1. Introduction — The First Amplifier Sets the Noise Floor

The low-noise amplifier (LNA) sits at the front of every receiver, immediately after the antenna and filter. Its job: amplify the weak RF signal enough that the following mixer and ADC do not drown in their own noise, while adding as little noise as possible and remaining stable and linear over the operating range. The first block’s noise figure (NF) dominates the whole chain’s noise figure by the Friis equation, so the LNA design is the single most important block in receiver sensitivity. This guide covers noise figure and the cascaded-noise mathematics, the gain/stability trade (even K-factor and stability circles), input and output matching (S-parameters, conjugate vs noise matching), the best-practice schematic for a discrete bipolar or FET LNA, biasing, the LC matching and biasing network for a 2.4 GHz example, layout rules, and the classic LNA failure modes. It complements the RF impedance matching and antenna guides on this site.

2. Noise Figure and the Friis Equation

The noise figure is the ratio (in dB) of the SNR at the output to the SNR at the input, for a standard 290 K source: NF = SNR_in − SNR_out. The noise factor F = 1 + T_noise/290. A receiver chain’s total noise factor is:

F_total = F1 + (F2 − 1)/G1 + (F3 − 1)/(G1·G2) + …

The implication is sharp: the first stage’s noise (F1) enters untamed, while the later stages’ noise is divided by the LNA’s gain G1. A 3 dB NF LNA with 15 dB gain suppresses the mixer’s noise by 15 dB — which is why improving the LNA is worth so much more than improving the mixer. Only when G1 is high (>15–20 dB) does the second stage’s contribution become negligible. For the input: a lossy filter before the LNA adds its loss directly to the NF (a 1 dB filter loss = 1 dB worse sensitivity) — putting the LNA right at the antenna tap point matters.

3. Matching — Noise Match vs Conjugate Match

An amplifier’s input reflection coefficient that gives the best noise figure (Γ_opt, the noise match) is generally NOT the conjugate of the source impedance (the power match that gives maximum gain and minimum VSWR). The design picks a compromise: match toward Γ_opt for sensitivity, toward S11* for gain/s-Max-power, or somewhere between by choosing noise circles. Two frequencies of the same device can force opposite choices, and wideband designs trade off both. The practical flow uses the device’s S-parameters (S11 is the input reflection) and noise parameters (NF_min, Γ_opt, Rn): commercial RF simulation tools draw constant-NF circles and constant-gain circles; the designer selects the Γ that lands inside the needed NF circle while staying well within the unity-gain (stability) circle.

For a quick sanity calculation of the matching network’s components — for example computing the series inductor/reactance needed to transform the source impedance at the operating frequency — the RF attenuator calculator and the impedance-matching guide’s tables are the companion references; the matching math itself is the same LC transformation the RF attenuator calculator formalizes for the loss side of the budget.

4. Stability — K Factor and the Circles

An amplifier is unconditionally stable when, for all passive source and load terminations, it does not oscillate. The Rollett stability factor:

K = (1 − |S11|² − |S22|² + |Δ|²) / (2·|S21·S12|)

with Δ = S11·S22 − S12·S21. Unconditional stability requires K > 1 and |Δ| < 1. When the device is potentially unstable, the Smith chart shows regions (stability circles) that must be avoided, or the design adds loss deliberately (a series resistor, a shunt resistor, or a resistive feedback) to push K safely above 1 — the cost is a small NF/ gain penalty that is far preferable to oscillation. At RF, S12 (reverse isolation) is the coupling path: without enough reverse isolation the LNA can sustain oscillation when the load presents certain impedances; stabilizing the load side is as important as the input.

5. Biasing and the DC Operating Point

The transistor must be biased at the collector/drain current where its NF_min and gain are best — typically a few mA to a few tens of mA. For a common E-pHEMT FET the recommended bias for low NF is a low Vds (2–3 V) and moderate Ids (10–40 mA, depending on the device). A self-biased scheme uses the source resistor to set the current with negative feedback, but for lowest NF a regulated gate bias with a source-follower reference is preferred. Degenerate biasing with an emitter/source inductor (L_deg) is nearly universal in the application notes: it provides negative feedback at RF that stabilizes the stage and — valuable here — the degeneration inductance also provides a real impedance at the base/gate that shifts the optimum noise match toward 50 Ω, easing the matching network. The bias network’s resistors/capacitors and the DC feed choke must not appear in the RF path: the RF choke is an inductor (high impedance at RF) feeding the collector, and the base bias divider is RF-bypassed with a capacitor to ground.

