TECHNOLOGICAL EDUCATIONAL INSTITUTE OF CENTRAL MACEDONIADEPARMENT OF INFORMATICS & COMMUNICATIONS

------------------Master of Science in Communication & Information Systems

Serres, December 2013

Georgia KontoglouSupervisor Dr.Tsitsos Stilianos

DESIGN OF A WILKINSON POWER DESIGN OF A WILKINSON POWER DIVIDER WITH ADDITIONAL DIVIDER WITH ADDITIONAL

TRANSMISSION LINESTRANSMISSION LINES

Abstract

Problem : In designing a conventional Wilkinson power divider, the isolation resistor must be connected to two quarter-wave transmission lines and two

output ports. This physical proximity creates more parasitics and undesirable coupling between the two transmission lines as frequency increases.

Objectives: A modified Wilkinson power divider with additional transmission lines, able to overcome the above problems will be designed, simulated, constructed and tested.

Methodology: Review of the relevant theory and then design, simulate and optimize the circuit using the Advanced Design System (ADS) software package, implement the circuit using microstrip transmission lines.

Microwave power dividers

• Power dividers are passive microwave devices used for power division or power combining.

• an input signal is divided into two (or more) output signals of lesser power. • may be symmetric, antisymmetric, may have any number of isolated or non-

isolated ports (which may be in-phase or out-of-phase) and equal (3 dB), or

unequal power division ratio.

• Applications : in distribution networks for antenna arrays , in microwaves amplifiers and oscillators , in digital high speed circuit interconnects.

Wilkinson power divider• Splits power in any ratio.• Lossless when the output ports are matched. Achieves isolation between the output

ports while maintaining a matched condition on all ports.

Figure 1: Wilkinson power divider(a)An equal-split Wilkinson power divider in microstrip form. (b) Equivalent transmission line circuit.

• This circuit can be analysed by reducing it to two simpler circuits driven by symmetric and antisymmetric sources at the output ports and apply the “even” and “odd” mode analysis technique.

Figure 2 : The Wilkinson power divider circuit in normalized and symmetric form.

• For simplicity, all impedances are normalised to the characteristic impedance Zo, and voltage generators are added to the output ports.

• Even and odd mode analysis is applied to the circuit in order to determine the parameters of the circuit.

Even mode analysis• No current flows through the r/2 resistors or the short circuit between the inputs of the two transmission lines at port 1.

Figure 3 : Bisection of the circuit

•Looking through port 2,the impedance is:

ineZ

2

2Z =

For matching port 2 , should Ζ=√2 , Ζin=1• We obtain V2eve=Vo• Using transmission lines equation : 21 jVV e

2 0eveV V

Odd mode analysis

• Vg2=-Vg3, so there is a voltage null along the middle of the circuit . • We can then bisect this circuit by grounding it at two points on its midplane.

Figure 4 : Bisection of the circuit

Looking into port 2, we see an impedance of r/2, since the parallel-connected transmission line is λ/4 long and shorted at port 1, and so looks like an open circuit at port 2.• In order port 2 to be matched we select r=2.• Thus we obtain : Vodd2= Vo and Vodd1=0

• The input impedance at port 1 :

1)2(2

1 2 inZ

• In summary we can establish the following S-parameters for the Wilkinson power divider:

011 S

2/3113 jSS 03223 SS

(Zin = 1 at port 1 ) (ports 2 and 3 matched for even and odd modes )

2112 SS 2/2

02

10

1j

VV

VVe

e

= (symmetry due to reciprocity )

(symmetry of ports 2 and 3 )

(due to short or open at bisection )

S22 = S33 = 0

A general model of modified Wilkinson Power Dividers with additional transmission lines

• The generalized circuit that is going to be discussed: Terminal loads are represented by Ra ,Rb , and Rc Zb1, Zc1 and θ1 stand for characteristic impedances and electrical lengths of the

upper and lower transmission lines Zb2, Zc2, and θ2 are the characteristic impedances and electrical lengths of

additional transmission lines

• Even and odd mode analysis is applied to the circuit in order to determine the parameters of the circuit.

