Please enter valid values in all stage blocks.
RESULTS
Input Parameters Specification
Stage Noise Figure (NF) Individual stage noise degradation coefficient measured in decibels.
Stage Active Gain (G) Logarithmic power amplification scaling added by each sequential receiver component.
System Outputs Integrated composite link attributes calculated uniformly across active nodes.
Practical Operational Examples
Cascade Stage Parameters
Stage 1: NF = 1.20 dB, Gain = 15.00 dB
Stage 2: NF = 3.00 dB, Gain = 10.00 dB
Computed Results
• Total Network NF = 1.274 dB
• Combined Link Gain = 25.000 dB
• Output Noise Temp = 98.922 K
Diagrams & Theory
Cascading configurations analyze cumulative attenuation performance. Early stage amplification factor attributes drastically scale down overall degradation boundaries.
Formulas & Mathematical Logic
F_total = F1 + (F2 - 1)/G1 + (F3 - 1)/(G1 * G2) + ...
Noise Temp = 290 * (10^(NF_total/10) - 1)
Logarithmic input variables are transformed into direct active scalars internally inside execution arrays to map cascading network layers safely.
Step-by-Step Example
Example: 2-stage cascade where Stage 1 has Noise Figure (NF1) = 1.20 dB, Gain (G1) = 15.00 dB, and Stage 2 has Noise Figure (NF2) = 3.00 dB, Gain (G2) = 10.00 dB.
Step 1: Convert all logarithmic decibel parameters to raw linear power factor ratios: F1 = 10^(1.20 / 10) = 1.318257, F2 = 10^(3.00 / 10) = 1.995262, and G1 = 10^(15.00 / 10) = 31.622777.
Step 2: Solve the total system noise factor using Friis cascade noise equation: F_total = F1 + (F2 - 1) / G1 = 1.318257 + (1.995262 - 1) / 31.622777 = 1.318257 + 0.031473 = 1.349730.
Step 3: Convert the total linear noise factor back to a logarithmic Noise Figure in decibels: Total NF = 10 * log10(F_total) = 10 * log10(1.349730) = 1.3025 dB.
Step 4: Solve the cumulative total linear gain of the system by summing up stage gains: Total Gain = G1 + G2 = 15.00 + 10.00 = 25.00 dB.
Step 5: Solve the effective input system noise temperature (Te) using standard room temperature reference (290 K): Te = 290 * (F_total - 1) = 290 * (1.349730 - 1) = 290 * 0.349730 = 101.42 K.
Result: The calculated composite parameters are Total NF = 1.3025 dB, Total Gain = 25.00 dB, and Noise Temperature = 101.42 K.
How to Use This Calculator
Select the total number of amplifier stages in your receiver lineup using the Number of Cascaded Amplifiers dropdown.
Input the respective NF dB (Noise Figure) and Gain dB values for each active stage generated in the form grid.
Click the orange Calculate button to initiate the Friis cascade noise computation.
Read the computed values for Total Noise Figure, Total Gain, and equivalent Noise Temperature on the Results cards.
About This Calculator
Analyze multi-stage receiver chains and optimize cascade noise factors with professional precision.
The CalcBoy Cascaded Noise Figure Calculator evaluates total noise figure, cumulative gain, and equivalent noise temperature across up to 10 sequential active receiver stages using Friis equations.
An RF link budget is a comprehensive mathematical accounting of all the power gains and losses that an electromagnetic signal experiences as it propagates from a transmitter through an open-air medium to a receiver. Designing a robust wireless network—whether it is a terrestrial Wi-Fi link, a long-range point-to-point microwave backhaul, or a satellite communication transponder—requires a detailed link budget analysis. If the signal reaching the receiving antenna is too weak, it falls below the receiver sensitivity threshold, resulting in packet loss, link degradation, or a complete connection dropout. An accurate budget ensures that there is sufficient margin to withstand temporary environmental attenuations.
To compute these transmission metrics, the calculator integrates several distinct physical layers. The active power of the transmitter radio is attenuated by the passive insertion losses of coaxial cables, connectors, and lightning protectors before reaching the feedpoint. The antenna then concentrates this energy, providing a directional gain (Gt). As the wave travels through free space, it spreads spherically, creating a high-loss propagation path (Free Space Loss) before being captured by the receiver's directional antenna (Gr) and attenuated again by receiver cabling. The net signal level reaching the receiver port—referred to as the Received Signal Strength Indicator (RSSI)—must exceed the receiver sensitivity by a safety threshold called the fade margin. This calculator solves for these variables, allowing RF engineers to predict link reliability under diverse operational configurations.
Ideal ApplicationLow-noise amplifier cascading, satellite receiver chains, radar front-ends, and link budget optimization.
Key OutputCumulative Noise Figure (dB), Total Power Gain (dB), and effective input Noise Temperature (Kelvin).
Crucial PhysicsGains of preceding stages divide and suppress the noise contributions of subsequent receiver components.
Design RuleAlways place your lowest noise figure, highest gain amplifier as the first active stage in the cascade.
Tip: Passive stages (like filters or cables with insertion loss) have a noise figure equal to their loss and a negative gain. Be sure to input negative gain values for these passive lossy stages.
Frequently Asked Questions
What physically is the purpose of Friis' cascade noise equation?
Friis' cascade equation calculates the cumulative noise figure of a series of active and passive components connected in series. It mathematically models how noise added by later stages is suppressed by the gains of the preceding stages.
Why is the noise figure of the first stage (LNA) the most critical?
Because the noise added by the first stage is amplified by the full gain of the system, whereas the noise added by later stages is divided by the cumulative gains of all the stages that came before them. Therefore, the first amplifier establishes the absolute noise baseline of the receiver.
How do passive, lossy components (like cables or filters) affect the cascade?
A passive component has a noise figure equal to its attenuation loss (in dB) and a negative gain equal to that same loss. If placed before the first LNA, a lossy cable directly adds to the system noise figure decibel-for-decibel, significantly degrading receiver sensitivity.
What is the relationship between cascaded noise figure and noise temperature?
They are different representations of the same physical noise power. Once the cumulative system noise figure is calculated, the equivalent noise temperature (Te) is computed relative to the standard room reference temperature of 290 Kelvin. This thermal temperature is highly favored in space and cryogenic systems.
Can this calculator handle negative gains or passive stages?
Yes. If a stage represents a passive filter, cable, or attenuator, simply enter its insertion loss (e.g., 3 dB) as a positive Noise Figure value, and input its negative loss (e.g., -3 dB) in the Gain field. The script will compute the cascade correctly.
What limits the maximum number of stages I can compute?
This calculator supports up to 10 cascaded stages, which is more than sufficient for almost all practical receiver topologies, including complex double-conversion superheterodyne architectures.
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