M
icrowave power splitters/combiners, such as Wilkinson dividers and hybrid rings, are commonly ud, mainly in microstrip circuits 1.Some of their applications include balanced ampli-fiers, high-power transmitters, and antenna array feed networks.
The power splitters generally employ quarter-wave transmission line ctions at the design cen-ter frequency, which can have unrealistic dimen-sions at frequencies in the RF and low microwave bands, where the wavelength is large.
For example, a λ/4 microstrip line with character-istic impedance Z o = 70.7Ωon FR-4 substrate (dielectric constant εr = 4.3, thickness h = 1.0 mm) is approximately 43 mm long at a frequency of 1 GHz.In some cas, it would be preferable to u lumped-element equivalent networks replacing the λ/4 transmission lines 2,3. It is possible to employ surface mount devices (SMD), as well as monolithic microwave integrated circuit (MMIC) lumped ele-ments 4, which allow saving circuit area.
Lumped element equivalents
As it is known, a λ/4 transmission line gment admits “Tee” and “Pi” lumped-element equivalent
networks. The same is valid for a 3λ/4 line g-ment. In particular, a quarter-wave line at a fre-quency f o , with characteristic impedance Z o , can be replaced 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 to the line ction only at the center frequency fo,but the approximation is still valid for modest bandwidths.
右眼跳是什么预兆Design of lumped-element Wilkinson dividers
Figure 2 shows the layout of a classical microstrip Wilkinson power splitter. In the simplest form, it consists of two quarter-wave line gments at the center frequency f o with characteristic imped-ance Z o •√2, and a 2•Z o lumped resistor connected between the output ports. It provides low loss,
equal split (ideally 3 dB), matching at all ports, and high isolation between output ports.
By replacing both λ/4 line ctions by equivalent Pi 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 f o .Conquently, the expected performance (inrtion loss, return loss, isolation, etc.) should be similar to that exhibited by the distributed-form power divider for a narrow bandwidth centered in fo, wide enough for most applications.
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Moreover, the Pi LC equivalent networks exhibit a low-pass behavior, rejecting high frequencies,while the respon of the classical Wilkinson divider repeats at odd multiples of center frequency (3f o and 5f o
, mainly). This behavior could be desir-
interconnects/interfaces
Designing LC Wilkinson power splitters
Wilkinson power splitters are common transmission path
elements. Designers can
implement them more effectively
by knowing their nuances.
By Fernando Noriega,
Pedro J. González
Figure 2. Layout of a classical microstrip Wilkinson power splitter.
able if harmonic filtering is needed. For comparison purpos, Figure 4 shows the split, matching and isolation char-acteristics expected for the two types of Wilkinson dividers.
At 1080 MHz, using (1) and (2) we obtain C p = 1.8 pF and L s = 10 nH. At port 1 we choo a 3.9 pF capacitor,and the balancing resistor is 100Ω. In all cas, standard low-cost 0805 SMD components are ud, featuring 5 per-cent tolerance.
Measurement results are prented in Figure 5. Inrtion loss at center frequency is about 3.6 dB, re
turn loss-es result 14 dB at port 1, 16 dB at ports 2 and 3 (not shown), and isola-tion between output ports reaches 20dB. The are typical values also attainable with a microstrip power divider. However, a 1 GHz microstrip Wilkinson splitter could occupy about 6 square centimeters on FR-4, while this lumped-element version occupies less than 1 square centimeter.
The actual behavior at higher fre-quencies differs expectations becau device parasitics were neglected in the simulations. Nonetheless, cond and third harmonics are still rejected more
than 25 dB. Better agreement could be achieved by considering an adequate modeling of device parasitics.
Three-way Wilkinson power splitter
The Wilkinson divider can be general-ized to an N -way power splitter/combin-er. For example, the diagram corre-sponding to a three-way divider is shown in Figure 6. As can be en, it requires crossovers for the balancing resistors 1. This makes fabrication diffi-cult in planar form (e.g.: microstrip).However, the lumped-element design is much easier to realize (e Figure 7).The board layout is depicted in Figure 8.For an 850 MHz design, we can obtain C p = 1.5 pF and L s = 15 nH. At port 1, we choo a 4.7 pF capacitor,and the three balancing resistors are 51Ω. The shunt capacit
or C o is ud to tune out the resistor and pad parasitics to avoid performance degradation (mainly in terms of isolation between ports). Its value is determined experi-mentally, varying typically in the 0.5 to 2 pF range for the frequencies.
