Download A general model of modified Wilkinson Power Dividers with

TECHNOLOGICAL EDUCATIONAL INSTITUTE OF CENTRAL MACEDONIA
DEPARMENT OF INFORMATICS & COMMUNICATIONS
-----------------Master of Science in Communication & Information Systems
DESIGN OF A WILKINSON POWER
DIVIDER WITH ADDITIONAL
TRANSMISSION LINES
Georgia Kontoglou
Supervisor Dr.Tsitsos Stilianos
Serres, December 2013
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 nonisolated 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.
• For simplicity, all impedances are normalised to the characteristic impedance Zo, and
voltage generators are added to the output ports.
Figure 2 : The Wilkinson power divider circuit in normalized and symmetric form.
• 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.
V2eve  V0
Figure 3 : Bisection of the circuit
•
Looking through port 2,the impedance is:
Z
e
in
Z2
=
2
For matching port 2 , should Ζ=√2 , Ζin=1
• We obtain V2eve=Vo
e
• Using transmission lines equation : V1   jV 2
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 :
Z in 
1
( 2)2  1
2
• In summary we can establish the following S-parameters for the Wilkinson
power divider:
S11  0
S22 = S33 = 0
S12 
V e 1  V 01
 j/ 2
S 21 = e
V 2  V 02
S13  S31   j / 2
S 23  S 32  0
(Zin = 1 at port 1 )
(ports 2 and 3 matched for even and odd modes )
(symmetry due to reciprocity )
(symmetry of ports 2 and 3 )
(due to short or open at bisection )
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
Figure 4 : Circuit model to
be discussed
• Even and odd mode analysis is applied to the circuit in order to determine the
parameters of the circuit.
Even mode analysis
• 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 :
Zb1  jRab tan 1
tan 2 1
j

b1 ( Rab  jZb1 tan 1 )
Zb 2
Rb
• From the real part of (4.6):
eve
YINb

Zb 2
Q

Zb1
P
(4.7)
Zb21
Zb21
P
 1

2
Rab Rb
(1  k ) Ra Rb tan21
(4.6)
Figure 7: Lower circuit
• From the imaginary part of (4.6):
1
Figure 6: Upper circuit
(4.8)
Odd mode analysis
• When port 2 and 3 are excited by an equal amplitude
and out-of-phase current, the circuit is divided.
odd
YINb

Z  jR tan 2
1
1


jZb1 tan 1 Zb 2 ( Rab  jZb 2 tan 2 ) Rb
b2
ab
(4.12)
• Solving the real and imaginary part we obtain :
(1  k 2 ) Z b22 Ra Rb
Zb1 
(1  k 2 ) Ra Rb  Z b22 (1  P)
Zb22 P
Rab 
(1  k 2 ) Ra
Figure 8: Upper circuit
(4.16)
Zb22 P
R  Rab  Rac  (1  1/ k ) Rab  2
k Ra
2

(1  k 2 ) Ra Rb P 


1  tan 
 (1  k 2 ) Ra Rb  Zb21 


1


k 2R

θ2  tan  P 1  (1  k 2 ) R

b

1
(4.15)


 
(4.17)
(4.18)
(4.19)
Figure 9: Lower circuit
If the sign of (4.18) is negative, the sign of (4.19) must be positive by (4.7) and (4.10)
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:
0  Zb1  (1  k 2 ) Ra Rb
(4.21)
(1  k 2 ) Ra Rb
0  Zb 2 
P
(4.22)
0  R  (1 k 2 )Rb
(4.23)
n 

 1  (n  1)  tan 1 P
(4.24)
m  2  m  tan1 P
(4.25)
2
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
Parameter
Value
Zb1 , Zc1
60 Ω
Zb2 , Zc2
60 Ω
R
72 Ω
θ1
117.89o
θ2
27.88ο
Table 1: Calculated electrical parameter values
Figure 10: Modified power divider circuit diagram with ideal 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
-3.010
-3.010
-3.010
-3.010
-83.121
-83.121
-83.078
-103.123
-103.123
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)
TL1
60
TL2
Electrical Length
(degrees)
Width (mm)
Lengh
(mm)
117.89
0.817713
30.0495
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.
Construction and results
Figure 14: Layout for the circuit
Figure 15: Constructed modified power divider with
microstrip transmission lines
• The circuit constructed with the values that were calculated and the dielectric substrate
that 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.
Table 5: Scattering parameter values vs frequency for Fig11 in 2GHz frequency
S21 (dB)
S31 (dB)
S32 (dB)
S11 (dB)
S22 (dB)
S33 (dB)
-3.5
-3.194
-27.973
-39.338
-42.932
-29.932
•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