Power, Linearity, and Distortion Practical Power Topics Informational

What is the Wilkinson combiner efficiency when combining amplifiers with different output power levels?

The Wilkinson combiner efficiency when combining amplifiers with different output power levels is reduced because the power difference between the two inputs creates a mismatch that dissipates energy in the isolation resistor. For a 2-way Wilkinson combiner: when both inputs have equal power and phase: 100% of the input power appears at the output (minus the combiner's insertion loss). When the inputs have unequal power (P1 ≠ P2): the output power is P_out = (sqrt(P1) + sqrt(P2))^2 / 4 (assuming in-phase signals), and the power dissipated in the isolation resistor is P_iso = (sqrt(P1) - sqrt(P2))^2 / 4, and the combining efficiency is eta = P_out / (P1 + P2) = ((sqrt(P1) + sqrt(P2))^2) / (4 x (P1 + P2)). For P1 = P2: eta = 100% (ideal). For P1 = 2 x P2: eta = (sqrt(2) + 1)^2 / (4 x 3) = 5.83/12 = 97.1%. For P1 = 10 x P2: eta = (sqrt(10) + 1)^2 / (4 x 11) = 16.32/44 = 82.5%. For P1 = 100 x P2: eta = (10 + 1)^2 / (4 x 101) = 121/404 = 30.0%. The key insight: moderate power imbalance (up to 2:1 or 3 dB difference) has minimal impact on efficiency (less than 3% loss). But large power imbalance (10:1 or greater) significantly degrades the efficiency because most of the weaker signal is dissipated in the isolation resistor.

Category: Power, Linearity, and Distortion

Updated: April 2026

Product Tie-In: Power Amplifiers, Combiners, Loads

Wilkinson Combiner Power Balance

Understanding the Wilkinson combiner's behavior with unequal inputs is important for: designing systems where PAs have different output powers, analyzing the impact of PA failure or gain variation, and optimizing the power distribution in adaptive transmitters.

Practical Implications

PA gain variation: In production, PAs have ±1-2 dB gain variation. A 2 dB gain difference (P1 = 1.58×P2): combining efficiency = 99.6%. The impact is negligible
Failed PA: If one PA fails completely (P2 = 0): efficiency = P1/(4×P1) = 25%. Only 25% of the remaining PA's power reaches the output; the other 75% is split between the failed port (reflected) and the isolation resistor. This is why high-isolation combiners are important for graceful degradation

Wilkinson Balance Parameters

2-way Wilkinson combining efficiency:
η = (√P₁ + √P₂)² / (4×(P₁+P₂))
For P₁=P₂: η = (2√P)²/(8P) = 4P/8P×4 → 100%
For P₁=2P₂: η = (√2+1)²/(4×3) = 5.83/12 = 97.1%
Power to isolation resistor: P_iso = (√P₁ - √P₂)²/4
For P₁=10W, P₂=5W: P_iso = (3.16-2.24)²/4 = 0.21W

Common Questions

Frequently Asked Questions

Does phase imbalance also cause loss?

Yes. Phase imbalance between the two inputs also reduces the combining efficiency: P_out = P1 + P2 + 2×sqrt(P1×P2)×cos(delta_phi). For equal-power inputs with phase error: P_out = 2P × (1 + cos(delta_phi)) / 2 = P × (1 + cos(delta_phi)). Efficiency: eta = (1 + cos(delta_phi)) / 2. For delta_phi = 10 degrees: eta = 98.5%. For delta_phi = 30 degrees: eta = 93.3%. For delta_phi = 90 degrees: eta = 50%. Combined amplitude and phase imbalance: both effects add, further reducing the efficiency.

How do I handle large power imbalance?

If the PAs intentionally produce different power levels: use an unequal-split combiner (known as an asymmetric Wilkinson or a tapered line combiner). The unequal combiner has different impedance arms designed to match the different PA impedances and combine unequal powers with high efficiency. For example: a 2:1 power ratio combiner has: port 1 impedance = 50×sqrt(3) = 86.6 ohms, port 2 impedance = 50/sqrt(3) = 28.9 ohms, and achieves 100% combining efficiency for the designed power ratio.

What about N-way combining with unequal PAs?

In an N-way binary Wilkinson combiner (cascaded 2-way stages): each 2-way stage independently combines its two inputs. If all PAs produce equal power: uniform efficiency at each stage. If some PAs produce different power: the efficiency loss accumulates through the combining tree. For best efficiency: pair PAs with the closest output powers at the first combining level (so each 2-way combiner sees the smallest imbalance). This minimizes the power dissipated in the isolation resistors.

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