Cascade gain & noise figure

Build an ordered signal chain and see how each stage changes its gain and noise figure.

Signal chain

Input → outputDrag to reorder

Drag a stage by its handle, use the Up and Down arrow keys, or click the handle to choose a position. Escape cancels a drag or closes the stage editor.

Stage 1 name
Gain (dB)
Stage NF (dB)
Added NF (dB)+1.5 dB
Noise share (%)71.07 %
Stage 2 namePassive · 290 K · gain -3 dB
Loss (dB)
Stage NF · auto (dB)3 Matched passive loss at 290 K. Gain is negative loss; noise figure equals loss. Source temperature does not change this preset.
Added NF (dB)+0.1 dB
Noise share (%)5.42 %
Stage 3 name
Gain (dB)
Stage NF (dB)
Added NF (dB)+0.39 dB
Noise share (%)23.5 %

Added NF is the increase in cumulative NF at each stage, in this order. Noise bars show each stage’s share of added noise, referred to the chain input; source noise is excluded.

Noise figure

1.99 dB

Total gain: 42 dB

More measurements

Signal, noise & sensitivity

Source temperature and input signal refer to the first stage’s input. Equivalent noise bandwidth is the width of an ideal rectangular filter passing the same noise power; it may differ from the −3 dB bandwidth. Required SNR may be negative.

Source noise temperature (K)

Equivalent noise bandwidth

Bandwidth unit

Input signal (dBm)

Required SNR (dB)

Output signal · small-signal model: -18 dBm
Output noise: -56.98 dBm
Output SNR: 38.98 dB
Input sensitivity: -88.98 dBm

Signal level after each stage, using the entered input signal and the small-signal gains.
Stage	Cumulative gain (dB)	Output signal (dBm)
LNA	15	-45
Filter	12	-48
IF amplifier	42	-18

Noise factors & temperature

The input-referred excess-noise terms are linear factors. Add 1 to their sum for the total noise factor.

Total noise factor: 1.58
Equivalent input noise temperature: 168.33 K

Stage	Excess-noise term
LNA	0.41
Filter	0.03
IF amplifier	0.14

Compression check · optional stage limits

Enter input P1dB at each stage, in dBm. Leave unknown limits blank. The weakest entered threshold is referred back through preceding gains; it is a screening estimate, not the cascade’s measured 1 dB compression point.

LNA · input P1dB (dBm)

Filter · input P1dB (dBm)

IF amplifier · input P1dB (dBm)

Weakest entered input threshold: -2 dBm
Headroom from entered signal: 58 dB

Using -60 dBm at chain input.

3 of 3 stage limits supplied. Limiting entered stage: IF amplifier.

Model & assumptions

Stage gains add in dB, but noise contributions must be combined as linear power ratios. For stage $i$ , convert its gain $G_i$ and noise figure $\mathrm{NF}_i$ from dB to linear gain $g_i$ and noise factor $F_i$ :

g_i=10^{G_i/10},\qquad F_i=10^{\mathrm{NF}_i/10}

Gain is available-power gain and noise figure uses a 290 K reference. The passive-loss preset describes a matched component physically at 290 K: its gain is the negative of its loss in dB, and its noise figure equals that positive loss. Source noise temperature is a separate input and does not change the preset.

Gain before a stage reduces that stage’s noise contribution referred to the chain input. For three stages, the combined noise factor is:

F_{\mathrm{total}}=F_1+\frac{F_2-1}{g_1}+\frac{F_3-1}{g_1g_2}

Each additional stage follows the same rule: divide its excess noise factor by the product of all preceding gains. Noise-share results include stage-added noise only, excluding source noise; shares are undefined when no stage adds noise.

Convert the combined linear factor back to dB to obtain the overall noise figure:

\mathrm{NF}_{\mathrm{total}}=10\log_{10}(F_{\mathrm{total}})

This assumes ordered, stable, linear stages with matched interfaces. Interstage mismatch and compression are excluded; mixer SSB/DSB conventions must be consistent. The lowest input-referred stage P1dB is only a compression screening limit, not the chain’s actual compression point. Missing limits remain unknown; IP3 and stability are not predicted.

Added NF is the rise in cumulative noise figure when stage $i$ is appended in the current order. If $F_{\le i}$ is the cascade noise factor through that stage, calculate the increment as:

\Delta\mathrm{NF}_i=10\log_{10}\!\left(\frac{F_{\le i}}{F_{\le i-1}}\right),\qquad F_{\le 0}=1

These order-dependent increments sum mathematically to the total NF. The entered stage NF and the share of added noise describe different quantities. Small differences can occur when adding rounded readings; numerical limits are reported when an increment cannot be represented. Reordering changes the increments because it changes the preceding gain and cumulative noise.

For example, three stages with gain/NF values of 15/1.5 dB, −3/3 dB and 30/5 dB give 42 dB total gain and approximately 1.99 dB noise figure.

SourcesKeysight, Fundamentals of RF and Microwave Noise Figure Measurements (opens in a new tab)NIST SP 330 (2019), The International System of Units (opens in a new tab)

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