What are the different types of gain?

Power gain (G_P): the ratio of power delivered to the load to power available from the source. Most commonly specified for amplifiers. Transducer gain (G_T): the ratio of power delivered to the load to the maximum power available from the source. Accounts for impedance mismatch at both input and output. G_T = G_P times (1 minus |gamma_in|^2) times (1 minus |gamma_out|^2) / |1 minus gamma_s gamma_in|^2. Available gain (G_A): the ratio of power available from the amplifier output to power available from the source. Represents the maximum gain achievable with a conjugate match at the output. Insertion gain: the ratio of power delivered to the load with the amplifier in the circuit to the power delivered without it. Accounts for the interaction between source, amplifier, and load impedances. Antenna gain: G = eta times D, where eta is the total antenna efficiency and D is the directivity. Referenced to isotropic (dBi) or to a half-wave dipole (dBd = dBi minus 2.15).

How does cascade gain work?

For cascaded components in a receiver or transmitter chain, the total gain in dB is simply the sum of individual gains: G_total = G_1 + G_2 + G_3 + ... (in dB). Losses are negative gains. Example receiver chain: LNA gain (+15 dB) + cable loss (minus 1 dB) + filter loss (minus 2 dB) + mixer conversion loss (minus 6 dB) + IF amp gain (+30 dB) = total gain of +36 dB. For noise analysis, the gain distribution matters enormously. The Friis equation shows that the first stage gain dominates the system noise figure: NF_total = NF_1 + (NF_2 minus 1)/G_1 + (NF_3 minus 1)/(G_1 times G_2). High gain in the first stage (LNA) reduces the noise contribution of all subsequent stages. But too much gain early in the chain can cause the mixer or ADC to saturate on strong signals, reducing dynamic range. The optimal gain distribution balances sensitivity against linearity.

What limits amplifier gain?

Several factors limit the achievable gain of an RF amplifier. Stability: an amplifier with too much gain at any frequency may oscillate. The Rollett stability factor K and the auxiliary condition delta determine unconditional stability: K greater than 1 and |delta| less than 1. Achieving high gain while maintaining stability requires careful attention to source and load impedances at all frequencies, including out-of-band. Gain-bandwidth product: for a given transistor technology, the product of gain and bandwidth is approximately constant. A transistor with 20 dB gain at 1 GHz might achieve only 10 dB at 10 GHz. The maximum available gain (MAG) decreases at 6 dB per octave above the frequency where K equals 1. Feedback: negative feedback (intentional or parasitic) reduces gain. At high frequencies, package parasitics create feedback paths that reduce gain and can cause instability. Temperature: gain typically decreases with temperature for GaAs and GaN (approximately minus 0.01 to minus 0.02 dB per degree C), requiring compensation for stable system performance.

Fundamental Parameter

Gain

/gayn/ — G

Power ratio: G = P_out/P_in (dB). Amplifier: 10-40 dB typical. Antenna: G = ηD (dBi). Cascade: G_total = G₁+G₂+G₃ (dB). Transducer gain: includes mismatch. Friis: NF_sys = NF₁ + (NF₂−1)/G₁. Stability: K>1, |Δ|<1. GBW product ≈ const. Flatness ±0.5 dB for wideband. Temp coeff: −0.01 dB/°C.

LNA: 15-25 dB

PA: 10-15 dB

Dish: 30-50 dBi

Understanding Gain

Gain is the most fundamental parameter in RF systems. Every component in a signal chain either adds gain (amplifiers, antennas) or subtracts it (cables, filters, free-space path). The link budget, the most important calculation in RF system design, is simply the sum of all gains and losses from transmitter to receiver.

The concept of gain applies differently to amplifiers and antennas, but the underlying meaning is the same: how much more signal comes out compared to what goes in. For amplifiers, gain comes from active devices (transistors). For antennas, gain comes from concentrating radiation into a beam.

Gain Equations

Amplifier gain:
G = 10log(P_out/P_in) dB
G = 20log(V_out/V_in) dB (same Z)

Antenna gain:
G = ηD (dBi)
G(dBd) = G(dBi) − 2.15

Cascade (Friis):
G_total = G₁ + G₂ + ... (dB)
NF_sys = NF₁ + (NF₂−1)/G₁
+ (NF₃−1)/(G₁×G₂)

Stability:
K = (1−|S₁₁|²−|S₂₂|²+|Δ|²)/
(2|S₁₂||S₂₁|) > 1

Gain by Component Type

Component	Gain	Freq	NF	Technology
LNA	15-25 dB	DC-100 GHz	0.3-3 dB	GaAs, InP, SiGe
Power amp	10-15 dB	DC-40 GHz	N/A	GaN, LDMOS
Patch antenna	5-7 dBi	1-77 GHz	N/A	PCB
Horn	10-25 dBi	1-300 GHz	N/A	Machined WG
1m dish @10GHz	38 dBi	Narrowband	N/A	Reflector

Common Questions

Frequently Asked Questions

Types?

Power gain (P_out/P_in). Transducer: includes mismatch at both ports. Available: max with conjugate match at output. Insertion: with/without device in circuit. Antenna: G=ηD, referenced to isotropic (dBi) or dipole (dBd = dBi−2.15). Link budget: always use gain, not directivity.

Cascade?

G_total = G_1+G_2+... (dB). Friis: NF_sys = NF_1 + (NF_2-1)/G_1. High G_1 (LNA) = low system NF. But too much early gain = mixer/ADC saturation (reduced DR). Optimal: enough LNA gain to dominate NF, not so much to saturate. Balance sensitivity vs linearity.

Limits?

Stability: K>1 required. Too much gain = oscillation. GBW ≈ constant for a technology. MAG drops 6 dB/octave. Feedback (parasitic): reduces gain, causes instability. Temp: −0.01 dB/°C typical (GaAs/GaN). Compensation needed for stable systems. Package parasitics limit HF gain.

Related Terms

← GaAs Gain-BW →

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