN1

ZN2, θN2

ZN1, θN1

Z1, θ1

Z1, θ1 TL2

TL1

TL1

Zo

R/2=Zo

ZN1, θN1

ZN2, θN2

ZN1, θN1

Z1, θ1 TL1

Z1, θ1 TL2

TL1

Zo 2Zo

(d) Fig. 8. (a) the layout of proposed WPD, (b) photograph of the proposed WPD, (c) equivalent circuit, (d) even- and odd-mode.

where,

Ceout ¼ Z eout

Z eout  Z o Z eout þ Z o

2Z o þ jZ N tan hN ¼ ZN : Z N þ j2Z o tan hN

S23 ¼ 

Z N ðZ N þ 2Z o ÞðZ N Z o 2 þ ðZ N 3  Z N 2 Z o þ 2Z N Z o 2  2Z o 3 Þ tan2 hN Þ

ð38Þ j ð39Þ

2

ð2Z N þ Z o Þð9Z N 2 Z o 2 þ ðZ N 2 þ 2Z o 2 Þ tan2 hN Þ Z N Z o ðZ N 2  4Z o 2 Þ tan hN 2

9Z N 2 Z o 2 þ ðZ N 2 þ 2Z o 2 Þ tan2 hN ð42Þ

and,

Coout ¼ Z oout ¼ so,

Z oout  Z o Z oout þ Z o

ð40Þ

Z N :Z o ZN þ Zo

ð41Þ

7. Results and discussion The advanced design system (ADS) software is used for simulating and optimizing of all sections and the structure. For investigation and analysis of all sections, Wolfram Mathematica and MATLAB software hvae been employed. The proposed Wilkinson power divider based on HSN is fabricated on RT/Duriod 5880

9

0

0

-10

-10

S-parameters (dB)

S-parameters (dB)

M. Hayati, S. Zarghami / Int. J. Electron. Commun. (AEÜ) 115 (2020) 153047

-20

-30

-40

Simulated S21 Measured S21 Simulated S31 Measured S31

-50

2

4

6

8

10

12

14

16

-30 Meaured S22 Simulated S22 Measured S33 Simulated S33 Measured S11 Simulated S11 Measured S23 Simulated S23

-40

-50

-60 0

-20

18

-60

20

0

2

4

6

Frequency (GHz)

-5

-3.2

-10

S-parameters (dB)

S-parameters (dB)

-3.1

-3.3 -3.4 -3.5 -3.6

-3.8 -3.9

10

12

14

16

18

20

0

-3

-3.7

8

Frequency (GHz)

Simulated S 21 Measured S 21 Simulated S31 Measured S 31

-4 0.2

0.4

0.6

-15 -20 -25 -30 -35

0.8

1

1.2

1.4

1.6

-40 0.2

Meaured S22 Simulated S22 Measured S33 Simulated S33 Measured S11 Simulated S11 Measured S23 Simulated S23

0.4

0.6

0.8

1

1.2

1.4

1.6

Frequency (GHz)

Frequency (GHz)

(a)

(b)

Fig. 9. Simulated and measured results of proposed WPD, (a) magnitude of S21 and S31, (b) magnitude of S11, S22, S33 and S23.

Table 1 The principal bandwidth in accordance with S11, S22, S33 and S23. S-parameters

S11 < 15 ðdBÞ

S11 < 10 ðdBÞ

S22 < 15 ðdBÞ

Bandwidth (GHz)

0.7–1.43

0.24–1.57

0.33–1.4

0.1–1.5

S-parameters Bandwidth (GHz)

S33 < 15 ðadBÞ 0.33–1.4

S33 < 10 ðdBÞ 0.1–1.5

S23 < 15 ðdBÞ 0.7–1.26

S23 < 10 ðdBÞ 0.4–1.37

Fig. 10. Simulated of proposed WPD at fCg = 4.2 GHz.

S22 < 10 ðdBÞ

10

M. Hayati, S. Zarghami / Int. J. Electron. Commun. (AEÜ) 115 (2020) 153047

Table 2 Suppressed harmonics of proposed power divider. Harmonics

fO = 1.2 GHz

2nd

3rd

4th

5th

6th

7th

8th

S21, S31 (dB)

3.17/-3.25

48/-47

39/-38

24/-24

41/-41

36/-35

34/–33.5

24/-25.8

Harmonics S21, S31 (dB)

9th –22/–23

10th 35/–33.4

11th 20.1/-20.3

12th –22/-21.2

13th 20/-20.6

14th 28/-27.7

15th 30/-28

16th 27/-25.7

Table 3 Comparison of the proposed wpd with references. f O (GHz)

IL (dB)

FBW %

Isolation dB

Area size (kg2)

Ref.

