Analyzing different directional coupler types in terms of performance tradeoffs can simplify the specification process when choosing a coupler for a particular application. As last month's Part 1 of this two-part article showed, directional couplers can be designed and fabricated in both discrete and printed-circuit-board (PCB) forms as well as part of an integrated circuit (IC). This second part will show how to perform a tradeoff analysis of directional couplers, including evaluating criteria from specifications. For planar directional couplers, these criteria include cost versus manufacturing tolerances, cost versus thermal characteristics, cost versus reliability, cost versus loss, the integration index4,6 versus cost, the integration index versus tolerances, the size versus quality factor (Q), the size versus tolerances, size versus maximum power-handling capability, and bandwidth versus amplitude balance and the number of sections.

The principle tradeoff is among frequency range, insertion loss, and amplitude balance. Broadband quadrature hybrids are cascaded single section elements of various resonant frequencies. The quantity of sections is related to the required amplitude balance and bandwidth. In coupledline coupler design there is trade-off between bandwidth and amplitude balance. For narrowband (less than 10 percent), a coupler provides very low insertion loss (0.1 to 0.2 dB), but the amplitude balance will degrade rapidly away from center frequency. If an amplitude balance requirement is across a broader bandwidth, the number of sections should be increased, which leads to an increase in coupler size and package; coupler insertion losses also increase. Another key tradeoff is between coupling and insertion loss, with larger coupling values translating into larger insertion loss (Table 3).

In a coupled-line microstrip directional coupler, there is a key tradeoff between coupling and directivity. In such couplers, odd-mode oscillations propagate in air and dielectric substrate while even-mode oscillations propagate in the dielectric substrate only. This gives rise to the difference between propagation constants for odd and even modes, a difference that grows with increased coupling. Thus, the microstrip coupled-line directional coupler has a low directivity (10 to 15 dB), which drops even more as the coupling becomes weaker.

Size versus insertion loss is perhaps the most contradictory pair of coupler requirements. The parameter "integration quality" is characterized by volume V (in cubic inches or cubic centimeters), the minimum dissipated losses in the operating bandwidth, A0 (in decibels), the bandwidth (Δf/f0)100 percent, and the number of sections. The relationship between these controversial parameters is described by the integration index.4

Any final documentation for an optimized planar directional coupler should include the following:
1. the particular type of planar directional coupler;
2. the main performance parameters, including frequency range, bandwidth, coupling, directivity, isolation, impedance, return loss, insertion loss, maximum power-handling capability, relative phase difference between output signals, and phase and amplitude imbalance;
3. an outline drawing with physical dimensions;
4. the technology process used;
5. the type of packaging (package hymaterial, technology process, hermetic or non-hermetic, physical dimensions of housing);
6. the results of the tolerance analysis;
7. the results of the thermal analysis;
8. the reliability analysis results; and
9. the cost analysis.

Figure 7(a) shows a chainlike connection of ring directional couplers for power combining applications. The ballast terminations R3 connected to port 3 of each coupler and output termination connected to port 2 of the third coupler are equal to the input/output impedances of the couplers. For equal powers of the four oscillators, the normalized characteristic admittances of different segments of ring couplers4 are Y1 = Y2 = 1/(2)0.5 for the first coupler; Y1 = (2/3)0.5, Y2 = 1/(3)0.5 for the second coupler, and Y1 = (3)0.5/2, Y2 = 1/2 for the third coupler.

The main limitations of the conventional ring coupler are its limited bandwidth and the high impedance of ring segments required for large power-split ratios (weak coupling). The cascadable ring couplers Fig. 7(b)>, described in ref. 16 offer improvement in bandwidth, reduction in size, and the probability of weak coupling. But practical implementation of a cascadable ring coupler network requires several crossovers that cause undesirable coupling, mismatches, and other parasitic effects.

Ramified connections of branch couplers for different applications are shown in Fig. 8. The first two circuits are applicable for beam-forming networks for antenna arrays. Figure 8(a) illustrates the well-known Butler matrix,17 which consists of four twobranch hybrids, two 45-deg. phase shifters, and a crossover to produce four antenna pattern beams in different directions.

Figure 8(b) shows a switched beam-forming network (SBFN) for the directional/omnidirectional antenna.18,19 It includes connection of four two-branch couplers and a switched 0/180-deg. phase shifter. Four ports (5, 6, 7, and 8) of the hybrid matrix are connected to four antenna monopoles (A1, A2, A3, and A4, respectively), and the other four ports of the hybrid matrix (1, 2, 3, and 4) are connected to a transmit/ receive network. During omnidirectional transmit mode, the transmit signal passes through only one port (2) of the SBFN with the switched phase shifter in 180-deg. phase-shift state. The antenna provides an omnidirectional pattern because the four monopoles are activated with equal magnitudes and progressive 90-deg. phase shift. The directional transmit mode is implemented by the alternative activation of a single port, 1, 2, 3, or 4, of the SBFN while the switched phase shifter provides a 0-deg. phase shift. During receive directional mode, all four SBFN ports are monitored.

Power combining of four oscillators can be realized by the network displayed in Fig. 8(c).4 In the ideal case, the combined power appears only on port 3 of each coupler, while port 4 is isolated. In a practical case, an unbalanced signal appears on port 4. Due to the specially introduced mismatching element (a short- or opencircuit segment of adjustable length), the unbalanced signal is reflected from the end of the mismatched element and travels into the two oscillators for mutual synchronization.

Figure 8(d) shows a conventional balanced network including divider H1, combiner H2, two identical devices I and II (amplifiers, phase shifters, or modulators), and two resistors R1 and R2. The input splitter H1 divides the input power equally between the output ports. The output combiner H2 recombines the output signals from devices I and II.

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A planar coupled-line directional coupler with tight coupling is difficult to realize because the small gap between coupled lines is difficult to etch. In Fig. 9, a direct port 3 and coupled port 2 of the left directional coupler are connected to input port 1 and isolated port 4 of the right directional coupler.4 A 3-dB directional coupler can be realized by this tandem connection of two directional couplers with coupling of 8.34 dB. The relationship between the tandem network coupling, C12, and coupling C012 of one directional coupler for n cascades can be found from Table 4. The results make it possible to choose the number of cascades and coupling of every directional coupler for a specified total coupling.

A dual directional coupler Fig. 9(b)> includes two directional couplers that are connected back-toback in series with a single main line and two independent secondary lines. The main application for a dual directional coupler is in monitoring signals simultaneously in both forward and reverse directions. The dual directional coupler provides precise samples of both the transmit power level to an antenna (by means of coupler I) and the transmit power that is reflected from the antenna (by means of coupler II), as shown by Fig. 9(b).

REFERENCES
16. K. S. Ang, Y. C. Leong, and C. H. Lee, "A New Class of Multisection 1800 Hybrids Based on Cascadable Hybrid_Ring Couplers," IEEE Transactions on Microwave Theory & Techniques" Vol. 50, No. 9, September 2002, pp. 2147-2152.

17. J. Butler and R. Lowe, "Beam Forming Matrix Simplifies Design of Electronically Scanned Antennas," Electronic Design, April 12, 1961, pp. 170-173.

18. L. G. Maloratsky et al., "Aircraft Directional/Omnidirectional Antenna Arrangement," United States Patent No. 7,385,560, June 10, 2008.

19. L. G. Maloratsky, "Switched Directional/Omnidirectional Antenna Module for Amplitude Monopulse System," IEEE Antenna Magazine, 2008.