Gain Method

The Gain Method is a measurement technique used to determine the noise figure (NF) of active electronic components, particularly in radio frequency (RF) and microwave systems. It relates a device's gain and its output noise power to quantify noise performance under defined test conditions.

Measurement Principle

The Gain Method is based on three fundamental steps:

1. Measure the linear gain: Determine the ratio of output power to input power.

2. Determine output noise power density: Measure the noise power per unit bandwidth at the device output.

3. Calculate the noise figure: Use gain and noise power data to compute the noise figure using a standardized formula.

Noise Figure Formulas

Two calculation approaches are commonly used:

• Theoretical formulation:
  NF = 10 log₁₀(Fa) = 10 log₁₀((P_no / T_ref) / (P_ni / T_0))
  where:

  • P_no: Output noise power

  • P_ni: Input noise power

  • T_ref, T_0: Reference temperatures (usually 290 K)

• Practical measurement formula:
  NF = PN_OUTD + 174 dBm/Hz − G
  where:

  • PN_OUTD: Output noise power density (dBm/Hz)

  • G: Device gain (dB)

  • 174 dBm/Hz: Thermal noise floor at 290 K

Gain Representation

Gain is expressed as:
G = 10 log₁₀(P_out / P_in)

where P_out is the output power and P_in is the input power under linear operating conditions.

Typical Test Procedure

• Terminate the device input with its characteristic impedance (e.g., 50 Ω)

• Configure spectrum analyzer settings (e.g., resolution bandwidth and video bandwidth with a typical RBW/VBW ratio of 0.3)

• Measure the device’s gain from P_in and P_out

• Record the output noise power density PN_OUTD using the spectrum analyzer

• Compare the result to the theoretical thermal noise floor

• Calculate the noise figure using the practical formula

Required Equipment

• Network analyzer for gain measurement

• Spectrum analyzer for noise power density

• Precision signal generator to ensure stable input

• Low-noise amplifier (optional, depending on signal level)

• Calibrated attenuators to control system losses

Use Case Example

An amplifier with a gain of G = 15 dB and a measured output noise power density of PN_OUTD = −150 dBm/Hz yields:

NF = −150 + 174 − 15 = 9 dB

This value reflects the excess noise introduced by the device compared to an ideal noiseless amplifier.

Practical Considerations

• Best suited for devices with moderate to high gain, typically above 20 dB

• Measurement accuracy decreases for devices with very low noise figures (e.g., < 1 dB), due to the spectrum analyzer’s intrinsic noise floor

• System losses and impedance mismatches must be accounted for

• Calibration is critical to minimize errors from non-ideal measurement conditions

• For low-noise devices or components with low gain, alternative methods such as the Y-Factor Method may offer improved accuracy

Applications

• Wireless communications: Receiver and LNA characterization

• Satellite systems: Measurement of noise contribution in RF front-ends

• Microwave engineering: Evaluation of amplifier chains and filter blocks

• Radar systems: Analysis of receiver sensitivity

• Telecommunications: Noise performance in signal chains

• Test and measurement: Laboratory and production validation of component NF