What is the noise contribution of the second stage in a cascaded system and when does it matter?
When the Second Stage Matters
The Friis cascade equation shows that each subsequent stage's noise contribution is reduced by the total gain preceding it. For the second stage, its excess noise factor (F2-1) is divided by the first stage gain G1. This division is the fundamental reason why LNA placement and gain are critical to receiver performance.
| 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 |
Noise Sources
Consider a practical example. If the first stage LNA has 25 dB gain (G1 = 316 linear) and the second stage mixer has 10 dB noise figure (F2 = 10), the second stage contributes (10-1)/316 = 0.028, which adds only 0.12 dB to the system noise figure. The LNA's high gain has effectively made the mixer's poor noise figure irrelevant.
Cascade Analysis
Now consider what happens with low first-stage gain. If the LNA has only 10 dB gain (G1 = 10) with the same 10 dB NF mixer, the second stage contributes (10-1)/10 = 0.9 in linear noise factor, adding approximately 2.5 dB to the system noise figure. This is a dramatic difference.
- Performance verification: confirm specifications against the application requirements before finalizing the design
- Environmental factors: temperature range, humidity, and vibration affect long-term reliability and parameter drift
- Cost vs. performance: evaluate whether the application demands premium components or standard commercial grades
- Interface compatibility: verify impedance, connector type, and mechanical form factor match the system architecture
Measurement Techniques
The practical rule is that the first stage gain should be high enough to suppress the second stage noise by at least 10 dB. This means G1 should be at least 10 times (F2-1) in linear terms. For a mixer with 10 dB NF following the LNA, the LNA needs at least 10·log10(10×9) = 19.5 dB gain to suppress the mixer noise contribution to under 0.4 dB.
Frequently Asked Questions
Does this apply to stages beyond the second?
Yes. The third stage contribution is divided by G1×G2, making it even smaller. After two stages of gain, subsequent noise contributions are almost always negligible unless there is significant loss between stages.
What if the first stage is a filter with loss?
A lossy first stage has gain less than one, which amplifies the second stage contribution instead of suppressing it. This is why preselector filter placement in noise-critical receivers requires careful analysis: the filter improves selectivity but degrades noise performance.
Can too much first-stage gain cause problems?
Yes. Excessive LNA gain can drive subsequent stages into compression with strong signals, degrading dynamic range. The optimal first-stage gain balances noise figure (wants more gain) against dynamic range (wants less gain).