Type

Suppressed Harmonics

[14]

Unequal power dividing

1

2.2 ± 0.2/5.5 ± 0.5

110 (RL = 15 dB)

15

NA

non

[17] [18] [19]

Narrow band band-pass Narrow band band-pass Narrow band band-pass

0.915 2.39 1.9

4.75 4.728 5/5.2

2.4 4.9 (IL = 1 dB) 0.1 (IL = 3 dB)

23 15 15

0.0200 0.0620 0.0750

22.2f O 2.56f O 2.3f O

[23] [24] [30]

Dual-band band-pass Dual-band band-pass Dual-band band-pass

3.45/5.2 1/1.74 1/1.95

4.3/4.4 3.14/4.22 4.124/2.124

8.2/69 (IL = 3 dB) 9.2/17.8 (IL = 3 dB) 16/12.3 (RL = 15 dB)

17/22 12/12 20

0.0430 0.082 NA

non non non

[35] [36]

Ultra-wide band band-pass Ultra-wide band band-pass

3.03 3

3.66 3.6

104.5 62

15 16.5

0.0300 NA

5 fO 1.1f O

[39] [42] This work

Elliptic-function low-pass filter Elliptic-function low-pass filter Elliptic-function low-pass filter

2.65 1 1.2

3.35/3.39 3.25 ± 0.02 3.17/3.25

48 25 57 (RL = 15 dB) 109.6 (RL = 10 dB)

22 20 15

NA 0.0208 0.0071

5 fO 4 fO 16f O

IL = insertion loss, RL = return loss, FBW = fractional bandwidth.

substrate, whose dielectric constant is 2.2, loss tangent is 0.009, and layer thickness is 0.787 mm. The overall size of the proposed Wilkinson power divider is 17.7  14.2 mm2. The S-parameters were measured using an Agilent N5230A network analyzer. The simulation and measurement results of the proposed Wilkinson power divider are shown in Fig. 9(a) and (b), which operates at 0.7–1.3 GHz. Due to the high attenuation level pole of the ACR structure, which is set at 1.2 GHz, the resultant measure of the proposed Wilkinson power divider has a low insertion loss and high return losses. The measured S21 and S31 at the 1.2 GHz frequency are 3.17 and 3.25 dB, respectively. According to Fig. 9(b), the measured S11, S22, S33 and S32 are 22.5 dB, 18.3, 17.5 and 15.8 dB at the center frequency of 1.2 GHz, respectively. The principal bandwidth from the measured result, in accordance with S11, S22, S33 and S23, are tabulated in Table 1. According to Table 1, the principal bandwidths are 0.7– 1.26 GHz (57.14%) and 0.4–1.37 GHz (109.6%). The two primary zeroes (TZ1 and TZ2) suppress the second and third harmonics, and the two third and fourth zero provide a proper suppression for the fourth to eighth harmonics. On the other hand, the HSN structure with reasonable stopband bandwidth, suppress harmonics up to 16th. As illustrated in Fig. 9, the measured results are in good agreement with the full wave simulated ones. As shwon in Fig. 9, the bandwidth of 0.8 to 1.3 GHz indicates the most appropriate response, and the 1.2 GHz is the best answer in this bandwidth. Transmission zeros are also set to suppress harmonics of frequency 1.2 GHz. According to Fig. 6 and with the fCg = 4.2 GHz, the PD parameters (Z3, Z4, h1, h2, h3 and h4) can be adjusted, so that the second and third TZs approach each other. In this case, the suppression will improve at frequencies of 4.2 GHz and 10.9 GHz. But the suppression level of the second (2.4 GHz) and the third (3.6 GHz) harmonics are decreased, as shown in Fig. 10. Table 2 is summarized the number of suppressed harmonics with the suppression level. Table 3, where area size, FBW, isolation, IL stand for the fractional bandwidth, return and insertion loss, respectively, compares the proposed power divider with those in other recent studies, categorized based on the types of the power divider. The proposed Wilkinson power divider has a more compact, less

insertion loss at the operating frequency, and a greater number of weakened harmonics than other references. The design results indicate that this structure has several advantages, such as low insertion loss at the operational frequency, suppression second and third harmonics with high suppression level, suppression of many harmonics up to the 16th harmonic, compact size and simple design process.