Figure 4 : Circuit model to be discussed

Figure 6: Upper circuit

• The fed power ratio of port 3 to port 2 is defined to be k2 to 1

• By the even-mode, the circuit can be divided into two equivalent circuits having symmetric voltage distribution, and no currents flow to the isolation resistor . The following equation denotes input admittance from port 2 to port 1 :

(4.6)

• From the real part of (4.6):

(4.7)

(4.8)

Even mode analysis

11 2

11 1 2

tan tan( tan )

1eve b abINb

b ab b b b

Z jRj

R jZ Z RY

2

1

b

b

Z QZ P

• From the imaginary part of (4.6):2 21 1

2 21

1(1 ) tan

1 b b

aab b b

Z Z PR R k R R

Figure 7: Lower circuit

• When port 2 and 3 are excited by an equal amplitude and out-of-phase current, the circuit is divided.

• Solving the real and imaginary part we obtain :

(4.12)

(4.15)

(4.16)

(4.17)

(4.18)

Odd mode analysis

2

2 2

2

11 2 ( tan )

tan1 1tan

b ab

ab b

oddINb

b b b

jR

R jZjZ Z RZY

2 22

1 2 22

(1 )(1 ) (1 )

ab bb

a b b

k Z R Rk R R Z P

Z

222(1 )

bab

a

Z Pk R

R

22 2

2(1 1/ ) bacab ab

a

Z PR k R

k RR R

21

1 2 21

(1 )tan

(1 )a b

a b b

k R R Pk R R Z

2

21 1

(1 )tan

b

kP

k R

R

θ2(4.19)

If the sign of (4.18) is negative, the sign of (4.19) must be positive by (4.7) and (4.10)

Figure 8: Upper circuit

Figure 9: Lower circuit

12(1 )0 b a bk R RZ

2

2(1 )0 ba bk R R

PZ

20 (1 ) bR k R

11 ( 1) tan

2n Pn

12 tanm Pm

Regarding the ranges of all values, firstly, (4.18) gives the ranges of Zb1 and θ1,

and, secondly, (4.15) gives the range of Zb2. Finally the ranges of θ2 and R are

determined. Consequently:

(4.21)

(4.22)

(4.23)

(4.24)

(4.25)where n and m are any integer.

Within these ranges, all other values are determined

Design and implementation of Wilkinson Power Divider with additional transmission lines

• The central operating frequency was selected to be 2 GHz.

Calculation of the electrical parameter values of the modified power divider

 The terminal loads Ra, Rb, Rc are selected to be 50 Ω

Table 1: Calculated electrical parameter values

Parameter Value

Zb1 , Zc1 60 Ω

Zb2 , Zc2 60 Ω

R 72 Ω

θ1 117.89o

θ2 27.88ο

Figure 10: Modified power divider circuit diagram with ideal transmission lines.

Scattering parameter values vs frequency

S12 S21 S13 S31 S23 S32 S11 S22 S33

-3.010 -3.010 -3.010 -3.010 -83.121 -83.121 -83.078 -103.123 -103.123

Scattering parameter values vs frequency in 2GHz frequency (dB)

In accordance with the above scattering parameter values, results the following:

• The Reflection Loss parameters in every port are having large negative values in dB. That means that in ports returns a signal of small power due to reflection. Therefore, all the ports are matched.• The isolation between port 2 and port 3,,is having a large negative value in dB. That means that the ratio of power that flows between these two ports is very small. This results to the fact that there is a good isolation between port 2 and 3.• The power that flows from port 1 to port 2 and port 3, is -3.010 dB (0.5).So the ratio of power that flows from port1 to the two others is 50%.As we can see, the circuit achieves an equal power division.

