Noise Figure Calculator Mini-Circuits

Calculate cascaded noise figure, noise temperature, and system sensitivity for RF/microwave systems.

Cascaded System
Single Stage
System Sensitivity

Cascaded Noise Figure Formula (Friis formula):

Ftotal = F1 + (F2-1)/G1 + (F3-1)/(G1G2) + ...

Noise Temperature: Te = T0(F-1) where T0 = 290K

Cascaded System Parameters

Add multiple stages to calculate total system noise figure

Stage Gain (dB) Noise Figure (dB) Type Actions
Receiver bandwidth for sensitivity calculation
K
Standard noise temperature: 290K (room temperature)

Single Stage Parameters

dB
dB
K

System Sensitivity Parameters

dB
dB
Signal-to-Noise Ratio for detection
K
Calculating...

Understanding Noise Figure

Noise Figure (NF) is a measure of degradation of the signal-to-noise ratio (SNR) caused by components in a signal chain. It is a critical parameter in RF and microwave systems that determines the system's sensitivity and overall performance.

Key Noise Figure Concepts:

  • Noise Figure (NF): The ratio of input SNR to output SNR, expressed in dB
  • Noise Factor (F): The linear equivalent of noise figure (F = 10^(NF/10))
  • Noise Temperature (Te): An alternative measure of noise performance in Kelvin
  • Cascaded Noise Figure: Total noise figure of a system with multiple stages

Noise Figure Performance Classification

Noise Figure Noise Temperature Performance Level Typical Applications
< 0.5 dB < 35 K Excellent Cryogenic amplifiers, satellite receivers
0.5 - 1.5 dB 35 - 120 K Very Good Low-noise amplifiers (LNAs), cellular base stations
1.5 - 3.0 dB 120 - 290 K Good General-purpose amplifiers, receivers
3.0 - 6.0 dB 290 - 864 K Fair Mixers, filters with loss, attenuators
> 6.0 dB > 864 K Poor High-loss components, cables, switches

Friis Formula for Cascaded Systems

The total noise figure of a cascaded system is calculated using Friis formula:

Friis Formula: Ftotal = F1 + (F2-1)/G1 + (F3-1)/(G1G2) + ...

Where Fn is the noise factor (linear) of stage n, and Gn is the gain (linear) of stage n.

Key Insight: The first stage in a receiver chain typically dominates the overall noise figure, especially if it has sufficient gain.

System Sensitivity Calculation

1

Noise Power: Pnoise = kTB where k is Boltzmann's constant (1.38×10-23 J/K), T is temperature in Kelvin, and B is bandwidth in Hz

2

Noise Figure Effect: Pnoise,sys = F × kTB where F is the noise factor (linear)

3

Minimum Detectable Signal: MDS = Pnoise,sys × SNRmin where SNRmin is the minimum required signal-to-noise ratio

4

Sensitivity in dBm: Sensitivity (dBm) = 10 log10(MDS/0.001)

Practical Applications

  • Receiver Design: Optimizing LNA placement and specifications
  • Satellite Communications: Maximizing signal reception from weak sources
  • Radar Systems: Improving detection range and accuracy
  • Wireless Networks: Enhancing coverage and data rates
  • Test & Measurement: Calibrating sensitive measurement equipment

Design Tip: Place the lowest noise figure amplifier as early as possible in the signal chain, with sufficient gain to overcome the noise contribution of subsequent stages. For most systems, a first-stage LNA with NF < 2 dB and gain > 20 dB provides optimal noise performance.

Frequently Asked Questions

According to Friis formula, the noise contribution of subsequent stages is divided by the gain of preceding stages. Therefore, a high-gain, low-noise first stage (LNA) effectively "masks" the noise of later stages. If the first stage has sufficient gain, the system noise figure is approximately equal to the noise figure of the first stage.

Noise Figure (NF) is expressed in dB and represents the degradation of SNR through a device. Noise Temperature (Te) is expressed in Kelvin and represents the additional temperature that would produce the same amount of noise in a perfect noiseless device. They are related by the formula: Te = T0(F-1) where T0 = 290K and F is the noise factor (10^(NF/10)). Noise temperature is particularly useful for very low-noise systems (like satellite receivers) where noise figures less than 1 dB are common.

Noise power is directly proportional to bandwidth (Pnoise = kTB). Doubling the bandwidth doubles the noise power (increases by 3 dB). Therefore, systems with wider bandwidths have higher noise floors and require stronger signals for detection. This is why narrowband systems typically have better sensitivity than wideband systems, all else being equal.

Typical noise figures vary by component type and frequency range:
  • LNAs (Low-Noise Amplifiers): 0.5-3 dB depending on frequency and technology
  • Mixers: 5-10 dB (single-balanced), 7-12 dB (double-balanced)
  • Filters: Equal to their insertion loss (e.g., 2-3 dB for many bandpass filters)
  • Cables/Attenuators: Equal to their loss (e.g., 1-6 dB depending on length and type)
  • Complete Receivers: 4-8 dB for typical wireless systems

Several strategies can improve system noise figure:
  • Use a lower noise figure LNA as the first stage
  • Increase the gain of the first stage (within stability limits)
  • Minimize losses before the first amplifier (use low-loss cables, connectors, filters)
  • Cool the first stage for cryogenic applications (reduces thermal noise)
  • Use components with better noise performance at your operating frequency
  • Optimize impedance matching for minimum noise figure (not maximum power transfer)