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 Ω[(50 Ω)^0.5]. 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.