Why is the balanced noise figure worse than a single LNA?

In a balanced amplifier, the input signal passes through a 90-degree hybrid coupler before reaching the two identical LNAs. This passive coupler inevitably has some insertion loss, typically 0.2 to 0.4 dB. According to Friis' equation for cascaded noise, any loss located directly at the front end of a receiver adds dB-for-dB to the total system noise figure. Therefore, if the individual LNAs have a noise figure of 1.0 dB, and the input hybrid has 0.3 dB of loss, the total balanced noise figure is 1.3 dB. The combining hybrid at the output does not significantly degrade the noise figure because its loss is divided by the high gain of the preceding LNAs.

Do the noise sources from the two LNAs cancel out?

No, they do not cancel out. The thermal and active noise generated internally by LNA A is entirely uncorrelated with the noise generated by LNA B. When the signals from both LNAs meet at the output hybrid coupler, the desired signals (which are correlated and phase-shifted deliberately) sum coherently, resulting in a 3 dB power boost. The noise signals, being uncorrelated, sum non-coherently, also resulting in a 3 dB power boost. Because the signal and the noise both increase by 3 dB, the Signal-to-Noise Ratio (SNR) remains exactly the same. The combining process itself does not improve or degrade the noise figure; only the passive loss of the input coupler degrades it.

If the noise figure is worse, why use a balanced LNA?

Because optimizing a single transistor for minimum noise figure (Gamma Opt) almost never aligns with the impedance required for a good input match (Gamma In). A single LNA might have a great noise figure of 0.8 dB, but a terrible return loss of 5 dB, which will cause massive ripples when connected to a bandpass filter. A balanced topology solves this. Any reflected energy from the mismatched LNA inputs travels backward through the input 90-degree hybrid, ends up 180 degrees out of phase, and is absorbed by the isolation resistor. This provides a near-perfect 50-ohm input match (often better than 20 dB return loss) while allowing the transistors to be biased and matched exclusively for minimum noise. It trades a fraction of a dB of noise for absolute stability and perfect matching.

System Design

Balanced Noise Figure

An RF engineer designs an ultra-low-noise receiver. A single transistor LNA achieves a phenomenal 0.6 dB noise figure, but its input impedance is 15 ohms, causing a massive reflection that detunes the preceding pre-select filter. The engineer switches to a balanced amplifier topology: two identical 0.6 dB LNAs sandwiched between 90-degree hybrid couplers. The reflections are absorbed by the input hybrid's isolation resistor, providing a perfect 50-ohm match to the filter. However, the system noise figure is no longer 0.6 dB; it degrades to 0.9 dB. The noise generated by the two amplifiers does not cancel out (it is uncorrelated and sums evenly with the signal), but the 0.3 dB physical insertion loss of the input hybrid coupler adds directly to the system noise floor. In RF design, a balanced noise figure represents the exact price paid—usually 0.3 to 0.5 dB—to buy perfect return loss and unconditional stability.

Category: System Design

Equation: NF_sys = NF_LNA + IL_{hybrid_in}

Design Trade-off: Sacrifices absolute NF for perfect VSWR

Single vs. Balanced LNA Performance

Parameter	Single Ended LNA (Matched for NF)	Balanced LNA (Matched for NF)
Noise Figure (NF)	0.6 dB (Optimal)	0.9 dB (Degraded by input coupler IL)
Input Return Loss	5 to 8 dB (Poor)	>20 dB (Excellent, absorbed by resistor)
Output P1dB / IP3	Baseline	+3 dB higher than baseline
Stability	Prone to oscillation if source Z changes	Unconditionally stable under all source Z
Redundancy	None (Fails entirely if transistor dies)	Soft-fail (Drops 6dB gain if one amp dies)

Why the noise doesn't cancel:
Signal Power out = P_sig1 + P_sig2 = +3 dB (Coherent voltage addition)
Noise Power out = N₁ + N₂ = +3 dB (Uncorrelated power addition)
Because signal and noise both increase by 3 dB, the intrinsic SNR of the combined amplifiers is identical to a single amplifier.

System Noise Figure Calculation:
NF_total (dB) = IL_{input_coupler} (dB) + NF_amplifier (dB) + [IL_{output_coupler} (dB) / Gain_amplifier (Linear)]
Because the LNA gain is high (e.g., 20 dB), the loss of the output coupler is mathematically negligible. The input coupler loss dominates the degradation.

Common Questions

Frequently Asked Questions

Why is the NF worse than a single LNA?

Because the signal must pass through a physical 90-degree hybrid coupler before it reaches the active transistors. This passive coupler has insertion loss (typically 0.3 dB). According to Friis' cascaded noise equation, any loss placed before the first stage of gain adds dB-for-dB to the total system noise figure.

Do the noise sources cancel out?

No. The desired signals sum coherently in the output hybrid, yielding a 3 dB power boost. The noise generated internally by the two LNAs is uncorrelated (random). Uncorrelated noise sums non-coherently, which also results in a 3 dB power boost. The Signal-to-Noise Ratio (SNR) remains exactly the same. Combining does not improve NF.

If the NF is worse, why use it?

To fix the input impedance. A transistor tuned for its absolute minimum noise figure almost never has an input impedance of 50 ohms. If connected directly to a filter, the massive reflections will ruin the filter's passband ripple. The balanced topology absorbs these reflections in the input hybrid's isolation resistor, providing a perfect 50-ohm match while allowing the transistors to stay tuned for minimum noise.

Related Terms

← Asymmetric Doherty Balanced Return Loss →

Receiver Front End

Cascaded NF Calculator

Enter the insertion loss of your input hybrid and the noise figure of your LNA stages. Calculate the exact balanced system noise figure and see how component loss impacts your overall receiver sensitivity.

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