Wilkinson power divider

                      Wilkinson power divider

M.H Mohd Hashim

mhasruzairin@gmail.com

Abstract— This paper is present to design and simulate the circuit for the of 2-section Wilkinson power divider in microstrip technology. Software ADS 2008 is use to simulate the circuit diagram and come out with output in graph frequency. Chebyshew transformer design with max reflection coefficient in passband = 0.05 use for reference to find Z1 and Z0.Center Frequency is 2.75Ghz and Z₀ is 50Ω.

 Keywords- Wilkinson power divider, Agilent ADS

         I.          Introduction

   In power division, an input signal is divided into two or more output signal. Power divider may have 2 port, 3 port, 4 port or more and may be lossless. Power divider  usually provide in phase output signals with an equal power division ratio (3dB).Power dividers in antenna have three-port especially important for antenna array systems that utilize a power-splitting network. The device that splits power between n outputs ports with a certain distribution while maintaining equal path lengths from input to output ports. The device implemented with n-way power splitters where three-port power dividers are commonly used. Normally we use incoming port 1 and output is port 2 and port 3.The flexibility of the two-way divider's feed structure allows use of multiple stepped-sections to achieve power division with the capability of wideband operation. The bandwidth is primarily limited by the match of the radiating elements, although using high-isolation power dividers reduces the dependence on the match of the loads.

The scattering matrix of 3 port network has nine independent elements :-

If all the port is matched then S11=S22=S33= 0 therefor the scattering matrix reduces to :-

                                                                          II. Methodology

A.    Design Procedure

To accomplish the design, ADS 2008 was used to design a power divider for the theoretically ideal case. An ideal half-split power divider would divide incident power at port 1 equally between ports 2 and 3. The S-matrix for the ideal Wilkinson divider is given below:

This ideal Wilkinson power divider would have perfect matching at all ports (S11 = 0, S22 = 0, S33=0). Also, there would be perfect isolation between ports 2 and 3 (S23 = 0). The insertion loss between ports 1 and 2 should be -j/√2, and the insertion loss between ports 1 and 3 should be √ -j/2, (|S12| = |S13| = -j/√2). The implementation of the divider uses quarter wavelength lines that cause the phase shift of π/2. Since the device is passive, the S-matrix is reciprocal.Even-odd mode analysis can be used to derive the proper three-port circuit to use to create the ideal Wilkinson power divider. The results are shown below, in Figure 6.

                                               Figure 1: Schematic diagram for three transmission lines.

In summary,we can establish the following scattering parameter for the wilkinson divider:

S11 = 0 Zin = 1 at port 1
S22 = S33 = 0 ( ports 2 and port 3 match for even and odd modes)
S12 = S21 = -j/√2 symmentry due to reciprocity
S13 = S31 = -j/√2 symmentry of ports 2 and 3
S23 = S32 = 0 Due to shot or open at bisection

B. Design Formulas

 

                                    Figure 2:Schmatic diagram for two section wilkinson power divider

From schematic in figure 2, it show that R₁ and R₂ are parallel. Function of port 1 is input port and port 2 and port 3 is output. From input it divide to two divider for port 2 and port 3.For this simulation, Z₀ is 50 Ω and f₀ = 2.75 GHz. In table 1 is show group of ideal values:-

Substrate Diaelectric constant	Substrate Thickness  h (mm)	Loss Tangent	metallization	Multisectiom Quarterwave Transformer
4.50	0.762	0.0020	17µm Copper	Chebyshev (Max reflection Coefficient in the Passband =0.05)

    









                                     Table 1

                                                                           

C. Simulation Using ADS

LINECALC was used to calculate the length and width microstrip. Figure 3 is show the section of microstrip line. It is one of the simplest forms of transmission lines, consisting of a conducting line above an infinite ground plane, separated by a substrate

Figure 3

It can be seen from Figure 3 that the microstrip structure is open, which means that the electric and magnetic fields, will (theoretically) extend to infinity. Along with the finite height of the conducting line, this makes the structure very difficult to analyze. Infinitely thin top conductor and metallic shielding is therefore normally assumed when analyzing the structure.

