L
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A rat-race (ring hybrid) gives sum and difference ports with nominally 0° / 180° splits. It is the planar cousin of a magic tee and shows up in balanced mixers, monopulse and push-pull PA drivers. The ring looks simple; the port phasing and isolation are what fail first.
1. Topology
Four ports on a closed ring. Classic design: three arcs of lambda/4 and one arc of 3*lambda/4, all at Z = sqrt(2)*Z0 ≈ 70.7 ohm for Z0=50. Opposite ports are isolated when the even/odd path lengths cancel.
2. Design sequence
1) Pick f0 and Z0.
2) Set ring impedance Zr = Z0*sqrt(2).
3) Place ports at 0, 90, 180, 270 deg electrical around a 1.5 lambda circumference (the long arc is the 270 deg path between one adjacent pair).
4) Translate electrical length to physical length with your microstrip beta(f), including the T-junction discontinuity.
5) Add a short taper or stepped width if Zr is awkward on your stackup.
3. Layout traps
- T-junction parasitics shift phase; compensate by shortening each arc a few degrees after EM.
- Ground via fences near the ring reduce radiation but can detune if too close to the inner edge.
- Bends: preferential use of mitered corners; chamfer errors show up as amplitude imbalance before S11 looks bad.
- Isolation (S41 class paths) is more sensitive to length error than the matched split.
4. Bandwidth reality
A textbook rat-race is narrowband relative to a branchline for the same process. Expect useful isolation and phase flatness over roughly 10 to 20% depending on substrate and junction modeling. If you need octave coverage, look at coupled-line or multi-section hybrids.
5. Verification
- |S21| and |S31| within 0.5 dB of each other at f0
- Phase difference 0° or 180° ±5° on the intended sum/diff pair
- Isolation >20 dB on the isolated port across your IF or LO band
- Re-sim with er ±0.2 and etch ±10 um
6. When not to use it
Need a tight 90° split → branchline or Lange. Need a broadband 180° → consider Marchand balun or active polyphase. Need high power with a discrete isolation resistor → Wilkinson (different job).
Draw the phase paths on paper before you draw copper. Most first-pass rings fail isolation, not matching.
1. Topology
Four ports on a closed ring. Classic design: three arcs of lambda/4 and one arc of 3*lambda/4, all at Z = sqrt(2)*Z0 ≈ 70.7 ohm for Z0=50. Opposite ports are isolated when the even/odd path lengths cancel.
2. Design sequence
1) Pick f0 and Z0.
2) Set ring impedance Zr = Z0*sqrt(2).
3) Place ports at 0, 90, 180, 270 deg electrical around a 1.5 lambda circumference (the long arc is the 270 deg path between one adjacent pair).
4) Translate electrical length to physical length with your microstrip beta(f), including the T-junction discontinuity.
5) Add a short taper or stepped width if Zr is awkward on your stackup.
3. Layout traps
- T-junction parasitics shift phase; compensate by shortening each arc a few degrees after EM.
- Ground via fences near the ring reduce radiation but can detune if too close to the inner edge.
- Bends: preferential use of mitered corners; chamfer errors show up as amplitude imbalance before S11 looks bad.
- Isolation (S41 class paths) is more sensitive to length error than the matched split.
4. Bandwidth reality
A textbook rat-race is narrowband relative to a branchline for the same process. Expect useful isolation and phase flatness over roughly 10 to 20% depending on substrate and junction modeling. If you need octave coverage, look at coupled-line or multi-section hybrids.
5. Verification
- |S21| and |S31| within 0.5 dB of each other at f0
- Phase difference 0° or 180° ±5° on the intended sum/diff pair
- Isolation >20 dB on the isolated port across your IF or LO band
- Re-sim with er ±0.2 and etch ±10 um
6. When not to use it
Need a tight 90° split → branchline or Lange. Need a broadband 180° → consider Marchand balun or active polyphase. Need high power with a discrete isolation resistor → Wilkinson (different job).
Draw the phase paths on paper before you draw copper. Most first-pass rings fail isolation, not matching.