Noise Figure Calculator
Calculate noise figure, noise factor, and SNR degradation for amplifiers and cascaded systems
Calculate Noise Figure
Signal-to-noise ratio at input (unitless)
Signal-to-noise ratio at output (unitless)
Noise Figure Results
Formula used:
NF = 10 × log₁₀(SNRᵢ / SNRₒ)
F = SNRᵢ / SNRₒ = 1.143
Analysis
Example Calculations
SNR Ratio Method
Given: SNRᵢ = 8, SNRₒ = 7
Calculation:
- Noise Factor F = SNRᵢ / SNRₒ = 8 / 7 = 1.143
- Noise Figure NF = 10 × log₁₀(1.143) = 0.580 dB
Result: NF = 0.580 dB, F = 1.143
SNR dB Method
Given: SNRᵢ = 40 dB, SNRₒ = 35 dB
Calculation:
- Noise Figure NF = 40 - 35 = 5 dB
- Noise Factor F = 10^(5/10) = 3.162
Result: NF = 5.000 dB, F = 3.162
Cascaded System Example
Two-stage amplifier:
- Stage 1: NF₁ = 3 dB (F₁ = 2.0), G₁ = 20 dB (100×)
- Stage 2: NF₂ = 6 dB (F₂ = 4.0), G₂ = 15 dB (31.6×)
Calculation:
- F_total = 2.0 + (4.0-1)/100 = 2.0 + 0.03 = 2.03
- NF_total = 10 × log₁₀(2.03) = 3.08 dB
- G_total = 20 + 15 = 35 dB
Noise Figure Guidelines
Excellent (≤ 1 dB)
Low noise amplifiers, sensitive receivers
Good (1-3 dB)
RF front-ends, satellite communications
Moderate (3-6 dB)
General purpose amplifiers
Poor (> 6 dB)
Needs optimization for sensitive applications
Key Concepts
Noise Figure (NF)
Logarithmic measure of SNR degradation in dB
Noise Factor (F)
Linear ratio of input to output SNR
SNR
Signal-to-Noise Ratio, measure of signal quality
Friis Formula
Used for calculating cascaded noise figure
First Stage Dominance
First stage noise figure is most critical
Understanding Noise Figure
What is Noise Figure?
Noise figure (NF) quantifies how much a device degrades the signal-to-noise ratio (SNR) of a signal passing through it. It's a critical parameter in RF and communication systems, expressed in decibels (dB). A lower noise figure indicates better performance, with 0 dB being ideal but unattainable in practice.
Noise Figure vs Noise Factor
- •Noise Factor (F): Linear ratio, F = SNRᵢ / SNRₒ ≥ 1
- •Noise Figure (NF): Logarithmic, NF = 10 × log₁₀(F) dB
- •Both measure the same phenomenon in different units
Applications
- RF Receivers: Determines sensitivity and range
- Amplifier Design: Critical for low-noise amplifiers (LNAs)
- Satellite Communications: Essential for weak signal reception
- Radar Systems: Affects detection capability
- Radio Astronomy: Critical for detecting faint signals
- Medical Imaging: Important in MRI and ultrasound systems
Design Considerations
- •First stage dominates overall noise performance
- •Higher gain in early stages reduces impact of later stages
- •Trade-off between noise figure and other parameters
Mathematical Formulations
Basic Formulas
Noise Factor:
F = SNRᵢ / SNRₒ
Noise Figure:
NF = 10 × log₁₀(F) dB
From dB SNR values:
NF = SNRᵢ(dB) - SNRₒ(dB)
Cascaded Systems (Friis Formula)
Cascaded Noise Factor:
F_total = F₁ + (F₂-1)/G₁ + (F₃-1)/(G₁×G₂) + ...
Where:
- Fᵢ = noise factor of stage i
- Gᵢ = power gain of stage i (linear)
- First stage dominates when G₁ >> 1