Design of the modified power divider using microstrip transmission lines

The parameters of the dielectric substrate :

• Substrate thickness H=0.52 mm • Conductor thickness T=0.035 mm • Relative dielectric constant Er=3.55 • Dielectric loss tangent TanD=0.0027 • Conductor surface roughness Rough=0 mm• Conductor conductivity in Siemens/meter Cond=5.813e7

Table 3: Calculated physical dimensions Line Characteristic

Impedance(Ohm)Electrical Length

(degrees)Width (mm) Lengh

(mm)

TL1 60 117.89 0.817713 30.0495

TL2 60 117.89 0.817713 30.0495

TL3 60 27.88 0.817713 7.10645

TL4 60 27.88 0.817713 7.10645

Figure 12: Power divider circuit diagram with microstrip transmission lines.

Scattering parameter values vs frequency

Scattering parameter values vs frequency in 2GHz frequency (dB)

S12 S21 S13 S31 S23 S32 S11 S22 S33

-3.077 -3.077 -3.077 -3.077 -55.599 -55.599 -48.734 -50.848 -50.848

In accordance with the above scattering parameter values, results the following:

• The Reflection Loss parameters in every port are having large negative values in dB. That means that in ports returns a signal of small power due to reflection. Therefore, all the ports are matched.• The isolation between port 2 and port 3,,is having a large negative value in dB. That means that the ratio of power that flows between these two ports is very small. This results to the fact that there is a good isolation between port 2 and 3.• The power that flows from port 1 to port 2 and port 3, is -3.077 dB (49.23%). As we can see, the circuit achieves an equal power division with a small deviation of 0.77%. This happens because of the losses to the dielectric substrate of the microstrip line.

Figure 14: Layout for the circuit

Figure 15: Constructed modified power divider with microstrip transmission lines

Construction and results

• The circuit constructed with the values that were calculated and the dielectric substratethat has been discussed

• The S-parameters was obtained using the Agilent E5071C microwave vector network analyzer

• The losses in the cable connected between the power divider and the network analyzer were calibrated

• The return loss associated with each port was measured while any unused ports were terminated with 50Ω loads.

S21 (dB) S31 (dB) S32 (dB) S11 (dB) S22 (dB) S33 (dB)

-3.5 -3.194 -27.973 -39.338 -42.932 -29.932

Table 5: Scattering parameter values vs frequency for Fig11 in 2GHz frequency

•A nearly equal power split is achieved by power divider. The parameter S21 is -3.5 dB, which means 44.6% of the input power is delivered to the one output. The parameter S31 is -3.194 dB, which means 47.9% of the input power is delivered to the second output. This further demonstrates the symmetry of device because S21 is essentially equal to S31.

•The isolation between the output ports for the modified power divider is -27.973 dB.That means that has a transmission coefficient that is close to zero, implying high isolation between ports two and three. Therefore there is not significant power transmission between the two output ports.

•The return losses for each port of the power divider are shown in Fig.16, Fig.17, and Fig.18.S11 parameter is -39.338 dB at the central operating frequency, this is almost equal to zero, so there are nearly no losses to port 1.The return loss for port 2 is -42.932 dB and for port 3 -29.932 dB. Therefore, there are not return losses due to reflection at port 2 and port 3 too. The ports are matched.

Figure 16: Power rate between port 1 and port 2 (S21 parameter)

Figure 17: Power rate between port 1 and port 3 (S31 parameter)

Figure 18: Isolation between the output ports (S23 parameter)

Figure 19: Input’s Return Loss (S11 parameter)

Figure 20: Output’s Return Loss(S22 parameter)

Figure 21: Output’s Return Loss (S33 parameter)

Conclusion

A generalized model for modified Wilkinson power divider has been presented and discussed using a modified even- and odd- modes method.

Experimental results showed the validity of the design equations and that modified power divider indeed can solve the problems of parasitics and undesirable coupling between the transmission lines.

Further development of this project can be achieved by designing the same circuit for dual band or for wideband.

Thank you very much for your interest