When to use: Use to calculate the cascaded noise figure of a multi-stage receive chain using the Friis formula. Add up to 4 stages (LNA, filters, cable, BDA/receiver). The first stage dominates — a low-noise LNA early in the chain dramatically improves system sensitivity. Output includes total system NF and receiver sensitivity (dBm) for a given bandwidth and required SNR. Critical for DAS uplink design and public safety BDA installations.
The Noise Figure & System Sensitivity Calculator applies the Friis noise figure formula to a cascaded multi-stage receive chain, computing total system noise figure and receiver sensitivity for a given bandwidth and minimum SNR. Engineers use it to evaluate DAS uplink chains, BDA receive paths, and LNA placement decisions where noise performance directly limits the range and reliability of the system.
The Friis noise figure formula for a cascaded chain is: F_total = F1 + (F2 − 1)/G1 + (F3 − 1)/(G1·G2) + ..., where F is the linear noise factor (F = 10^(NF_dB/10)) and G is the linear gain of each stage. The first stage contributes its full noise factor, while subsequent stage contributions are divided by the cumulative gain of all preceding stages. This means the first amplifier in the chain dominates the system noise figure — a 1.5 dB LNA in the first stage can reduce total system NF from 20 dB to 3 dB compared to putting the LNA after a 6 dB cable loss.
System sensitivity = kTB + NF_total + SNR_min, where kTB = −174 dBm/Hz + 10·log10(bandwidth in Hz). For a 25 kHz P25 channel: kTB = −130 dBm. With a 5 dB system NF and 12 dB SNR minimum (DAQ 3.0 SINAD), sensitivity = −130 + 5 + 12 = −113 dBm.
IEEE Std 60268-1 defines noise figure measurement methods for audio and signal equipment. ITU-T G.174 provides noise figure analysis procedures for optical amplifier chains. For public safety radio, APCO P25 standards (TIA-102 series) define receiver sensitivity requirements — DAQ 3.0 corresponds to 12 dB SINAD for FM voice. BDA units for public safety bands must meet FCC Part 90 receiver noise figure requirements. For DAS systems, the uplink noise figure of the BDA is specified in the FCC equipment authorization data and should be verified in the link budget.
The first stage dominates — always place the LNA (Low Noise Amplifier) as early in the receive chain as possible, before any cables, connectors, or filters that add loss. A high-gain LNA (15–20 dB) with a low noise figure (1–2 dB) placed at the antenna output will reduce the contribution of all subsequent stages to near zero. A passive filter before the LNA adds its insertion loss directly to the system noise figure — if the bandpass filter has 2 dB insertion loss, the effective noise figure of the entire chain increases by 2 dB.
For BDA installations, the receiver noise figure of the BDA sets the uplink sensitivity floor. A BDA with a 7 dB noise figure and 25 kHz channel bandwidth has a theoretical sensitivity of −174 + 44 + 7 + 12 = −111 dBm, which is well above the −95 dBm NFPA threshold and represents 16 dB of sensitivity margin.
Enter each stage of the receive chain in order from antenna toward the receiver. For each stage, enter the noise figure in dB and the gain in dB (enter a negative value for a passive loss stage such as a cable or filter). The Friis formula computes the cumulative system noise figure after each stage. Set the channel bandwidth and minimum SNR to compute system sensitivity. The bandwidth and SNR fields use land mobile radio defaults (25 kHz, 12 dB SINAD) — adjust for other systems such as LTE (20 MHz bandwidth, 1 dB sensitivity implementation margin) or Wi-Fi.
Each subsequent stage's noise contribution is divided by the cumulative gain of all preceding stages. If the first stage has 20 dB (100×) of gain, the second stage noise factor of F2 is reduced to (F2 − 1)/100 before being added to F1. With sufficient gain in the first stage, the second and third stage contributions become negligible. This is Friis's key insight and explains why LNA placement is the most critical decision in a sensitive receive chain design.
FCC-certified public safety BDA units typically specify an uplink noise figure of 5 to 10 dB. Higher-performance units designed for rural or weak-signal environments target 5–7 dB NF. BDA noise figure is found in the FCC equipment authorization database under the device's FCC ID. For comparison, a high-quality LNA for 800 MHz has a noise figure of 0.5–1.5 dB.
P25 digital voice (IMBE vocoder) requires approximately 12 dB SINAD (Signal-plus-Interference-plus-Noise-and-Distortion to Noise ratio) at the receiver IF stage for DAQ 3.0 (Good audio quality). This is equivalent to approximately 12 dB SNR at the receiver input in a noise-limited environment. NFPA 1221 uses −95 dBm as the proxy for DAQ 3.0, which accounts for typical portable receiver noise figures and antenna gain.
Wider bandwidth captures more thermal noise power. Sensitivity degrades by 10 dB for every 10× increase in bandwidth: a 25 kHz P25 channel has kTB = −130 dBm, while a 5 MHz LTE component carrier has kTB = −107 dBm — 23 dB worse. This is why cellular data systems require higher transmit power and shorter link distances than narrowband voice systems for the same coverage.
Yes — adding a low-noise amplifier between the donor antenna and the BDA input reduces the total receive chain noise figure. For example, if the BDA has a 7 dB NF and you add a 1.5 dB NF / 20 dB gain LNA before it, the system NF becomes approximately 1.5 + (10^(0.7)−1)/100 ≈ 1.55 dB. However, the LNA must be approved by the BDA manufacturer and coordinated with the licensed carrier, as it amplifies all signals including potential interference.
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