8. Conclusion A Wilkinson power divider based on harmonic suppression network is proposed in this paper. In the first step, symmetric coupled lines and asymmetric coupled lines are analyzed to create a large number of transmission zeros. Then, using two asymmetric coupled lines, a harmonic suppression network is designed to suppress spurious harmonics of 1.2 GHz frequency. The proposed harmonic suppression network suppress the second and third harmonics with a high suppression level and creates an appropriate suppression level for other spurious harmonics. However, proposed Wilkinson power divider based on harmonic suppression network is designed and fabricated. The measured results show a frequency operation range from 0.7 to 1.26 GHz (109.6%) with a more than 10- dB return loss and isolation in the entire operation range. The number of suppressed harmonics are up to the 16th harmonic with > 20 dB suppression level. The size of the proposed power divider is only 0.165kg  0.067kg, and results indicate that the proposed filter achieves a low insertion losses in the frequency range of 0.7–1.3 GHz. Consequently, With this excellent performance, the proposed Wilkinson power divider can be used in modern communication systems.

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

M. Hayati, S. Zarghami / Int. J. Electron. Commun. (AEÜ) 115 (2020) 153047

References [1] Pozar D. Microwave engineering. 2nd ed. David Pozar; 2008. [2] Ananth C, Rajavel SE, Devaraj SA, Chinnathampy MS. RF Microwave Eng (Microwave Eng) 2014. [3] Hong J-SG, Lancaster MJ. Microstrip filters for RF/microwave applications, vol. 167. John Wiley & Sons; 2004. [4] Gupta KC, Garg R, Bahl I, Bhartia P. Microstrip lines and slotlines, 2nd ed.; 1996. [5] Hilberg W. From approximations to exact relations for characteristic impedances. IEEE Trans Microw Theory Tech 1969;17(5):259–65. [6] Sabban A, Gupta KC. A planar-lumped model for coupled microstrip lines and discontinuities. IEEE Trans Microw Theory Tech 1992;40(2). [7] Cristal EG. Coupled-transmission-line directional couplers with coupled lines of unequal characteristic impedances. IEEE Trans Microw Theory Tech 1966;14 (7):337–46. [8] Bedair SS. Characteristics of some asymmetrical coupled transmission lines. IEEE Trans Microw Theory Tech 1984;32(1):108–10. [9] Velidi VK, Sanyal S. Sharp roll-off lowpass filter with wide stopband using stub-loaded coupled-line hairpin unit. IEEE Microw Wirel Components Lett 2011;21(6):301–3. [10] Hayati Mohsen, Zarghami Sepehr, Kazemi Amir Hossein. Very sharp roll-off ultrawide stopband low-pass filter using modified flag resonator. IEEE Trans Compon, Packag Manufact Technol 2018;8(12):2163–70. https://doi.org/ 10.1109/TCPMT.2018.2797211. [11] Chen CJ. A coupled-line coupling structure for the design of quasi-elliptic bandpass filters. IEEE Trans Microw Theory Tech 2018;66(4):1921–5. [12] Cheng KKM, Li PW. A novel power-divider design with unequal powerdividing ratio and simple layout. IEEE Trans Microw Theory Tech 2009;57 (6):1589–94. [13] Du ZX, Zhang XY, Wang KX, Kao HL, Zhao XL, Li XH. Unequal Wilkinson power divider with reduced arm length for size miniaturization. IEEE Trans Components, Packag Manuf Technol 2016;6(2):282–9. [14] Honari MM, Mirzavand L, Mirzavand R, Abdipour A, Mousavi P. Theoretical design of broadband multisection wilkinson power dividers with arbitrary 2016;6 (4):605–12. [15] Li B, Wu X, Wu W. A 10:1 unequal wilkinson power divider using coupled lines with two shorts. IEEE Microw Wirel Components Lett 2009;19 (12):789–91. [16] Wang X, Wu KL, Yin WY. A compact gysel power divider with unequal powerdividing ratio using one resistor. IEEE Trans Microw Theory Tech 2014;62 (7):1480–6. [17] Chau W, Hsu K, Tu W. Filter-based Wilkinson power divider2014;24 (4):239– 41. [18] Luo M, Tang X, Lu D, Zhang Y, Yu X. Balanced-to-unbalanced filtering power divider with compact size and high common-mode suppression. 2018;54 (8):19–20. [19] Xu K, Shi J, Zhang W, Mbongo GM. The compact balanced filtering power divider with in-phase or out-of-phase output using H-shape resonators. IEEE Access 2018;6(c):38490–7. [20] Lu D, Yu M, Barker NS, Li M, Tang S-W. A simple and general method for filtering power divider with frequency-fixed and frequency-tunable fully canonical filtering-response demonstrations. IEEE Trans Microw Theory Tech 2019;67(5):1812–25. [21] Chen CJ. A coupled-line isolation network for the design of filtering power dividers with improved isolation. IEEE Trans Components, Packag Manuf Technol 2018;1:1–8. [22] Chen FJ, Wu LS, Qiu LF, Mao JF. A four-way microstrip filtering power divider with frequency-dependent couplings. IEEE Trans Microw Theory Tech 2015;63 (10):3494–504.

