Quadrature (90-degree) hybrid couplers play an important role in various RF system like receivers, transmitters, signal analysis/processing circuits etc., for phase shifting, power combining, and power sampling applications. Most of the times, they are used stand alone connecting with other components using RF cables. They frequently are used along with other microwave circuits like amplifiers, mixers, and power dividers. It is important to design and simulate these hybrids along with amplifiers, mixers, etc., to get the necessary data regarding overall system performance.
To achieve ultra wide band widths, number of sections are increased which results in the increase of coupling at the center section. To realize these tight couplings, one has to choose Triplate stripline configuration. The impedance values available in the literature are not always suitable for a given Triplate stripline substrate configuration.
These hybrids are symmetric in nature, ie., coupling increases gradually from edge to center and reduces from center to edge. By properly tuning / optimizing these coupling values (for smooth transitions), it is possible to achieve acceptable amplitude and phase ripple. The transition of impedance at the central section is the most critical one and if the given impedances do not form a broadside coupling, this transition (usually cross-over) becomes asymmetric. It is possible to take the existing coupling data and 'force' the central section to become a broadside coupling and then optimize adjacent coupling values to improve overall response using modern EDA tools. In this article, such methodology is described using Agilent's Advanced Design System software. It is possible to generate correct layout (for fabrication) and compare circuit results with Electromagnetic simulation results. Quadrature hybrids are 4-port networks dividing input power equally between two output ports with 90deg phase difference, as shown in Figure 1.
1. A quadrature hybrid with 4-port network.
The amount of power coupled depends on the coupling coefficient, or on the even mode impedance Zoe of the coupler.
The coupling factor is defined as, k = (ρ-1)/ (ρ+1), where ρ = (Zoe) / (Zoo).
Zoe, Zoo and Z0 are related by, Zoe * Zoo = Z02 , where Z0 is the characteristic impedance.
For loose coupling values (typically below 15dB) and narrow bandwidths, an edge coupler, in microstrip configuration, is sufficient. However, for tighter couplings, the gap between the coupled lines becomes unrealistic and designers must use the offset type of coupling using Triplate configuration. For larger bandwidths, multiple sections are required, resulting in higher values of Zoe.
The theory and design of multiple coupled sections is well established and available in various articles . Cristal and Leo Young  provide tables for Zoe and Zoo values for variety of coupling, bandwidth and ripple values.
It is impossible to realize a 3-dB coupler directly, as Zoe values will be too large for practical realization. In this case, a cascaded configuration of two loose couplers (8.34dB each) is used to realize such couplers, as shown in Figure 2.
2. A cascaded configuration of two loose couplers.
For practical realization, there should be a cross over at the center section, as shown in Figure 2B. This can only be achieved by a Triplate offset coupling configuration. This configuration is well suited for mass production and also for integration with other passive components. 3dB Lange coupler is often used for integration with active circuits (such as mixers and amplifiers) and has limited band width. To remove unwanted parasitic effects of the offset coupler at the center section, a broadside coupler is recommended, as shown in Figure 3A. Figures 3B and 3C show cross sections of offset and broadside configurations.
3. Triplate stripline configurations.
The triplate configuration has one circuit card (normally very thin), on which the circuit is printed on either side, and two "dummy" cards. All of them are firmly fixed by a pair of ground plates, as shown in Figure 4. The proper combination of card thicknesses should be chosen to realize given Zoe values. Typical thickness combinations for the Rogers RT/Duriod substrate could be 25-5-25mil, 31-5-31mil, or 31-10-31mil. Choosing proper substrate combination to get broad side coupling (at the center section) is quite cumbersome and most of the times, it may not be possible to realize broadside coupling for a given substrate combination.
4. Triplate configuration with ground plates.
However, it is possible to get an optimum set of impedance values-with center section 'forced to be broadside' by using modern day EDA tools like Agilent-ADS. In this article, a general procedure to design such a multi section, multi octave 3dB hybrid coupler is described.
Design Method: Number of sections 'N' can be chosen for a given bandwidth and ripple from Ref  for 8.34dB coupling. With those impedances, for a given Triplate configuration, the center section may not always result in broadside coupling. Using Agilent-ADS, center section is forced to be a broadside coupler (SBCLIN) and the other sections are simulated and optimized as offset couplers (SOCLIN) as shown in Fig (5). Variable equations shown in the box make sure that the coupling reduces gradually from center to the edges.
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In this example, Rogers material with 31-5-31mil (B=67mil) combination is considered and the design is optimized to get a reasonably good performance (coupling -8.34dB) from 2-8GHz, as shown in Fig (6). In a similar way, it is possible to optimize for W and Wo parameters for any other combination of substrates.
Next step is to auto generate the layout from the above schematic. Keeping default port parameters in the schematic, the coupled sections will not be joined together, as shown in Fig (7A). The coupler sections should be symmetric along the gap parameter as shown. To achieve this, it is necessary to shift the ports considering widths & gaps of next / previous sections. Layout Fig (7B) shows the correct layout generated after using proper port transformations. The variable equations used to shift the ports of coupled sections are shown in Fig (8).