How do I calculate the total noise figure of a cascaded receiver chain with multiple stages?
The Friis Cascade Equation
When multiple RF components are connected in series, each one adds noise to the signal. The Friis equation, developed by Harald T. Friis in 1944, provides the method for calculating the total noise factor of the entire chain from the individual noise factors and gains of each stage.
| Parameter | Superheterodyne | Direct Conversion | Digital IF |
|---|---|---|---|
| Image Rejection | 60-90 dB (filter) | 30-50 dB (mismatch) | N/A (digital) |
| DC Offset | No issue | Major issue | No issue |
| LO Leakage | Low | High | Low |
| Integration | Difficult | Easy (single chip) | Moderate |
| Dynamic Range | 80-120 dB | 60-90 dB | 70-100 dB |
Frequently Asked Questions
Does the Friis equation work for passive components?
Yes. A passive component has a noise factor equal to its loss factor (1/gain). For a 3 dB attenuator, F = 2 and G = 0.5. Insert these values into the Friis equation like any other stage.
What if the stages are not impedance matched?
The standard Friis equation assumes matched conditions. Impedance mismatch between stages changes the effective noise figure and gain, requiring modified versions of the equation or S-parameter based noise analysis.
How many stages do I need to include?
Include every component in the signal path: cables, connectors, filters, amplifiers, mixers, and attenuators. After the first high-gain stage, contributions become small, but lossy components anywhere in the chain should be accounted for.