11

[23] Li Q, Zhang Y, Wu CTM. High-selectivity and miniaturized filtering wilkinson power dividers integrated with multimode resonators. IEEE Trans Components, Packag Manuf Technol 2017:1–8. [24] Lu Y, Dai G, Wang Y, Liu T, Huang J. Dual-band filtering power divider with capacitor-loaded centrally coupled-line resonators. IET Microwaves, Antennas Propag 2017;11(1):36–41. [25] Song K, Hu S, Zhang F, Zhu Y, Fan Y. Compact dual-band filtering-response power divider with high in-band frequency selectivity. Microelectronics J 2017;69:73–6. [26] Wu Y, Liu Y, Xue Q, Li S, Yu C. Analytical design method of multiway dual-band planar power dividers with arbitrary power division. IEEE Trans Microw Theory Tech 2010;58(12 PART 1):3832–41. [27] Liu Y, Chen W, Li X, Feng Z. Design of compact dual-band power dividers with frequency-dependent division ratios based on multisection coupled line. IEEE Trans Components, Packag Manuf Technol 2013;3(3):467–75. [28] Tang CW, Hsieh ZQ. Design of a planar dual-band power divider with arbitrary power division and a wide isolated frequency band. IEEE Trans Microw Theory Tech 2016;64(2):486–92. [29] Cheng K-KM, Law C. A novel approach to the design and implementation of dual-band power divider. IEEE Trans Microw Theory Tech 2008;56(2):487–92. [30] Wu Y, Zhuang Z, Yan G, Liu Y, Ghassemloo Z. Generalized dual-band unequal filtering power divider with independently controllable bandwidth. EEE Trans Microw Theory Tech 2017;65(10):3838–48. [31] Wang X, Sakagami I, Ma Z, Mase A, Yoshikawa M. Generalized, miniaturized, dual-band wilkinson power divider with a parallel RLC circuit. AEU - Int J Electron Commun 2014;69(1):418–23. [32] Wu Y, Liu Y, Zhang Y, Gao J, Zhou H. A dual band unequal wilkinson power divider without reactive components. IEEE Trans Microw Theory Tech 2009;57 (1):216–22. [33] Woo DJ, Lee TK. Suppression of harmonics in wilkinson power divider using dual-band rejection by asymmetric DGS. IEEE Trans Microw Theory Tech 2005;53(6 II):2139–44. [34] Song K, Mo Y, Zhuge C, Fan Y. Ultra-wideband (UWB) power divider with filtering response using shorted-end coupled lines and open/short-circuit slotlines. AEU - Int J Electron Commun 2013;67(6):536–9. [35] Tang CW, Chen JT. A design of 3-dB wideband microstrip power divider with an ultra-wide isolated frequency band. IEEE Trans Microw Theory Tech 2016;64(6):1806–11. [36] Yu X, Sun S. A novel wideband filtering power divider with embedding threeline coupled structures. IEEE Access 2018;6:41280–90. [37] Zhu H, Abbosh AM, Guo L. Wideband four-way filtering power divider with sharp selectivity and wide stopband using looped coupled-line structures. IEEE Microw Wirel Components Lett 2016;26(6):413–5. [38] Yang X, Zhang XC, Liao ZH. A novel planar four-way power divider with large dividing ratio. AEU - Int J Electron Commun 2018;85(December 2017):1–6. [39] Wang J, Ni J, Guo YX, Fang D. Miniaturized microstrip wilkinson power divider with harmonic suppression. IEEE Microw Wirel Components Lett 2009;19 (7):440–2. [40] Jiang D, Huang Y, Huang T, Xu R, Shao Z. Implementation of a compact microstrip power divider using novel split ring resonator. Optik (Stuttg) 2015;126(19):1782–6. [41] Wu Y, Zhuang Z, Kong M, Jiao L, Liu Y, Kishk AA. Wideband filtering unbalancedto-balanced independent impedance-transforming power divider with arbitrary power ratio. IEEE Trans Microw Theory Tech 2018;66(10):4482–96. [42] Cheng KM, Ip W. A novel power divider design with enhanced spurious suppression and simple structure. IEEE Trans Microw Theory Tech 2010;58 (12):3903–8.