6. Worked Example — 2.4 GHz LNA, NF 1.5 dB, Gain 15 dB

Target: a 2.4 GHz LNA for ISM-band receiver, target NF 1.5 dB, gain 15 dB, unconditionally stable, 50 Ω interfaces.

• Select an RF transistor (e.g. a dual-gate MOSFET or bipolar with fT > 6 GHz); bias at the recommended NF_min point.
• Add source degeneration: a ~1 nH series inductor at the emitter/source provides the real input impedance and helps for the noise match.
• Input match: from the device S11 and noise parameters, pick a series-L/shunt-C (or a shunt-L/series-C) network to move Γ toward Γ_opt; verify the NF circle contains the chosen Γ.
• Output match: conjugate-match S22; keep |Δ| and K checked — if K < 1, add a small series output resistor or rc feedback until K > 1 at 2.4 GHz and across the whole band.
• Biasing: VCC feed through an RF-choke inductor; base/gate divider bypassed with a 100 pF capacitor to ground; decouple each supply pin.
• Layout: microstrip with controlled 50 Ω trace; the input trace from the antenna splitter to the transistor is part of the matching network; ground the source/emitter vias as close to the pads as possible (the degeneration inductance is literally the via inductance if you are not careful).
• Add a bias-tee and a resistive-attenuator pad for test; use the RF attenuator calculator if a L-pad in the test fixture needs a quick value.
• Measure with a network analyzer: S11/VSWR, S21 gain, NF (via a noise-figure meter or the Y-factor method); the measured NF should land within ~0.2 dB of the design.

7. LNA Application Table

Frequency band	Typical LNA type	NF target	Key concern
VHF/UHF (100–900 MHz)	GaAs / SiGe / BJT	0.5–1.5 dB	Desensitization by strong signals
1–3 GHz (2.4/5 GHz)	E-pHEMT / SiGe Bipolar	0.8–1.8 dB	NF vs stability, layout
5–6 GHz (WiFi6)	GaAs pHEMT, MMIC LNA	1.0–2.0 dB	Matching bandwidth, ESD
mmWave 24–60 GHz	MMIC LNA	2–4 dB	Assembly, waveguides, gain flatness

8. Common Mistakes

• Assuming the conjugate match gives the best NF: noise match and power match differ; chasing S11*=0 can cost 1–2 dB of NF.
• Unstable at some load: the LNA passes the 50 Ω bench test but oscillates when the real antenna/load presents an out-of-circle impedance; verify K over the whole band.
• Loss before the LNA: every filter/connector dB before the amplifier adds directly to the receiver NF; keep the LNA at the antenna side of the switch/filter.
• Vias as inductance: an extra 0.5–1 nH of source via inductance shifts the noise match; use multiple parallel vias and short paths.
• Ignoring the DC path interaction: the bias divider capacitance resonates with the matching inductance if not bypassed properly.
• Not verifying with real measurements: simulated NF on a 4-layer board with uncontrolled Z0_trace and a floating ground plane is fiction; the 40 dB dynamic-range measurement tells the truth.

9. FAQ

Q: Why is the LNA nearest the antenna? A: The noise of all later stages is suppressed by the LNA’s gain; any passive loss before the LNA adds directly to the noise figure — so the LNA must see the antenna almost directly.

Q: What is the difference between S11 and the noise match? A: S11 describes the impedance seen looking into the device (power match); the noise match Γ_opt is the source impedance that minimizes NF. They rarely coincide; the design trades one against the other via the noise circles.

Q: Do I need a separate LNA if my receiver has a good mixer? A: Almost always yes for sensitivity — the mixer’s noise dominates unless the LNA provides 15–20 dB of gain ahead of it (see the Friis equation).

Q: Why does the LNA oscillate at some frequencies but not others? A: Potentially unstable device with an unlucky load; the K factor and stability circles tell you exactly which terminations to avoid or how much loss to add.

10. Conclusion

The LNA design is a controlled negotiation between noise figure, gain, stability and matching. Place it at the antenna, compute the Friis budget, choose the noise match over blind power matching, guarantee K > 1 across the band, bias at the low-NF operating point, and validate on the board with a noise-figure meter. When the S-parameter number does not match the measured one, the layout — the vias, the reference plane, the un-decoupled bias — is almost always the culprit. With the attenuator and matching references on this site, the loss and impedance bookkeeping stay honest from simulation to the lab.