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The Friis cascade tells you what the noise figure should be. The Y-factor method is how most labs actually measure it, with a calibrated noise source and a noise figure analyzer or a spectrum analyzer with a noise figure application. Here is the math, a worked example and the error sources that matter in practice.
1. Definitions
- A noise source is a diode with an output noise temperature T_hot when on and T_cold (ambient) when off.
- ENR (excess noise ratio) = (T_hot - T0) / T0, with T0 = 290 K. It is quoted in dB and calibrated versus frequency; the table lives on the source label or in an ENR file.
- Y = N_hot / N_cold, the linear ratio of measured noise power with the source on and off.
2. The core equations
Equivalent noise temperature of the system being measured:
Te = (T_hot - Y * T_cold) / (Y - 1)
If T_cold = T0, the noise factor reduces to:
F = ENR_lin / (Y - 1)
or in dB: NF = ENR_dB - 10 log10(Y - 1)
If the source is not at 290 K (a warm lab or a source sitting on hot equipment):
F = (ENR_lin - Y * (T_cold/T0 - 1)) / (Y - 1)
Most analyzers do this correction if you enter or measure T_cold.
3. Second-stage correction
The analyzer has its own noise figure, so the raw number is the system NF of DUT plus analyzer. Calibration (source straight into the analyzer) measures the analyzer's own noise factor F2. Then, with the DUT inserted:
- DUT gain from the change in hot/cold power: G1 = (N_hot,DUT - N_cold,DUT) / (N_hot,cal - N_cold,cal)
- DUT noise factor: F1 = F_sys - (F2 - 1) / G1
Worked example
ENR = 15.0 dB (31.6 linear). With the DUT in place you measure Y = 12.0 dB (15.85 linear).
F_sys = 31.6 / (15.85 - 1) = 2.13, so NF_sys = 3.28 dB.
Analyzer NF from calibration = 8 dB (F2 = 6.31), DUT gain = 20 dB (100).
F1 = 2.13 - 5.31/100 = 2.08, so NF_DUT = 3.17 dB.
The correction is only 0.11 dB because of the 20 dB of DUT gain. With a 5 dB gain DUT the same analyzer would add a much larger correction, and its uncertainty grows accordingly. Add a low-noise preamplifier in front of the analyzer for low-gain DUTs.
4. Choosing ENR
- Low-NF, high-gain DUTs: use a low-ENR source (about 5 to 6 dB). The hot noise power is lower, which reduces compression risk, and the change in source match between on and off states is usually smaller.
- High-NF DUTs (mixers, receivers with 10+ dB NF): a 15 dB ENR source keeps Y large enough to measure reliably.
For a DUT with NF = 1 dB, Y is about 14.2 dB with a 15 dB ENR source and about 5.8 dB with a 5.5 dB ENR source. Both are measurable; the choice is about linearity and match.
5. Error sources that dominate
- ENR uncertainty. Because NF = ENR_dB - 10 log10(Y - 1), an ENR error of 0.2 dB becomes a 0.2 dB NF error directly. For a 1 dB NF LNA that is a 20 % error. Use the source's calibrated ENR table at each frequency, and recalibrate the source on schedule.
- Mismatch. The Y-factor method assumes the DUT sees the same source impedance in calibration and in measurement, and in hot and cold states. A DUT with a poor input match, or a source whose reflection changes when it turns on, causes errors that no simple correction removes. A well-matched source or a small attenuator or isolator at the source output helps (and its loss must be accounted for).
- Compression. Check the total noise power, not just the noise density. A wideband DUT with 40 dB of gain and a 15 dB ENR source can push the analyzer front end toward compression. Add attenuation or a band-pass filter before the analyzer, then include it in the calibration.
- Jitter. Noise is random, so the measured power fluctuates. Uncertainty falls with the square root of the measurement bandwidth times time. Increase averaging or the measurement bandwidth (where the DUT is flat) until readings repeat within about 0.05 dB.
- Interference. Wi-Fi, cellular and switching-supply spurs in the measurement band add to N_cold and make the DUT look worse. Screen the setup and look at a spectrum display before trusting a number.
- Frequency-converting DUTs. For mixers and receivers, decide whether you are measuring single- or double-sideband noise figure, and tell the analyzer, otherwise the result can be off by about 3 dB.
6. When to use a different method
For on-wafer or poorly matched devices, VNA-based cold-source methods with vector correction of the source match can be more accurate than a Y-factor setup. Y-factor remains the workhorse for connectorized amplifiers and receivers.