Since the electromagnetic field will propagate in both air and the substrate, the propagating wave cannot be a pure transverse electromagnetic (TEM) wave, and both the electric and the magnetic fields must have a longitudinal component. The reason for this is that the phase velocity in air and the substrate is different, and therefore a TEM mode can, in theory, only exist at DC.

Figure 4

All microstrip transmission lines suffer from loss, which can be divided into three categories:-

a.       conductor loss

b.       substrate loss

c.       radiation loss.

The conductor loss is due to the electrical properties of the material used. Different materials have different loss, so it is advantageous to use a material with high conductivity. As the frequency is increased, most of the current will be concentrated in the outer part of the conductor.

The gain is the amplification of the signal from input to output. It can be expressed in decibel or as a scalar value. It can also be expressed as a complex number by including the phase.

The insertion loss reveals how much power is lost due to the insertion of the device into the rest of the circuit.

The return loss reveals how much of the incident power is lost due to mismatch at the input. It is expressed in decibel

Table 2 show the result below after simulate with LINECALC:-

Port	W	L
Z1	0.521154 mm	15.4187 mm
Z2	0.987237 mm	15.0493 mm

Table 2

These resulting microstrip widths and lengths were used in generating the layout for the circuit. This schematic was convert to layout below:-

Figure 5 : Layout generate  in ADS

Simulate the layout to get the result frequency response an equal-split Wilkinson power divider.

                                                        III. Result and finding

The return loss, insertion loss, coupling, and isolation between ports were evaluated to determine the optimized final design. A minimal return loss of -10 dB or better over the band and isolation between output ports is a critical design requirement. Also, approximately -3 dB coupling (half of the power) between input and output ports for each stage is anticipated

Figure 6:S-Parameter vs Frequency

The above plot was generated in Agilent ADS using ideal transmission line components to model the Wilkinson divider. The frequency response over the band 1Ghz -5GHz has -3dB coupling and return loss and isolation approaching negative at center frequency which coincides with the Wilkinson S-matrix.

From graph when S11 at center frequency 2.75 GHz and approximate magnitude is -15 dB For S23 when at center frequency 2.75 GHz and magnitude is -11 dB For S21 when at center 2.75 and magnitude is -3 dB

                                             Figure 7: Phase different on frequncy respon

From the phase plot we see that S21 and S31 is in same phase  and s-parameters show resonance at the design frequency.

                                                   

IV. Conclusion

The Wilkinson divider can meet the ideal three-port network conditions (if it is matched at all ports) being lossless, reciprocal, matched. Therefore, the Wilkinson divider is the best choice in the above comparison and will be used in the optimized design of the corporate-fed network for the array. Wilkinson is losses if impedance match of all port. Passive components, R, L, and C in parallel gives good isolation level between output ports.

  

References

[1]     “Microwave Engineering”,Fourth Edition,David M.Pozar.

[2]     Tron Torgeson,”Wilkinson Power Divider”.NTNU master paperwork.

[3]     Daniel D. Harty, “Novel Design of a Wideband Ribcage-Dipole Array and its Feeding         
          Network”,Master Thesis,Worcester Polytechnic Institute.

[4]     Ashraf S. Mohra and Majeed A. Alkanhal,” Dual Band Wilkinson Power Dividers Using T- 
          Sections” Department of Electrical Engineering, King Saud University.

[5]     Jong-Sik Lim, Sung-Won Lee, Chul-Soo Kim, Jun-Seok Park, Dal Ahn, and Sangwook Nam,” 
          A 4 : 1 Unequal Wilkinson Power Divider”.

[6]     Lecture note,Dr Norhudah Seman,Universiti Teknologi Malaysia.

[7]     “ Design and Analysis of an Equal Split Wilkinson Power Divider”,master asigment, Bajee 
          Bobba,Dominic Labanowski,Tom Zajdel ,Cameron Zeeb