Figure 9 prents the measured per-formance provided by the prototype.
Return loss are better than 12 dB at port 1 at center frequency (around 15dB at output ports, not shown for clari-ty). Measured split loss from port 1 to
all three output ports are only about 0.7 to 1.2 dB higher than in the ideal ca (4.77 dB). Excellent isolation char-acteristics between the output ports,exceeding 25 dB, are achieved by adjusting the value of capacitor C o .
Unequal Wilkinson power splitter
It is also possible to design power dividers with unequal power split and matching at all three ports 2. In Figure 10, transmission lines 3 and 4 are quarter-wave transformers ud to match output ports to 50Ω. This would lead to a lumped-element design con-sisting of additional LC components.However, in some cas it may be fea-sible to simplify the circuit configura-tion (i.e., to reduce the component
count) by removing some non-critical elements without noticeably degrading the performance characteristics.
For a center frequency of 850 MHz,an unequal Wilkinson power splitter with output power split ratio of 8 dB was designed. In Figure 11, the final circuit schematic is prented. This topology was obtained after empirically tuning the initial circuit elements and detecting which of them were esntial to prerve acceptable split, matching and isolation characteristics over the desired bandwidth. The final element
values are listed in Table 1. In particu-
element Wilkinson divider.Figure 3. Schematic of the two-way lumped-ele-ment Wilkinson divider.
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见多识广的意思Figure 4. Comparison of simulated performance of a microstrip Wilkinson power splitter (a), and its lumped-element equivalent (b).
divider.
熬煎Figure 7. Schematic of the three-way lumped -ele-ment Wilkinson divider.
(a)(b)
lar, resistor R i must be lected to pro-vide good isolation level.
Measurement results are plotted in Figure 13. Inrtion loss are 10.5 dB and 1.3 dB for ports 2 an
d 3, respec-tively, thus corresponding to a split ratio of 9 dB. An excellent isolation value is achieved, better than 20 dB.On the other hand, matching results are quite good, except at port 2, where return loss is wor than 10 dB. If this value is not acceptable, it should be
developed as a less simplified circuit
Figure 9. Measurements of the three-way
lumped-element Wilkinson divider.
ment Wilkinson divider.
Figure 10. Diagram of an unequal Wilkinson
power splitter.
Figure 11. Schematic of the simplified lumped-
element unequal Wilkinson power splitter.
Table 1. List of components for the unequal power splitter.
水浒传内容概括configuration, comprising additional LC elements.
Summary
Lumped-element Wilkinson power splitters can be ud to replace the classi-cal microstrip realization at frequencies from RF to veral GHz, where quarter-wave line gments become large.
iversonSeveral power splitters (two-, three-way, unequal split) employing low-cost SMD passive components have been designed in the 1 GHz band, pro-
viding excellent performance, similar to that expected for a transmission line divider for a modest bandwidth.They are also compact, allowing reduced circuit dimensions, and exhibiting a low pass behavior (not repeated at odd multiples of the cen-ter frequency), filtering the harmonic components of the input signal.
References
[1]David Pozar, “Microwave Engineering,” Addison-Wesley, 1993.[2]Peter Vizmuller, “The RF Design Guide,” Artech Hou, 1995.[3]Norm Dye and Helge Granberg, “Radio Frequency Transistors, Principles and Practical Applications,” Butterworth-Heinemann, 1993.[4]V. F. Fusco, S.B.D.O’Caireallain, “Lumped Element Hibrid Networks for GaAs MMICs,”Microwave and Optical Technology
如何种植草莓Letters, Vol. 2, No. 1, Jan. 1989.
About the authors
Fernando Noriega is a develop-ment engineer in ACORDE S.A.,where he is involved in design and development of DC to microwave cir-cuits and systems. He received his Telecommunication Technical Engi-neer degree from the University of Cantabria, Spain, in 2000.
Pedro J. González is a managing director of ACORDE S.A. He man-ages veral RF and Microwave R&D projects including frequency convert-ers and solid-state power amplifiers.He received his Telecommunication Engineer degree from the University of Cantabria, Spain, in 1999. The a u t h o r s c a n b e r e a c h e d a t : f n o r i e g a @a c o r d e c o m.c o m a n d p e d r o j @a c o r d e c o m.c o m ,o r
Figure 12. Photograph of the unequal Wilkinson
power splitter.