What uncertainty do you typically achieve on sub-1 dB LNAs? Share your setup and budget.
1. Definitions
- A noise source is a diode with an output noise temperature T_hot when on and T_cold (ambient) when off.
- ENR (excess noise ratio) = (T_hot - T0) / T0, with T0 = 290 K. It is quoted in dB and calibrated versus frequency; the table lives on the source label or in an ENR file.
- Y = N_hot / N_cold, the linear ratio of measured noise power with the source on and off.
2. The core equations
Equivalent noise temperature of the system being measured:
Te = (T_hot - Y * T_cold) / (Y - 1)
If T_cold = T0, the noise factor reduces to:
F = ENR_lin / (Y - 1)
or in dB: NF = ENR_dB - 10 log10(Y - 1)
If the source is not at 290 K (a warm lab or a source sitting on hot equipment):
F = (ENR_lin - Y * (T_cold/T0 - 1)) / (Y - 1)
Most analyzers do this correction if you enter or measure T_cold.
3. Second-stage correction
The analyzer has its own noise figure, so the raw number is the system NF of DUT plus analyzer. Calibration (source straight into the analyzer) measures the analyzer's own noise factor F2. Then, with the DUT inserted:
- DUT gain from the change in hot/cold power: G1 = (N_hot,DUT - N_cold,DUT) / (N_hot,cal - N_cold,cal)
- DUT noise factor: F1 = F_sys - (F2 - 1) / G1
Worked example
ENR = 15.0 dB (31.6 linear). With the DUT in place you measure Y = 12.0 dB (15.85 linear).
F_sys = 31.6 / (15.85 - 1) = 2.13, so NF_sys = 3.28 dB.
Analyzer NF from calibration = 8 dB (F2 = 6.31), DUT gain = 20 dB (100).
F1 = 2.13 - 5.31/100 = 2.08, so NF_DUT = 3.17 dB.
The correction is only 0.11 dB because of the 20 dB of DUT gain. With a 5 dB gain DUT the same analyzer would add a much larger correction, and its uncertainty grows accordingly. Add a low-noise preamplifier in front of the analyzer for low-gain DUTs.
4. Choosing ENR
- Low-NF, high-gain DUTs: use a low-ENR source (about 5 to 6 dB). The hot noise power is lower, which reduces compression risk, and the change in source match between on and off states is usually smaller.
- High-NF DUTs (mixers, receivers with 10+ dB NF): a 15 dB ENR source keeps Y large enough to measure reliably.
For a DUT with NF = 1 dB, Y is about 14.2 dB with a 15 dB ENR source and about 5.8 dB with a 5.5 dB ENR source. Both are measurable; the choice is about linearity and match.
5. Error sources that dominate
- ENR uncertainty. Because NF = ENR_dB - 10 log10(Y - 1), an ENR error of 0.2 dB becomes a 0.2 dB NF error directly. For a 1 dB NF LNA that is a 20 % error. Use the source's calibrated ENR table at each frequency, and recalibrate the source on schedule.
- Mismatch. The Y-factor method assumes the DUT sees the same source impedance in calibration and in measurement, and in hot and cold states. A DUT with a poor input match, or a source whose reflection changes when it turns on, causes errors that no simple correction removes. A well-matched source or a small attenuator or isolator at the source output helps (and its loss must be accounted for).
- Compression. Check the total noise power, not just the noise density. A wideband DUT with 40 dB of gain and a 15 dB ENR source can push the analyzer front end toward compression. Add attenuation or a band-pass filter before the analyzer, then include it in the calibration.
- Jitter. Noise is random, so the measured power fluctuates. Uncertainty falls with the square root of the measurement bandwidth times time. Increase averaging or the measurement bandwidth (where the DUT is flat) until readings repeat within about 0.05 dB.
- Interference. Wi-Fi, cellular and switching-supply spurs in the measurement band add to N_cold and make the DUT look worse. Screen the setup and look at a spectrum display before trusting a number.
- Frequency-converting DUTs. For mixers and receivers, decide whether you are measuring single- or double-sideband noise figure, and tell the analyzer, otherwise the result can be off by about 3 dB.
6. When to use a different method
For on-wafer or poorly matched devices, VNA-based cold-source methods with vector correction of the source match can be more accurate than a Y-factor setup. Y-factor remains the workhorse for connectorized amplifiers and receivers.
What uncertainty do you typically achieve on sub-1 dB LNAs? Share your setup and budget.