Transmission Line and Lumped Element Quadrature Couplers

By Gary Breed Editorial Director

uadrature cou- This month’s tutorial article plers are used for reviews the basic design Qpower division and operation of power and combining in circuits divider/combiners with where the 90º phase shift ports that have a 90- between the two coupled degree phase difference ports will result in a desirable performance characteristic. Common uses of quadrature couplers include: Antenna feed systems—The combination of power division/combining and 90º phase shift can simplify the feed network of phased array antenna systems, compared to alternative net- Figure 1 · The branch line quadrature works using delay lines, other types of com- hybrid, implemented using λ/4 transmission biners and impedance matching networks. It line sections. is especially useful for feeding circularly polarized arrays. Test and measurement systems—The phase each module has active devices in push-pull shift performance performance may be suffi- (180º combined), both even- and odd-order ciently accurate for phase comparisons over a harmonics can be reduced, which simplifies substantial fraction of an octave. A less critical output filtering. use is to resolve phase ambiguity in test cir- In an earlier tutorial [1], I introduced a cuits. A number of measurement techniques range of 90º coupler types without much anal- have a discontinuity at 180º—as this value is ysis. In this article, we focus on the two main approached, a 90º phase “rotation” moves the coupler types—the branch-line and coupled- system away from that point. line hybrids—in both their transmission line Image-reject mixers—Two signal paths, and lumped element implementations. using two mixers with quadrature LO signals The term “hybrid” comes from the tele- and quadrature combining will mathematical- phone wireline tradition, and refers to the ly cancel either the sum or difference term of presence of a port where there is a complete the output. In practice, the unwanted mixing cancellation of the signal when the circuit is product can be reduced by 30 to 50 dB, perfectly balanced—with equal amplitudes depending on the operating frequency, band- and accurate phases at all ports. width and level of precision. Power amplifier combiners—Combining The Branch-Line Hybrid Coupler power amplifier modules in quadrature sup- Figure 1 shows the branch line quadrature presses the third harmonic output, as well as hybrid, composed of four λ/4 transmission some odd-order intermodulation products. If lines. Two lines have a characteristic

44 High Frequency Electronics High Frequency Design QUADRATURE COUPLERS

Figure 2 · Replacement of trans- Figure 3 · The circuit of Figure 2, Figure 4 · The coupled-line hybrid mission lines with lumped element simplified by combining capacitors provides quadrature coupling in a equivalent lowpass circuits. at branch junctions. relatively compact physical size.

impedance of Z0, and two have an Lumped Element Implementation es unity—as is the case when they √ λ impedance of Z0/ 2. For a 50-ohm The branch line hybrid can be are /4 in length—the through and system, these lines will be 50 ohms implemented using lumped element coupled ports have equal 3 dB power and 70.7 ohms. The transmission circuits that are equivalent to the λ/4 division and a 90 degree phase differ- lines may be coaxial, stripline or transmission line sections. Figure 2 ence. The coupled line hybrid has the microstrip; whichever is a good fit for shows this implementation with the primary advantage of compact size, the frequency range and construction line sections replaced by equivalent since the line sections must be adja- method. lowpass π-networks. This circuit is cent to one another for near-perfect This coupler has four ports: a com- further simplified in Figure 3 by com- coupling. mon port, an isolated port, and two bining the two shunt capacitors at [Note: This circuit is a directional coupled ports with a 90-degree phase the network junctions into a single coupler. When coupling is less than difference. When all ports are termi- component. unity due to increased line spacing, nated with Z0, the isolated port load The lumped-element equivalents line impedance differences, and/or will dissipate no power, and the cou- of the transmission line sections can line lengths less than λ/4, the coupled pled ports will have identical power take the form of lowpass or highpass port will receive less of the incident levels. The coupler structure is bilat- networks, depending on the design- signal. Such directional couplers are eral and may be used equally well as er’s preference. The passband charac- normally specified by the magnitude a power divider or power combiner. teristics of the network can be useful difference between the coupled and The signal path through the cou- in reducing filtering requirements through ports, e.g., a “10 dB coupler” pler is straightforward. A signal elsewhere in the system. or “20 dB coupler.”] applied to the common port has two The lumped element design has a In microstrip circuits, the result- paths to the isolated port, of λ/4 and narrower bandwidth than the trans- ing edge-coupled lines may not 3λ/4, with the λ/2 delay difference mission line coupler. This is often an achieve sufficient coupling. A more (180 degree phase difference) effec- acceptable tradeoff, especially at fre- complex arrangement, the Lange tively cancelling one another. quencies where the physical length of Coupler, with multiple interlaced The useful bandwidth of the the transmission line segments is “fingers” as the line sections is some- branch line hybrid depends on the problematic. This is typically consid- times used. Stripline techniques may degree of amplitude and phase accu- ered an issue at lower frequencies, also be used; with the lines on adja- racy required by the application. but it also applies to very small cir- cent layers, their width (not edges) Generally, it is considered to have a cuits such as MMICs. provides the necessary coupling. bandwidth of 10 to 20 percent, although the bandwidth can be read- The Coupled-Line Hybrid Lumped Element Implementation ily extended through the use of cas- The coupled line hybrid shown in Like the branch line hybrid, the caded coupler sections. A two-section Figure 4 is another well-known coupled line hybrid may also be coupler has a bandwidth of approxi- design. When the mutual coupling implemented in lumped element mately half-octave. between the parallel lines approach- form. The equivalent circuit is shown

