RF Electronics Chapter4: Transmission Line Transformers and Hybrids Page 86
2022, C. J. Kikkert, James Cook University, ISBN 978-0-6486803-9-0.
It is possible to produce a wider bandwidth Branchline coupler, by having two loops
together as shown in figures 4.35 and 4.36. For a 3 dB double loop Branchline coupler
the characteristic impedances of the lines are given by equations 4.19 and 4.20 [8]:
�
�
�
�� �
√
2� Eqn. 4.19
�
�
√
2
�
�
/
�
Eqn. 4.20
Using these equations and optimising the double loop Branchline coupler for the lowest
phase difference from 90 degrees results in Z
1
= Z
3
=50/2=35.35 Ω. The resulting circuit
and its layout for a RO4003 RF PCB substrate is shown in figures 4.35 and 4.36.
Figure 4.35. Double Branchline coupler schematic.
Figure 4.36. Double loop Branchline coupler PCB layout.
Using TXLine, for a RO4003 RF PCB substrate with a 0.8128 mm thickness at 1 GHz,
the 120.7 transmission lines require 0.27 mm wide tracks, which is close to the smallest
track width that can be realised. The track width are so small that warnings are generated
for the MTEEX sections connecting to them, as W3/W2 being too small for the model.
The quarter wavelength long track for the Z1=Z3=35.36 impedance is 41.98 mm long,
while the corresponding length for the Z3=120.7 track is 45.77 mm long. For straight
lines, all three vertical lines should be the same length. This, together with the resistive
losses in the 0.27mm wide tracks limits the isolation that can be obtained and the best line
length must be obtained by optimisation. The resulting performance of the double loop
Microstrip Branchline coupler is shown in figure 4.37.
RF Electronics: Design and Simulation
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