Designing LC Wilkinson.pdf

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18 www.rfdesign.com August 2002

M icrowave power splitters/combiners, such asWilkinson dividers and hybrid rings, arecommonly used, mainly in microstrip circuits1.Some of their applications include balanced ampli-fiers, high-power transmitters, and antenna arrayfeed networks.

These power splitters generally employ quarter-wave transmission line sections at the design cen-ter frequency, which can have unrealistic dimen-sions at frequencies in the RF and low microwavebands, where the wavelength is large.

For example, a /4 microstrip line with character-istic impedance Zo = 70.7 on FR-4 substrate(dielectric constant r = 4.3, thickness h = 1.0 mm) isapproximately 43 mm long at a frequency of 1 GHz.

In some cases, it would be preferable to uselumped-element equivalent networks replacing the/4 transmission lines2,3. It is possible to employsurface mount devices (SMD), as well as monolithicmicrowave integrated circuit (MMIC) lumped ele-ments4, which allow saving circuit area.

Lumped element equivalentsAs it is known, a /4 transmission line segment

admits Tee and Pi lumped-element equivalent

networks. The same is valid for a 3/4 line seg-ment. In particular, a quarter-wave line at a fre-quencyfo, with characteristic impedanceZo, can bereplaced for a Pi LC equivalent network as

shown in Figure 1.The element values are given by the following

equations:

(1)

(2)

The Pi LC network is perfectly equivalent tothe line section only at the center frequency fo,but the approximation is still valid for modest

bandwidths.

Design of lumped-element Wilkinson dividersFigure 2 shows the layout of a classical

microstrip Wilkinson power splitter. In the simplestform, it consists of two quarter-wave line segmentsat the center frequencyfo with characteristic imped-ance Zo2, and a 2Zo lumped resistor connectedbetween the output ports. It provides low loss,

equal split (ideally 3 dB), matching at all ports, andhigh isolation between output ports.

By replacing both /4 line sections by equivalentPi LC networks, it is possible to obtain a lumped-element version of the Wilkinson divider, as shown

in Figure 3. As noted above, this network is equiva-lent to the original only at the center frequency fo.Consequently, the expected performance (insertionloss, return loss, isolation, etc.) should be similar tothat exhibited by the distributed-form powerdivider for a narrow bandwidth centered in fo, wideenough for most applications.

Moreover, the Pi LC equivalent networks exhibita low-pass behavior, rejecting high frequencies,while the response of the classical Wilkinsondivider repeats at odd multiples of center frequency(3fo and 5fo, mainly). This behavior could be desir-

LZ

fs

o

o

= 2

Cf Z

p

o o

=

1

2

Figure 1. Lumped element "Pi" equivalent network of a l/4 transmission line section

interconnects/interfaces

Designing LC

Wilkinsonpower splitters

Wilkinson power splitters arecommon transmission path

elements. Designers canimplement them more effectively

by knowing their nuances.

By Fernando Noriega,Pedro J. Gonzlez

Figure 2. Layout of a classical microstrip Wilkinson powersplitter.


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able if harmonic filtering is needed. Forcomparison purposes, Figure 4 showsthe split, matching and isolation char-

acteristics expected for these two typesof Wilkinson dividers.At 1080 MHz, using (1) and (2) we

obtain Cp = 1.8 pF andLs = 10 nH. Atport 1 we choose a 3.9 pF capacitor,and the balancing resistor is 100. Inall cases, standard low-cost 0805 SMDcomponents are used, featuring 5 per-cent tolerance.

Measurement results are presentedin Figure 5. Insertion loss at centerfrequency is about 3.6 dB, return loss-es result 14 dB at port 1, 16 dB atports 2 and 3 (not shown), and isola-tion between output ports reaches 20

dB. These are typical values alsoattainable with a microstrip powerdivider. However, a 1 GHz microstripWilkinson splitter could occupy about6 square centimeters on FR-4, whilethis lumped-element version occupiesless than 1 square centimeter.

The actual behavior at higher fre-quencies differs expectations becausedevice parasitics were neglected in thesimulations. Nonetheless, second andthird harmonics are still rejected more

than 25 dB. Better agreement could beachieved by considering an adequatemodeling of device parasitics.

Three-way Wilkinson power splitter

The Wilkinson divider can be general-ized to anN-way power splitter/combin-er. For example, the diagram corre-sponding to a three-way divider isshown in Figure 6. As can be seen, itrequires crossovers for the balancingresistors1. This makes fabrication diffi-cult in planar form (e.g.: microstrip).However, the lumped-element design ismuch easier to realize (see Figure 7).The board layout is depicted in Figure 8.

For an 850 MHz design, we canobtain Cp = 1.5 pF and Ls = 15 nH. Atport 1, we choose a 4.7 pF capacitor,and the three balancing resistors are

51. The shunt capacitor Co is used totune out the resistor and pad parasiticsto avoid performance degradation(mainly in terms of isolation betweenports). Its value is determined experi-mentally, varying typically in the 0.5 to2 pF range for these frequencies.

Figure 9 presents the measured per-formance provided by the prototype.

Return losses are better than 12 dB atport 1 at center frequency (around 15dB at output ports, not shown for clari-ty). Measured split losses from port 1 to

all three output ports are only about0.7 to 1.2 dB higher than in the idealcase (4.77 dB). Excellent isolation char-acteristics between the output ports,exceeding 25 dB, are achieved byadjusting the value of capacitor Co.

Unequal Wilkinson power splitter

It is also possible to design powerdividers with unequal power split andmatching at all three ports2. In Figure10, transmission lines 3 and 4 arequarter-wave transformers used tomatch output ports to 50. This wouldlead to a lumped-element design con-sisting of additional LC components.However, in some cases it may be fea-sible to simplify the circuit configura-tion (i.e., to reduce the componentcount) by removing some non-criticalelements without noticeably degradingthe performance characteristics.

For a center frequency of 850 MHz,an unequal Wilkinson power splitterwith output power split ratio of 8 dBwas designed. In Figure 11, the finalcircuit schematic is presented. Thistopology was obtained after empiricallytuning the initial circuit elements anddetecting which of them were essentialto preserve acceptable split, matchingand isolation characteristics over thedesired bandwidth. The final element

values are listed in Table 1. In particu-

Figure 5. Measurements of the 1080 MHz lumped-element Wilkinson divider.

Figure 3. Schematic of the two-way lumped-ele-ment Wilkinson divider.

Figure 4. Comparison of simulated performance of a microstrip Wilkinson power splitter (a), and itslumped-element equivalent (b).

Figure 6. Diagram of a three-way Wilkinsondivider.


Figure 7. Schematic of the three-way lumped -ele-ment Wilkinson divider.

(a) (b)


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lar, resistorRi must be selected to pro-vide good isolation level.

Measurement results are plotted inFigure 13. Insertion losses are 10.5 dBand 1.3 dB for ports 2 and 3, respec-tively, thus corresponding to a split

ratio of 9 dB. An excellent isolationvalue is achieved, better than 20 dB.On the other hand, matching resultsare quite good, except at port 2, wherereturn loss is worse than 10 dB. If this

value is not acceptable, it should bedeveloped as a less simplified circuit

Figure 9. Measurements of the three-waylumped-element Wilkinson divider.

Figure 8. Layout of the three-way lumped-ele-ment Wilkinson divider.

Figure 10. Diagram of an unequal Wilkinsonpower splitter.

Figure 11. Schematic of the simplified lumped-element unequal Wilkinson power splitter.

Table 1. List of components for the unequalpower splitter.


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