Cascaded Noise Figure Calculator Formula
Understand the math behind the cascaded noise figure calculator. Each variable explained with a worked example.
Formulas Used
Total Noise Figure
total_nf = 10 * log10(f_total)Equivalent Noise Temperature
noise_temp = 290 * (f_total - 1)Total Chain Gain
total_gain = gain1_db + gain2_dbVariables
| Variable | Description | Default |
|---|---|---|
nf1_db | Stage 1 Noise Figure(dB) | 1.5 |
gain1_db | Stage 1 Gain(dB) | 20 |
nf2_db | Stage 2 Noise Figure(dB) | 6 |
gain2_db | Stage 2 Gain(dB) | 10 |
nf3_db | Stage 3 Noise Figure(dB) | 10 |
f1 | Derived value= pow(10, nf1_db / 10) | calculated |
g1 | Derived value= pow(10, gain1_db / 10) | calculated |
f2 | Derived value= pow(10, nf2_db / 10) | calculated |
g2 | Derived value= pow(10, gain2_db / 10) | calculated |
f3 | Derived value= pow(10, nf3_db / 10) | calculated |
f_total | Derived value= f1 + (f2 - 1) / g1 + (f3 - 1) / (g1 * g2) | calculated |
How It Works
Friis Noise Formula for Cascaded Stages
The overall noise figure of a chain is dominated by the first stage, especially if it has high gain.
Formula
F_total = F_1 + (F_2 - 1)/G_1 + (F_3 - 1)/(G_1 x G_2)
All values in linear (not dB). Convert: F = 10^(NF_dB/10), G = 10^(Gain_dB/10).
NF_total(dB) = 10 x log10(F_total)
This is why low-noise amplifiers (LNAs) are placed at the front of receiver chains.
Worked Example
Three-stage receiver: LNA (1.5 dB NF, 20 dB gain), mixer (6 dB NF, 10 dB gain), IF amp (10 dB NF).
nf1_db = 1.5gain1_db = 20nf2_db = 6gain2_db = 10nf3_db = 10
- 01F1 = 10^(1.5/10) = 1.413, G1 = 10^(20/10) = 100
- 02F2 = 10^(6/10) = 3.981, G2 = 10^(10/10) = 10
- 03F3 = 10^(10/10) = 10
- 04F_total = 1.413 + (3.981-1)/100 + (10-1)/(100 x 10) = 1.413 + 0.030 + 0.009 = 1.452
- 05NF_total = 10 x log10(1.452) = 1.62 dB
Ready to run the numbers?
Open Cascaded Noise Figure Calculator