Compact UWB Power Divider , Analysis and Design

In this paper, two ultra-wide band power dividers are introduced. Compact equal power divider is considered firstly where an extended transmission lines and double open stubs are used in order to increase the bandwidth. Secondly, an unequal UWB power divider is introduced where multi-stage impedance is used. The proposed power dividers are fabricated and measured. The overall sizes of the proposed power dividers are 11.37 × 17.87 mm for the equal one and 12.13 × 29.03 mm for the unequal power divider. The simulated results are compared with the measured results and good agreement is obtained.


Introduction
Power dividers play an important role in many microwave systems such as balanced mixers, phase shifters, power amplifiers, and antenna array feed networks.Wilkinson power dividers are the most popular dividers which achieve completely matched output ports with high isolation between them and a fractional bandwidth of 20%.There is a great interest in designing ultra-wideband (UWB) components due to the rapid growth of the short range broadband communications, indoor wireless networks, and UWB radar imaging systems.
Different UWB power dividers had been designed [1] [2] [3] [4] in order to achieve that goal.A tapered slot and a fan-shaped slot were introduced into the circuit design to improve the performance of the UWB non-coplanar power divider [2].A compact UWB power divider based on microstrip-to-slotline transition was introduced in [3].
In [5], a single open circuited radial stub was introduced at each of the Wilkinson power divider output port to broaden the bandwidth.The power divider presented in [6] was based on signal interference technique where the short ended symmetrical coupled line and transversal transmission line were introduced at both output ports of the divider.A high isolation was achieved between output ports due to the microstrip-to-slotline transitions [7].Also, for bandwidth enhancement purpose, a short ended stub was combined with an open ended microstrip line in the power divider structure, as stated in [8].In [9] [10], the proposed UWB power divider with notched band was based on square ring multiple mode resonator.
In this paper, an UWB equal power divider is analyzed and proposed.The analysis is based on the idea of double stub matching.It includes an extended transmission line and double open circuited stubs at each of the output ports in order to increase the bandwidth of operation.Also, an unequal UWB power divider analysis based on the idea of two section transmission line is proposed.On contrary to the unequal power dividers presented in [11] [12] [13], the proposed design is simple and efficient because it can be viewed as two section quarter wave transformer.open stubs lengths can shift the suppressed harmonics outside the UWB range [14].By tuning the length of the extended line ( )

Equal Power Divider Analysis and Design
, Z θ , a better impedance matching can be achieved for input and output ports over wide frequency band.
In order to analyze the proposed equal power divider in simple and efficient manner, it can be represented by a cascade connection of five two-port networks using ABCD matrices and even-odd mode analyses.In the even mode, Figure 2, the isolation resistance can be neglected.By substitution of Z 3 with 0 2Z and considering the 8 λ distance, the A B C D matrix will be: Similarly, for the odd mode case, Figure 3, the symmetry plane is across the isolation resistance.The admittance of the 6 th stage will have a value of 2 R .The A B C D matrix will be: The calculated A B C D parameters are converted to S-parameters [15].The S-parameters are the scattering parameters that relate between the reflected to incident or transmitted to incident.The proposed power divider is symmetric in structure, so it can be analyzed by the even-odd decomposition method.For 3 In the case where two signals of the same magnitude but out of phase (180˚ phase shift), such case is known as an odd mode, when such two signals are applied to ports 2 and 3 of the circuit shown in Figure 1, the plane of symmetry is an electric wall, which is known as short circuit case.Accordingly, the circuit can be bisected to the one shown in Figure 3 for odd mode analysis.For arbitrary electrical lengths for the extended transmission line θ 3 and the two open circuited shunt stubs θ 1 and θ 2 in addition to their impedances Z 1 and Z 2 , the A B C D parameters are obtained using Equation (2) as:  4. The optimized parameters of the proposed power divider are listed in Table 1.
The layout of the proposed UWB power divider is presented in Figure 5, where it is done by using extended transmission lines and two open stubs with cascaded impedances.The s-parameters of the proposed UWB power divider calculated from the analysis mentioned above has been verified using CST full wave analysis simulator and a good agreement is obtained.The S-parameters Table 1.Optimized dimensions of the proposed power divider.
( )  solution of the full wave equation, so some discrepancy must be appearing between analytical and simulation results.The dimensions of the proposed power divider were optimized to obtain good return loss and good isolation between output ports over the UWB frequency range.

