Why does microstrip coupling produce unequal even/odd mode velocities?

In microstrip, the electric field distribution differs between even and odd modes. The even mode has more field in the substrate (higher effective dielectric constant), while the odd mode has more field in the air between the coupled lines (lower effective dielectric constant). This velocity difference means the even and odd mode waves arrive at the coupled port at different times, degrading directivity and causing the coupling to vary with frequency. In stripline (symmetric), both modes travel at the same velocity, giving ideal performance. The Lange coupler partially compensates by using interdigitated fingers that equalize the mode velocities.

What coupling values can backward wave couplers achieve?

Standard edge-coupled microstrip: -6 to -20 dB coupling (limited by minimum gap spacing, typically 3-4 mil). Broadside-coupled stripline: -3 to -20 dB. Lange coupler (interdigitated): -3 dB (quadrature hybrid), the tightest practical coupling for planar structures. For couplings tighter than -3 dB, tandem configurations (two couplers in cascade) are used. The coupling is set by the even and odd mode impedances: C = (Z0e - Z0o) / (Z0e + Z0o), where Z0e and Z0o are the even and odd mode characteristic impedances of the coupled lines.

Passive Components

Backward Wave Coupler

Q: What is the difference between backward and forward wave couplers?

In a backward wave coupler, the coupled port is at the same end as the input port (contra-directional coupling). The coupled wave travels backward relative to the input wave. In a forward wave coupler, the coupled port is at the opposite end from the input (co-directional coupling). Most microstrip and stripline coupled-line couplers are backward-wave because TEM mode coupling is inherently contra-directional. Waveguide multi-hole couplers can be either type depending on hole spacing. The Lange coupler and branch-line coupler are backward-wave devices. The Bethe-hole coupler is a forward-wave device.

/bak-werd wayv kup-ler/ (contra-directional)

A Backward Wave Coupler is a directional coupler where the coupled port is at the same end as the input port, meaning the coupled electromagnetic wave propagates contra-directionally (backward) relative to the main through-line wave. Most microstrip and stripline coupled-line couplers, including the Lange coupler and branch-line hybrid, are backward-wave devices. The coupling coefficient is determined by the even and odd mode impedances of the coupled lines.

Category: Passive Components

Coupling: -3 to -20 dB

Length: λ/4 (center freq)

Understanding Backward Wave Couplers

When two parallel transmission lines are placed close together, electromagnetic coupling occurs between them. In TEM (transverse electromagnetic) mode structures like microstrip and stripline, this coupling is inherently contra-directional: the coupled energy propagates backward along the secondary line. The coupling strength depends on the gap between the lines, the line width, the substrate properties, and the coupling length (typically quarter-wave at center frequency).

Coupling Theory

Backward Wave Coupler:
A Backward Wave Coupler is a directional coupler where the coupled port is at the same end as the input port, meaning the coupled electromagnetic...

Key specifications:
-20 dB | -40 dB | 4 a | -15 dB | -30 %

Wave: ∇²E + k²E = 0

Backward Wave Coupler Types

Coupler Type	Coupling	Directivity	Bandwidth	Technology
Edge-coupled microstrip	-6 to -20 dB	10-15 dB	20-30%	PCB
Broadside stripline	-3 to -20 dB	30-40 dB	25-40%	Multilayer PCB
Lange coupler	-3 dB (hybrid)	15-25 dB	Octave	MMIC, thin-film
Branch-line hybrid	-3 dB (90°)	20-30 dB	10-20%	PCB, waveguide
Tandem coupler	-3 to -1 dB	20-30 dB	Octave+	Cascaded pair

Key Equations

Insertion loss:
IL = −20log|S₂₁| dB

Return loss:
RL = −20log|S₁₁| dB

VSWR from Γ:
VSWR = (1+|Γ|)/(1−|Γ|)

Comparison

Aspect	Backward Wave Coupler Spec	Typical Range	Impact	Design Note
Primary function	Most microstrip and stripline coupled-li...	Application-dep.	Critical	Verify in sim
Operating range	The coupling coefficient is determined b...	Application-dep.	Critical	Verify in sim
Performance	Understanding Backward Wave Couplers Whe...	Application-dep.	Critical	Verify in sim
Integration	In TEM (transverse electromagnetic) mode...	Application-dep.	Critical	Verify in sim
Trade-off	The coupling strength depends on the gap...	Application-dep.	Critical	Verify in sim

Common Questions

Frequently Asked Questions

Backward vs. forward wave coupler?

Backward: coupled port at same end as input (contra-directional). Forward: coupled port at opposite end (co-directional). Microstrip/stripline couplers are backward-wave (TEM coupling is inherently contra-directional). Waveguide multi-hole couplers can be either type. Lange coupler = backward. Bethe-hole coupler = forward.

Why does microstrip have poor directivity?

Even and odd modes have different velocities in microstrip (different effective dielectric constants). Waves arrive at the coupled port at different times, degrading directivity to 10-15 dB. Stripline has equal mode velocities (symmetric structure), giving 30-40 dB directivity. Lange couplers partially compensate with interdigitated fingers.

What coupling values are achievable?

Edge-coupled microstrip: -6 to -20 dB (limited by minimum gap). Broadside stripline: -3 to -20 dB. Lange: -3 dB (tightest practical planar coupling). For tighter than -3 dB, use tandem configurations. Coupling set by C = (Z0e - Z0o)/(Z0e + Z0o).

Related Terms

← Backward Wave BWO →