🔗 Cascaded Noise Figure Calculator

Friis cascade — NF, noise temperature & gain through an RF chain

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RF Chain Stages

Add stages in order from antenna port to demodulator input. Order matters — loss before the LNA hurts most. 按天线端口到解调器输入的顺序添加各级。顺序很重要——LNA 之前的损耗影响最大。

# Stage Type NF / Loss (dB) Gain (dB) Tphys (K)

Results

Cascaded NF
– dB
Receiver noise temp Te
– K
System noise temp Tsys
– K
Total chain gain
– dB
Stages
–
Show per-stage noise breakdown
# Stage NF / Loss Gain Device Te Te at input Contribution Cum. NF
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📖 How to use

  1. Start with a preset that matches your system, or build from scratch with + Add stage. 选择一个与你系统匹配的预设,或点击 + 添加级 从头构建。
  2. Set each stage Type: Amplifier (enter NF + Gain) or Loss / Filter (enter loss in dB; gain and effective NF are auto-computed using the given physical temperature). 设置每级的类型:放大器(填 NF + 增益)或损耗 / 滤波器(填损耗 dB;增益与等效 NF 按物理温度自动计算)。
  3. Watch the Contribution bar — the tallest bar is your noise bottleneck. Moving a low-NF amplifier earlier in the chain will reduce it most effectively. 关注贡献条——最长的条是噪声瓶颈。将低 NF 放大器前移到链路更前端,可最有效地降低整体噪声。
  4. Copy Te straight into the G/T calculator or the link budget's system noise temperature field. 将 Te 直接填入 G/T 计算器或链路预算的系统噪温输入框。
  5. Arrived via a ↗ link from the Link Budget? Click the return bar at the top to carry Te straight back into the field you came from (the bar never appears on a direct visit). 如果是点链路预算里的 ↗ 链接跳转而来,点顶部的返回条即可把 Te 直接带回原字段(直接访问不会显示返回条)。

What is cascaded noise figure?

Every stage in an RF receiver chain — waveguide, amplifier, filter, mixer — adds its own noise. The Friis formula combines them into a single cascaded noise figure referred to the chain input:

F_total = F₁ + (F₂−1)/G₁ + (F₃−1)/(G₁·G₂) + …

where Fi = 10NFi/10 is the linear noise factor and Gi = 10Gaini/10 is the linear gain. In terms of equivalent noise temperature (T₀ = 290 K):

T_e = T₁ + T₂/G₁ + T₃/(G₁·G₂) + …

For an amplifier: Ti = (Fi−1)·290 K. For a lossy element at physical temperature Tphys: Ti = (L−1)·Tphys, where L = 10loss/10.

Why the first stage dominates

Stage 2's noise contribution is divided by G₁, stage 3's by G₁·G₂, and so on. A first stage with high gain suppresses all subsequent stages. This is why real receivers put the lowest-NF LNA as close to the antenna as possible — even 0.3 dB of feed loss before a 0.8 dB LNA raises the system NF to ≈ 1.1 dB.

Loss at non-ambient temperature

Losses at temperatures other than 290 K are modelled by Ti = (L−1)·Tphys. A cryogenic feed cooled to 20 K with 0.3 dB loss contributes only ≈ 1.4 K instead of ≈ 20 K at room temperature — a big deal for radio astronomy and deep-space ground stations.

Use the resulting Te in the G/T calculator or the link budget. All computation runs locally in your browser.

什么是级联噪声系数?

射频接收链中的每一级——波导、放大器、滤波器、混频器——都会引入自身噪声。 Friis 公式将它们合并为折算到链路输入端的总噪声系数:

F_total = F₁ + (F₂−1)/G₁ + (F₃−1)/(G₁·G₂) + …

其中 Fi = 10NFi/10 为线性噪声因子,Gi = 10增益i/10 为线性增益。等价的噪声温度形式(T₀ = 290 K):

T_e = T₁ + T₂/G₁ + T₃/(G₁·G₂) + …

对于放大器:Ti = (Fi−1)·290 K。对于物理温度 Tphys 下的损耗元件:Ti = (L−1)·Tphys,其中 L = 10损耗/10。

为什么第一级最重要

第 2 级噪声贡献被 G₁ 除,第 3 级被 G₁·G₂ 除,以此类推。若第一级增益高,后续各级的噪声均被压低。这正是真实接收机总是将最低 NF 的 LNA 尽量靠近天线放置的原因——LNA 前仅 0.3 dB 馈线损耗就会使系统 NF 从 0.8 dB 升至约 1.1 dB。

非常温下的损耗

温度不同于 290 K 的损耗通过 Ti = (L−1)·Tphys 建模。降温至 20 K 的深冷馈线(0.3 dB 损耗)仅贡献约 1.4 K,而常温下同样损耗会贡献约 20 K——对射电天文和深空地面站影响显著。

将得到的 Te 填入 G/T 计算器或链路预算。全部计算在浏览器本地完成。