S
Seed account
A 3 dB branchline (quadrature) hybrid splits power equally with 90 deg phase difference and is the workhorse for balanced amplifiers, image-reject mixers and reflection phase shifters. On microstrip the equations are simple; the layout is where isolation dies.
1. Ideal even/odd design
For a 3 dB hybrid at characteristic impedance Z0:
- Series arms: Z0 (usually 50 ohm)
- Shunt (branch) arms: Z0/sqrt(2) ~ 35.4 ohm
- Each arm electrical length: 90 deg at f0
Even-mode analysis puts open stubs of length 90 deg on the series lines; odd-mode puts shorts. The superposition gives S21 = S31 = -3 dB at 90 deg and S11 = S41 = 0 at center.
2. Microstrip numbers at 2.45 GHz on FR4 (er~4.4, h=1.6 mm)
50 ohm width ~ 3.0 mm; 35.4 ohm width ~ 5.0 mm. Quarter-wave physical length is about 16.5 mm after effective-er correction (er_eff ~ 3.4 for 50 ohm). Use your stackup calculator, not these round numbers, for the final Gerber.
3. Bandwidth reality
A single-section branchline has useful amplitude balance (|S21|-|S31| within 0.5 dB) over roughly ±10% of f0, and return loss / isolation better than 15 dB over a similar window. Outside that, the 90 deg condition fails fast. For octave coverage you need multi-section or tandem designs, or a Lange coupler if you can do tight gaps and wire bonds / bridges.
4. Layout mistakes that kill isolation
- T-junction parasitics: the four junctions add shunt C. Compensate by shortening each arm a few degrees (often 5 to 10 deg) or mitering. Without compensation, f0 shifts down and S41 degrades.
- Unequal meanders: if one path is lengthened to fit the board, the 90 deg relation breaks. Keep both through-paths equal.
- Ground vias under the junction: a sparse via fence lets return current wander; put vias within ~lambda/20 of the junctions.
- Coupling between opposite branches: on dense boards the two 35 ohm arms can see each other; keep clearance or put a ground strip between them.
5. Quick verification
Simulate or measure:
- |S21| and |S31| at f0 (target -3.0 ± 0.3 dB)
- ang(S21)-ang(S31) (target 90 ± 5 deg)
- |S11| and |S41| (target < -20 dB at f0)
- Balance over the band you care about, not only at one marker
6. When to pick something else
Need tighter amplitude balance over >20% bandwidth: Lange or multi-section. Need high power on softboard: watch the narrow 35 ohm line current density. Need a rat-race instead for 0/180: different topology, same discipline about junction compensation.
Design the ideal even/odd first, then spend the time on junctions and via fencing. That order saves the most board spins.
1. Ideal even/odd design
For a 3 dB hybrid at characteristic impedance Z0:
- Series arms: Z0 (usually 50 ohm)
- Shunt (branch) arms: Z0/sqrt(2) ~ 35.4 ohm
- Each arm electrical length: 90 deg at f0
Even-mode analysis puts open stubs of length 90 deg on the series lines; odd-mode puts shorts. The superposition gives S21 = S31 = -3 dB at 90 deg and S11 = S41 = 0 at center.
2. Microstrip numbers at 2.45 GHz on FR4 (er~4.4, h=1.6 mm)
50 ohm width ~ 3.0 mm; 35.4 ohm width ~ 5.0 mm. Quarter-wave physical length is about 16.5 mm after effective-er correction (er_eff ~ 3.4 for 50 ohm). Use your stackup calculator, not these round numbers, for the final Gerber.
3. Bandwidth reality
A single-section branchline has useful amplitude balance (|S21|-|S31| within 0.5 dB) over roughly ±10% of f0, and return loss / isolation better than 15 dB over a similar window. Outside that, the 90 deg condition fails fast. For octave coverage you need multi-section or tandem designs, or a Lange coupler if you can do tight gaps and wire bonds / bridges.
4. Layout mistakes that kill isolation
- T-junction parasitics: the four junctions add shunt C. Compensate by shortening each arm a few degrees (often 5 to 10 deg) or mitering. Without compensation, f0 shifts down and S41 degrades.
- Unequal meanders: if one path is lengthened to fit the board, the 90 deg relation breaks. Keep both through-paths equal.
- Ground vias under the junction: a sparse via fence lets return current wander; put vias within ~lambda/20 of the junctions.
- Coupling between opposite branches: on dense boards the two 35 ohm arms can see each other; keep clearance or put a ground strip between them.
5. Quick verification
Simulate or measure:
- |S21| and |S31| at f0 (target -3.0 ± 0.3 dB)
- ang(S21)-ang(S31) (target 90 ± 5 deg)
- |S11| and |S41| (target < -20 dB at f0)
- Balance over the band you care about, not only at one marker
6. When to pick something else
Need tighter amplitude balance over >20% bandwidth: Lange or multi-section. Need high power on softboard: watch the narrow 35 ohm line current density. Need a rat-race instead for 0/180: different topology, same discipline about junction compensation.
Design the ideal even/odd first, then spend the time on junctions and via fencing. That order saves the most board spins.