Reflection Attenuator

Overview

Wideband matched attenuator using a 3 dB 90° hybrid coupler with resistive terminations on the isolated ports. Provides excellent impedance match.

Topology

        Port 1 ┌──────────────┐ Port 3
   Input ──────┤              ├────── Output
               │   3dB 90°    │
               │    Hybrid    │
        Port 2 │   Coupler    │ Port 4
            ┌──┤              ├──┐
            │  └──────────────┘  │
           [Ri]                 [Ri]
            │                    │
           GND                  GND

Hybrid coupler:

  • Coupling factor: -3 dB (k = 0.7071 = 1/√2)

  • Phase shift: 90° between coupled ports

  • Ports 1-3 and 2-4 are isolated

Both termination resistors: Ri (equal value)

Principle of Operation

  1. Input signal enters Port 1

  2. Hybrid splits power equally between Ports 2 and 4 (with 90° phase difference)

  3. Resistors Ri reflect a portion of the power based on mismatch

  4. Reflected signals recombine at Port 3 with controlled attenuation

  5. Remaining power is absorbed in the resistors

Design Equations

L = 10^(-0.05 × Attenuation)

Ri = Z₀ × (1 - L) / (1 + L)

Constraint: Requires Zin = Zout = Z₀ (bilateral matched design).

Derivation

The S-parameter from Port 1 to Port 3 is:

S₂₁ = (1/√2) × e^(jπ/2) × Γ₂ + (1/√2) × e^(jπ/2) × Γ₄

where Γ = (Z₀ - Ri) / (Z₀ + Ri)

For equal resistors (Ri at Ports 2 and 4):

S₂₁ = (Z₀ - Ri) / (Z₀ + Ri) × e^(jπ/2)

|S₂₁| = |Z₀ - Ri| / (Z₀ + Ri)

Attenuation:

α = -20 × log₁₀(|S₂₁|) = -20 × log₁₀(|Z₀ - Ri| / (Z₀ + Ri))

Solving for Ri when Ri < Z₀:

10^(-0.05×α) = (Z₀ - Ri) / (Z₀ + Ri)

Ri = Z₀ × (1 - 10^(-0.05×α)) / (1 + 10^(-0.05×α))

Power Dissipation

Each resistor dissipates half of the total dissipated power:

Pdiss_total = Pin × (1 - 10^(-0.1 × Attenuation))

Pdiss_Ri = 0.5 × Pin × (1 - 10^(-0.1 × Attenuation))

Both resistors dissipate equal power.

Example: 10 dB, Z₀ = 50 Ω, Pin = 1 W

L = 10^(-0.05 × 10) = 10^(-0.5) ≈ 0.316

Ri = 50 × (1 - 0.316) / (1 + 0.316)
   = 50 × 0.684 / 1.316
   ≈ 26.0 Ω

Power dissipation:

Pdiss_total = 1 × (1 - 10^(-0.1 × 10))
            = 1 × (1 - 0.1)
            = 0.9 W

Pdiss_R1 = Pdiss_R2 = 0.45 W each

Resistor Values vs. Attenuation

Attenuation (dB)

Ri (Ω, Z₀=50Ω)

Pdiss per resistor (Pin=1W)

3

39.4

0.25 W

6

31.2

0.37 W

10

26.0

0.45 W

20

20.5

0.50 W

30

18.9

0.50 W

Observation: As attenuation increases, Ri approaches Z₀/2 ≈ 25Ω, and power dissipation approaches 50% in each resistor.

Advantages

  1. Very wideband: DC to >20 GHz (limited only by hybrid coupler)

  2. Excellent impedance match: Return loss >20 dB at all frequencies

  3. Less sensitive to tolerances: Slight resistor value errors cause minimal performance degradation

  4. High power handling: Limited by hybrid coupler, not resistors

Limitations

  1. Requires hybrid coupler:

    • Bulky at low frequencies (<100 MHz)

    • More expensive than resistor-only designs

    • Adds extra insertion loss

  2. Higher cost: Hybrid coupler more expensive than three resistors

  3. Matched at both: Cannot provide impedance transformation

References

[1] Doherty, W. E., & Joos, R. D. (1998). The PIN Diode Circuit Designer’s Handbook, Chapter 5: Reflection Attenuators. Microsemi Corp.

See Also