# Convert Distributed MICs To MMICs

July 1, 2003
Proven passive MIC components can be redesigned as MMICs with equivalent electrical performance, although at a fraction of the size and weight of their MIC counterparts.

Monolithic microwave integrated circuits (MMICs) offer considerable size and weight advantages over their microwave-integrated-circuit (MIC) counterparts. But realizing proven passive MIC components as MMIC designs can present a challenging set of trade-offs for most high-frequency engineers. To aid in the transition, some guidelines have been assembled, along with several examples of circuits that have made the switch.

Choosing between distributed-element and lumped-element designs depends on a number of factors. Some of these include size, performance, materials, quantities, and frequency. For example, lower-frequency microwave components are often based on lumped-element designs (chip capacitors and inductors). Higher-frequency designs (2 to 30 GHz) can use lumped rather than distributed elements, although designers must be aware of the trade-offs.

At very high frequencies, even MMIC designs can employ distributed elements since quarter-wave structures become reasonably small. An example of this is a Ka-band MMIC phase shifter designed with distributed couplers, since quarter-wave elements at 32 GHz are reasonably sized for GaAs MMIC implementation.1 Several other examples will be highlighted here, along with simulation results using linear simulation software and electromagnetic (EM) simulation software as well as measured results are shown for a 90-deg. hybrid circuit and a Wilkinson combiner using lumped elements in a GaAs MMIC.

A lossless transmission-line element can be modeled with circuit elements as a series inductor plus shunt capacitor in a pi or tee configuration (Fig. 1). Given the impedance of a transmission line, the ratio of the inductance and capacitance of the lumped-element equivalent can be calculated (Z0 = (L/C)0.5). Once the length of the transmission line is known, it is possible to calculate fixed values for the inductor and capacitor for a given frequency. However, this transformation from lumped elements to distributed elements only works at certain frequencies. Quarter-wavelength transmission lines repeat at odd multiples of the fundamental design frequency but lumped-element equivalents do not. This can be an advantage or disadvantage depending on the design requirements. Values for the inductors and capacitors can be calculated for these quarter-wave lumped-element equivalent circuits and are found to be L = Z0/W0 and C = 1/Z0W0 where W0 = 2piF0 (where F0 is the design frequency and Z0 is the impedance of the transmission line). For a given impedance and frequency, there are two lumped-element circuits equivalent to the quarter-wave distributed circuits.

For a three-quarter-wavelength transmission line, inductors are substituted for capacitors and vice versa to create a highpass rather than a lowpass network. The calculated values for the L and C components are the same as the one-quarter-wave transmission-line lumped-element equivalent.

For the distributed 90-deg. hybrid, there are basically four quarter-wavelength distributed transmission lines connected in a "square" arrangement (Fig. 2). Two opposite transmission lines have an impedance of 50 Ω(assuming a characteristic impedance of 50 Ω) and the other two lines have an impedance of 35.35 Ω0.5>. It is very important to get the orientation of the coupler input and isolated port correct (see ref. 2).

As noted previously, there are two simple lumped-element equivalent circuits in a pi or tee arrangement. Either arrangement will work, although the choice may depend on other factors: for example, MMIC inductors tend to have more loss than MMIC capacitors. By choosing the pi arrangement to reduce the number of inductors, the lumped-element circuit of Fig. 3 results. Note the combining of capacitors at the "corners" of the 35- and 50-Ω branches.

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The branchline or 90-deg. hybrid can be used for many functions. Some of these include image-reject mixers, attenuators, phase shifters, modulators, and power combiners/dividers. This is true of both the lumped element and distributed implementations of the branchline hybrid. However, the distributed equivalent will repeat at three times the fundamental frequency. Also, the bandwidths of the two implementations are different near the fundamental frequency, F0. The input match of the hybrid is good provided the terminations at the direct and coupled ports are nearly identical. Mismatches at the direct and coupled ports reflect to the isolated port. By adding a switch or variable resistor to the direct and coupled ports of the branchline hybrid, one can create a switched or variable attenuator using the input and isolated ports. Likewise, a switch or variable capacitor can be used to build an analog or digital phase shifter or phase modulator. In an image-reject mixer, one branchline hybrid at RF helps distinguish between the upper sideband and the lower sideband of the signal. An additional 90-deg. hybrid at the intermediate frequency (IF) combines or cancels the two mixed signals to select just the upper or lower sideband.

The hybrid can also be used as a combiner or power splitter with the properties that the input match is good provided that the loads at the coupled and direct ports are matched. As a combiner, reflections from the coupled and direct port are absorbed by a resistor at the isolated port. The difficulty with the hybrid as a combiner/divider is controlling the impedances and lengths of the 35- and 50-Ω transmission lines to obtain an equal 3-dB split at the two ports.

The Wilkinson coupler is often used as a power combiner or splitter. It divides an input signal equally between two outputs, or can be used to create unequal split or an n-port divider. In a Wilkinson, two quarter-wavelength 70.7-Ω lines—assuming a 50-Ω characteristic impedance—split the input to two output ports (Fig. 4). A 100-Ω resistor is tied between the two output ports to provide isolation in the odd-mode case. Placing this resistor can be much easier in a MMIC lumped-element layout than in a distributed layout (Fig. 5). For this example, a pi arrangement was chosen to reduce the number of lossy inductors. The input shunt capacitors combine into a single capacitor yielding two inductors, one shunt capacitor at each port, and the 100-Ω isolation resistor plus interconnect for the MMIC Wilkinson.

