Cascaded Noise
Understanding Cascaded Noise
Thermal Noise Accumulation in Receivers
In any wireless receiver, the ability to detect weak signals is limited by the amount of thermal noise present in the system. As an RF signal passes through successive stages, each active component adds its own thermal noise to the signal. The cumulative effect of these contributions is called cascaded noise. Managing cascaded noise is the primary task of receiver design, directly determining the noise figure and the minimum discernible signal (MDS) at the input.
Unlike linearity calculations where downstream stages dominate, cascaded noise calculations show that the input stage dominates. Under Friis' formula, the noise factor contribution of each successive stage is divided by the cumulative gain of all preceding stages. If the first amplifier (the Low Noise Amplifier) has high gain and a low noise figure, it suppresses the noise contributions of all subsequent stages, securing a low system noise figure.
Pre-Amplifier Loss and Sensitivity Degradation
Because the first stage is critical, any insertion loss introduced before this stage has a devastating effect on the cascaded noise figure. Passive components such as coaxial cables, RF switches, and pre-selection filters degrade the noise figure decibel-for-decibel. For example, if a bandpass filter with 2 dB of insertion loss is placed before a LNA with a 1 dB noise figure, the combined noise figure of those two stages is 3 dB. To maximize sensitivity, engineers minimize the physical distance between the antenna and the first LNA stage.
Key Mathematical Relations
Technical Specifications Comparison
| Stage Number | Component Type | Stage Gain (dB) | Stage Noise Figure (dB) | Cumulative Gain (dB) | Cumulative NF (dB) |
|---|---|---|---|---|---|
| 1 | Antenna Cable (Loss) | -1.2 | 1.2 | -1.2 | 1.20 |
| 2 | Low Noise Amplifier | +18.0 | 0.9 | 16.8 | 2.10 |
| 3 | Pre-Selection Filter | -1.5 | 1.5 | 15.3 | 2.11 |
| 4 | RF Mixer (Loss) | -6.0 | 7.0 | 9.3 | 2.24 |
Frequently Asked Questions
Why is the first amplifier stage critical for the cascaded noise figure?
The first amplifier is critical because it provides the initial gain that boosts the signal power. According to Friis' formula, the noise contributions of all downstream mixers, filters, and amplifiers are divided by this gain, making their noise contributions negligible.
How do passive components before the first amplifier affect the system noise figure?
Any passive component placed before the low-noise amplifier introduces insertion loss. This loss directly increases the system noise figure decibel-for-decibel because it attenuates the signal before any amplification can take place, while adding thermal noise.
How is cascaded noise calculated for a receiver with a lossy mixer?
The mixer is treated as a stage with a noise figure equal to or greater than its conversion loss. Its noise factor contribution is added to the preceding stages, divided by the linear gain of the LNA, showing that high LNA gain is needed to suppress mixer noise.