Directional couplers are an important part of analog signal processing in microwave systems, including as portions of power dividers and combiners, in directional filters, attenuators, phase shifters, mixers, amplifiers, modulators, and beam-forming networks for antenna arrays.^1-19 They are also essential in test applications allowing, for example, measurements of high-power signals with sensitive test equipment by coupling a small sample of the total power. To build on a report begun in this magazine in September 2008, the first part of this two-part article will examine methods for implementing planar directional couplers, which can be fabricated both in discrete forms on printed-circuit boards (PCBs) or as part of monolithic- microwave integrated circuits (MMICs). Next month, Part 2 of this article will explore a tradeoff analysis of different coupler design approaches and how to choose among them to meet a specific set of requirements.

A directional coupler is a reciprocal four-port device. With a signal applied to its input port, it provides two amplitude outputs. It is characterized by a number of parameters, including frequency range, bandwidth, coupling, directivity, isolation, matching, insertion loss, relative phase difference between output signals, phase imbalance, and amplitude imbalance (Fig. 1).

Coupling is calculated as the ratio in decibels of the incident power fed into the input port of the main line of the directional coupler to the coupled port power of the secondary line when all ports are terminated by reflectionless terminations. A 3-dB directional coupler (hybrid network) is a special class of directional couplers in which signals at the two output ports are equal. Its insertion loss is the ratio (in decibels) of input power and output power of the main line with reflectionless terminations connected to ports of the directional coupler. Insertion loss is a combination of coupling loss, conductor loss, dielectric loss, isolation loss, and mismatched loss. Directivity is calculated as the ratio (in decibels) of power of the couple port and the isolated port when all ports are terminated by reflectionless terminations. Isolation is the ratio in decibels of power at an isolated port to available power at the input port. The isolation is equal to the sum of the directivity and coupling.

A directional coupler’s relative phase difference can be quadrature (Δφ = 90 deg.) or in-phase/out-of-phase (Δφ = 0 deg. or 180 deg.). A coupler’s bandwidth is the range of frequencies for which a parameter falls within a specified limit with respect to certain characteristics. Couplers can be generally separated into narrowband (less than 20 percent) and broadband (greater than 20 percent) designs.

Figure 2 shows a design flow for a planar directional coupler. Defining a system-level specification is the first step in the design flow. This involves system-level requirements applied directly to a directional coupler, as well as derived requirements that depend on the system requirements. Directional couplers specifications include electrical, cost, size, and other requirements. The major parameters that define RF and microwave planar directional couplers are bandwidth, type of directivity, relative output phases (Δf), phase imbalance, coupling (C), amplitude imbalance, insertion loss (IL), matching or return loss (RL), isolation (ISO), integration level, and cost. A coupler’s RF specifications include margin for manufacturing tolerances, environmental conditions, and performance degradation over a system’s life.

For all requirements, a designer must choose consecutive integer values of weighting coefficients, ki, corresponding to each parameter (the second step of design flow in Fig. 2), from k = 1 for the most important parameter. The maximum value of k can be less than or equal to the number of parameters, depending on whether some parameters are considered to have the same importance or not. Selection of a directional coupler prototype depends on all requirements, and must take into account the corresponding weighting coefficients.

Selecting a directional coupler can be accomplished by using the following procedure:

1. Compare a prototype’s normalized parameters, P_pri/P_reqi with the normalized requirements, P_pri/P_reqi = 1 and determine the deviations, Δ_i = 1 – (P_pri/P_reqi) for each prototype, from 1 to n.

2. Choose the weighting coefficients, k_i, for each parameter as described above, using k = 1 for the most important parameter (such as insertion loss).

3. Normalize the parameter deviation with respect to the weighting coefficient for each prototype, by means of Δ_i/k_i.

4. Add all the deviation values for each prototype,

5. Compare the sum of the deviations from prototype 1 to prototype n and choose the one with the minimum value of

The final selection of a directional coupler prototype can be made by analysis of a circle diagram.6 The optimum prototype should have the minimum area between real and goal performance.

Synthesizing a planar directional coupler is based on both system requirements and derived requirements. Synthesis results are the physical dimensions of a directional coupler. The analysis of a printed-circuit directional coupler entails definition of the electrical performance resulting from given physical dimensions. An electromagnetic (EM) software simulation may be used to create an S-parameter model of a directional coupler.

Four-port directional couplers symmetrical with respect to one or two planes are frequently implemented in RF and microwave devices. A mirrorreflection method,^4,13 is widely used for analyzing symmetrical networks. For RF/microwave couplers, it is popular to analyze directional couplers by means of matrix representations. For analyzing and calculating the dimensions of symmetrical directional couplers, the following approach can be used⁴:

1. Determine the transfer matrices of the two-port networks (the symmetrical parts of the four-port coupler) with even- and odd-mode excitation. In case of a cascade connection of two-port networks, the transfer matrix is equal to the product of transfer matrices of the component four–port coupler.

2. Determine the most important scattering element of the four-port coupler, for example, coefficient S₁₁, which characterizes the input matching.

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