46 High Frequency Electronics High Frequency Design QUADRATURE COUPELRS

Common Through C/2 C/2

Isolated Coupled Z 1 Z = √ L/C 0 0 L = π C = π 2 f3dB 2 f3dB·Z0

Figure 5 · Lumped element equivalent circuit, replac- Figure 6 · This is the most common implementation of ing transmission line sections with L-C sections. The pri- a lumped element coupled-line hybrid, with both mary difficulty in implementation is the need for two inductors wound on a single magnetic core and end separate inductors with mutual coupling of unity. capacitors combined into single components. in Figure 5. In this simplified form, it this hybrid achieves amplitude bal- C/2 = 159 pF is not realizable, since the two ance of approximately ±0.5 dB over a branches must be coupled with near- bandwidth of f0 ±10%. Amplitude These are very practical values unity mutual coupling. dominates the total error; the rela- for a low frequency circuit. The induc- The typical implementation is tive magnitude of the phase error is tor can be achieved using a twisted shown in Figure 6, where the two much smaller. pair or parallel bonded wires, with a inductors are implemented as paral- Also note that the actual values of winding of 14 turns on a T37-2 core lel or twisted-pair windings on a the end capacitors are C/2, since (0.375 inch dia., µ = 10). magnetic core. The magnetic core is a these components are the series com- Winding these inductors is a sim- reliable method for achieving maxi- bination of two capacitors (see Fig. 5), ple task in the lab. In production, mum magnetic flux required for near- each having a value of C. smaller diameter wire and a smaller unity mutual coupling. However, Using the design equations magnetic core allows the construction various parallel-wire inductor wind- included in Fig. 6, a particular hybrid of extremely compact networks. With ings with air dielectric or a non-mag- can be developed. For example, with a the capability for such small size, it is netic supporting core may be accept- design frequency (f3dB, commonly easy to appreciate the popularity of able, usually resulting in narrower given as f0) of 100 MHz and Z0 of 50 this lumped element hybrid. bandwidth. The end capacitors are ohms: nearly always combined into single References components, as was done with the L = 50 / (2π·108) = 79.6 nH 1. G. Breed, “Classic Designs for branch line hybrid. Lumped Element and Transmission In the final design of Figure 6, the C = 1 / (2π·108)· 50 = 31.8 pF Line 90-Degree Couplers,” High values for L and C are derived from a Frequency Electronics, Sep. 2007. classic equivalent circuit for a 90- C/2 = 15.9 pF 2. A. Grebennikov, “Power degree transmission line section. This Combiners, Impedance Transformers may be more familiar to some readers The 79.6 nH inductor can be real- and Directional Couplers: Part III,” as a π-network, often used for ized using a twisted pair of small- High Frequency Electronics,Feb. impedance matching. In this case, diameter wires, wound on a low per- 2008. there is no impedance transforma- meability iron powder core, such as 3. J. Walker, D. Myer, F. Raab, C. tion, but the network has the same eight turns on a T25-12 core (0.25 Trask, Classic Works in RF Engin- 90-degree phase shift as a λ/4 trans- inch dia., µ = 4). eering: Combiners, Couplers, Trans- mission line. Other readers may best Scaling the hybrid to a much formers, and Magnetic Materials, understand this equivalent circuit as lower frequency of 10 MHz, results in Artech House, 2006, Ch. 6. being derived from a lowpass filter, values of: 4. A. Grebennikov, RF and which is also a valid approach. Microwave Power Amplifier Design, The lumped element version of L = 796 nH McGraw-Hill, 2005, Ch. 5.

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