Cascaded Noise Figure
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Calculate the total system noise figure for a chain of RF components using the Friis noise equation. Add stages for LNAs, filters, mixers, and cables to optimize your receiver design.
RF Chain Stages
Typical Noise Figure Values by Component
Use these values as starting points when building your cascade analysis. Actual values vary by manufacturer, frequency, and operating conditions.
| Component | Typical NF (dB) | Typical Gain (dB) | Notes |
|---|---|---|---|
| Low Noise Amplifier (LNA) | 0.5 – 3.0 | 15 – 30 | First stage sets system NF |
| Bandpass Filter (passive) | = insertion loss | -0.5 – -3.0 | NF equals loss for passive devices |
| Mixer (passive) | 6.0 – 10.0 | -6.0 – -10.0 | NF ≈ conversion loss |
| Mixer (active) | 8.0 – 15.0 | -2.0 – +5.0 | Lower conversion loss than passive |
| Cable / Connector | = insertion loss | -0.2 – -3.0 | Varies with length and frequency |
| IF Amplifier | 2.0 – 5.0 | 15 – 25 | Less critical after LNA gain |
| Variable Attenuator | = attenuation | -1.0 – -30.0 | NF equals attenuation setting |
How the Friis Noise Equation Works
The Friis noise equation is the foundational tool for analyzing noise performance in RF receiver chains. It calculates the total noise factor of cascaded stages by accounting for the fact that each stage's noise contribution is reduced by the gain of all preceding stages.
Where:
F = noise factor (linear, NOT in dB)
G = gain (linear, NOT in dB)
NF (dB) = 10 × log₁₀(F)
F (linear) = 10^(NF_dB / 10)
G (linear) = 10^(G_dB / 10)
Why LNA Placement Is Critical
The equation reveals a fundamental principle: the first stage dominates system noise performance. If stage 1 has 20 dB of gain (G₁ = 100 linear), the second stage's noise contribution is divided by 100. This is why the LNA should always be the first active component in a receive chain, placed as close to the antenna as possible.
Placing even a low-loss cable (1 dB) before the LNA adds 1 dB directly to the system noise figure. At mmWave frequencies where cable losses are higher, this effect becomes even more significant, driving the use of feed-mounted LNAs and LNBs.
Worked Example: Satellite Receiver Front-End
Consider a Ka-band (28 GHz) satellite receiver with the following signal chain:
Stage 2: Bandpass Filter (Gain = -1.5 dB, NF = 1.5 dB)
Stage 3: Mixer (Gain = -7 dB, NF = 7.0 dB)
Stage 4: IF Amplifier (Gain = 20 dB, NF = 3.0 dB)
Convert to linear:
F₁ = 10^(2.0/10) = 1.585, G₁ = 10^(25/10) = 316.23
F₂ = 10^(1.5/10) = 1.413, G₂ = 10^(-1.5/10) = 0.708
F₃ = 10^(7.0/10) = 5.012, G₃ = 10^(-7/10) = 0.200
F₄ = 10^(3.0/10) = 1.995
F_total = 1.585 + (1.413-1)/316.23 + (5.012-1)/(316.23×0.708) + (1.995-1)/(316.23×0.708×0.200)
F_total = 1.585 + 0.001 + 0.018 + 0.022 = 1.626
NF_total = 10 × log₁₀(1.626) = 2.11 dB
The total system noise figure is 2.11 dB, only 0.11 dB higher than the LNA alone. This demonstrates the effectiveness of high-gain first-stage amplification.
Passive Component Noise Figure
For passive devices (filters, cables, attenuators, power dividers), the noise figure equals the insertion loss. A cable with 2 dB of loss has a noise figure of 2 dB. This follows from thermodynamic principles: a lossy passive component at room temperature adds thermal noise proportional to its loss.
Design Guidelines for Minimum System Noise
- Place the LNA as close to the antenna as physically possible
- Minimize any loss between the antenna and LNA (cables, connectors, switches)
- Select an LNA with the lowest available NF at your operating frequency
- Ensure the LNA has sufficient gain (typically 20 dB or more) to suppress downstream noise
- Use low-loss filters and minimize the number of passive components before the first amplifier
- For extreme sensitivity, consider cryogenic cooling of the LNA
Frequently Asked Questions
What is cascaded noise figure?
Cascaded noise figure is the total noise figure of a chain of RF components calculated using the Friis noise equation. Each stage's noise contribution is reduced by the cumulative gain of all preceding stages, which is why the first stage (typically an LNA) has the most significant impact on system noise performance.
What is the Friis noise equation?
The Friis noise equation calculates total noise factor: F_total = F₁ + (F₂-1)/G₁ + (F₃-1)/(G₁×G₂) + ... where F is noise factor (linear, not dB) and G is gain (linear). Convert dB values to linear before using: F = 10^(NF_dB/10) and G = 10^(Gain_dB/10).
Why is the first stage noise figure so important?
The first stage noise figure adds directly to the total system noise figure. All subsequent stages' contributions are divided by the cumulative gain preceding them. With 20 dB of first-stage gain, the second stage's noise contribution is divided by 100, making it nearly negligible.
What is a good noise figure for an LNA?
Sub-6 GHz: 0.3 to 1.0 dB. Ka-band (26-40 GHz): 1.5 to 3.0 dB. E-band (60-90 GHz): 3.0 to 5.0 dB. Cryogenic LNAs can achieve below 0.1 dB. The required NF depends on your system sensitivity requirements and the available link margin.
What is the noise figure of a passive component?
For any passive device at room temperature (cables, filters, attenuators), the noise figure equals the insertion loss. A filter with 2 dB insertion loss has a 2 dB noise figure. This is a direct consequence of thermodynamics.