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RF Electronics Chapter4: Transmission Line Transformers and Hybrids Page 88 2022, C. J. Kikkert, James Cook University, ISBN 978-0-6486803-9-0. Figure 4.39. Ideal Multi-loop Quadrature hybrid phase response. Figure 4.38 shows that for less than 0.5 variation in phase from 90 the single loop Branchline coupler has a bandwidth of 14.76%, the double loop Branchline coupler has a bandwidth of 28.8% and the triple loop Branchline coupler has a bandwidth of 44.56%. For a 1dB difference in S21 and S31 amplitudes, the single loop Branchline coupler has a bandwidth of 27.2% MHz, the double loop Branchline coupler has a bandwidth of 31.8% and the triple loop Branchline coupler has a bandwidth of 34.8%. Branchline couplers can thus be used to provide the I and Q signals, required for image suppressing mixers, with good phase and amplitude accuracy over a >20% bandwidth. Backward Travelling Wave Hybrid If two lines are in close proximity, then there is coupling between the lines. The amount of coupling depends on the spacing between the lines. Consider the two Microstrip coupled lines as shown in figures 4.41 and 4.42. The maximum coupling will occur when the coupled lines are a quarter wavelength long. The resulting coupling is related to the even and odd mode impedances by: C C Z Z OE 1 1 0 Even mode impedance. Eqn. 4.21 C C Z Z OO 1 1 0 Odd mode impedance. Eqn. 4.22 Where C is the voltage at the coupled output relative to the input, Z OO is the odd mode impedance, where the two lines of the transmission line are of opposite polarity, so that most of the field is between the conductors. Z OE is the even mode impedance, where both the lines are at the same potential, so that most of the field is between the conductors and the ground-plane. Edge-Coupled Lines Edge-coupled lines are Microstrip lines that are placed in parallel with each other, with a small spacing (S), as shown in the figures 4.41, 4.42, 4.45 and 4.46. The coupled lines are RF Electronics: Design and Simulation 88 www.cadence.com/go/awr

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