As a splitter, the input is divided into two equal in-phase outputs, ideally at −3-dB levels from the input signal level. When fed at the outputs by two signals in phase and of comparable signal level, the Wilkinson acts as a power combiner. The major differences between using a Wilkinson as a divider/combiner versus the branchline hybrid is that the input match now depends on the match at the other two ports. However, it is much easier to get an equal-phase, equal-power split, as well as wider bandwidth, with the Wilkinson than with a hybrid combiner.

A 90-deg. lumped-element MMIC hybrid coupler is a useful for a variety of designs, such as a phase modulator MMIC developed by a student in the Johns Hopkins University MMIC Design Course.3 Students in that course learn to develop practical MMIC layouts that are then fabricated at the TriQuint Semiconductor foundry. Those students developed several lumped-element hybrid layouts, planned around a central substrate via shared by four capacitors and four spiral inductors to make up the four transmission lines of the lumped element equivalent hybrid (Fig. 6). Using the pi arrangement for the lumped-element branches and combining the capacitors at the ends, the layout has a single capacitance value and two inductance values that can be tuned for performance. Arranging the layout allows performance trade-offs by tuning the single capacitance and the size of the two inductors. Careful use of symmetry makes it easier to tune the circuit without "breaking" the layout. A 2.1-GHz hybrid coupler fabricated on a 34 × 54 mil die is an example of the several hybrid couplers fabricated with the TriQuint process (Fig. 6). Hybrid couplers for other frequency ranges can use the same topology by changing the capacitor and two inductor values (plus interconnect).

The performance of the hybrid coupler was simulated (Fig. 7) with the Advanced Design System (ADS) software from Agilent Technologies and the TriQuint TQTRX device library, as well as with EM simulation software from Sonnet Software (Liverpool, NY). Only the "core" of the hybrids were simulated and assumptions were made that the effects of the ground-signal-ground probe pads and off-chip wire bonds were minimal at these frequencies. Given additional time, the matches can be tuned to offset the off-chip wire bond inductance and provide a better 50-Ω termination.

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A 7.5-GHz Wilkinson divider/combiner was also fabricated with the MMIC process. It consists of two 71-Ω transmission lines and a 100-Ω resistor to provide isolation for the coupled ports. Symmetry was used to ensure proper equal phase and equal amplitude split. The hybrid pi lumped-element equivalent was chosen for the MMIC implementation since it has the least number of lossy inductors. Capacitors on the input side can be combined resulting in one value for the two inductors and two values for the three capacitors—the first capacitor is twice the value of the other two. Optimizing the simulation is done by tuning the one inductor value and "one" or "two" capacitor values. A single shared substrate via was used for the shunt capacitor to ground connections. The Wilkinson was also computer simulated, although the ADS simulations did not include the isolation resistor in the layout because its effect was considered to be minimal. The layout for the 7.5-GHz X-band Wilkinson looks similar to half of the hybrid coupler layout (Fig. 8). The 100-Ω isolation resistor was added to the layout along with the ground-signal-ground probe pads in the final layout using the ICED layout software.

The 7.5-GHz Wilkinson measures 34 × 29 mils, and measured performance compared closely with ADS and EM simulations (Fig. 9). Various branchline hybrids from 2.1 to 8.4 GHz were all fabricated on a 34 × 54 mil MMIC tile with room to spare. The higher-frequency hybrids had some additional room for test circuits. Of course, the great advantage of MMICs over MICs is size, and a quarter wavelength on an alumina substrate (dielectric constant of 9.8), for example, is almost 600 mils. If one needs to incorporate additional circuits such as switches, varactors, diodes, FETs, etc., the size, weight, and power savings of a MMIC over an MIC circuit can be substantially higher, although for small volumes, MICs still offer cost advantages compared to the high price of a MMIC wafer run.

These designs were part of a TriQuint PDQ prototype fabrication process in which multiple designs can be placed on a 7 × 7 mm MMIC mini tile. One challenge is arranging the multiple designs on common scribe lines for dicing. Once common die sizes are chosen, bond pads (and probe pads) are added to the initial hybrid layouts. If an isolated port (achieved with the addition of a 50-Ω terminating resistor) is not needed, it can be wire-bonded to a terminating resistor on the MMIC making the circuit a compact three-port coupler or as the standard four-port coupler. Text is added to identify the direct, coupled, input, and isolated ports as well as the operating frequency of the hybrid.

For those interested in fabricating only passive devices monolithically, the TQTRL process from TriQuint Semiconductor is less expensive than the company's standard process that includes active devices. Active elements, such as varactor diodes or switching elements, can turn those hybrid couplers into phase modulators, phase shifters, and attenuators. When active circuit elements are needed, however, the designer should use a full-featured process such as TriQuint's TQTRp or TQTRX process.

ACKNOWLEDGMENTS
The author would like to acknowledge his co-workers in the RF & Microwave Group of the Johns Hopkins University Applied Physics Laboratory (JHU/APL) Space Department (Laurel, MD) who supported and helped enable the MMIC designs presented here. Also, the author would like to acknowledge his co-teacher in the JHU/APL MMIC Design Course, Craig Moore, who has been a wealth of information and support for many years.

REFERENCES

1. John Penn, "A Broadband, Four-Bit, Ka-Band MMIC Phase Shifter," Microwave Journal, December 2001, pp. 84-96.
2. David Pozar, Microwave Engineering, Wiley, New York, 1997, Chap. 7.
3. John Penn and Craig Moore, "Review the basics of MMIC design," Microwaves & RF, June 2001, pp. 55-70.

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