Unequal Power Divider Analysis and Design
Figure 7 shows the schematic diagram of the proposed unequal UWB power divider.This design incorporates an input quarter wave transformer with This design can be viewed as a two section quarter wave transformer.By this way, this design will achieve a significant increase in the performance.According to [16], the characteristic impedance of each transmission line can be calculated as follows: ( ) ( ) where 2 k denotes the power dividing ratio of port 3 to 2, and Z c is the characteristic port impedance which is equal to 50 Ω .The layout of the proposed unequal UWB power divider is shown in Figure 8. Same low cost FR4 substrate has been used.The overall size of the proposed unequal UWB power divider is 12.13 × 29.03 mm 2 .For example, if it is required to design unequal power divider with division ratio, S 31 = 0.7962 or −1.98 dB and S 21 = 0.6046 or −4.37 dB, then the power dividing ratio (k) is equal to 1.3168.By substituting into Equations ( 11)-( 14), the values of the characteristic impedances for the power divider are as follows, 41.64

Fabrication and Measurement
Finally, the proposed UWB equal power divider is fabricated and measured with a vector network analyzer.Figure 10 shows the photos of the fabricated UWB equal power divider, where their sizes are compact.Figure 11 and Figure 12 demonstrate the comparison between the simulated and measured results.From On the same manner, the designed UWB unequal power divider is fabricated and its photo is shown in Figure 13; while the divider has a small size.The S-parameters for the simulated and measured power divider are shown in    The deviations of the measurements from the simulations came from tolerance in fabrications; mismatch due to soldering of launchers and due to the losses of FR4 substrate material especially at higher frequency above 6 GHz.

Conclusion
In this work, an UWB equal power divider based on double stub matching was proposed.The UWB performance was achieved by introducing an extended transmission line and double open circuited stubs to each of the output ports of the Wilkinson power divider.The proposed divider was investigated by using even and odd mode analysis.In addition, the UWB power divider with unequal power ratio was presented.There was a good agreement between simulated and measured results.Simple structure and compact size characteristics of the proposed dividers make them very useful in UWB applications and antenna array feed networks.

Figure 1 Figure 1 .
Figure 1 shows the schematic diagram of the proposed UWB power divider.In order to broaden the bandwidth, extended transmission line and open circuited stubs have been added [1].The extended transmission line has the same characteristic impedance as the main line but with different electrical length θ 3 .The double open stubs ( ) 1 1 , Z θ and ( ) 2 2 , Z θ

Figure 2 .
Figure 2.Even mode equivalent circuit of the proposed power divider.

Figure 3 .
Figure 3. Odd mode equivalent circuit of the proposed power divider.

Figure 4 .
Figure 4.The flowchart for the S-parameters optimization process.

Figure 5 .
Figure 5. Layout of the proposed UWB divider with equal power division by using extended transmission lines and two open stubs with cascaded impedances.

Figure 6 .
Figure 6.Proposed power divider s-parameters, analytically and by CST.

Figure 7 .
Figure 7. Schematic diagram for the proposed unequal UWB power divider.

Figure 11 ,
Figure 11, it can be seen that the input reflection coefficient is below −10 dB from 1 GHz up to 12 GHz; which cover the entire region for The UWB range (3.1 -10.6 GHz).Form Figure 12, the coupling coefficient S 21 and S 31 are around (−3 dB ± 1) overall the UWB range.

Figure 14 andFigure 8 .
Figure 14 and Figure 15.The return loss S 11 for simulation and measurement

Figure 9 .
Figure 9. Simulated results of the proposed unequal UWB power divider.

Figure 10 .
Figure 10.Photograph of the fabricated equal UWB power divider.

Figure 11 .
Figure 11.Simulated and measured return loss of the proposed UWB equal power divider.

Figure 14 .
Figure 14.Simulated and measured return loss of the proposed UWB unequal power divider.

Figure 15 .
Figure 15.Simulated and measured insertion loss of the proposed UWB unequal power divider.