Amplifier Noise Matching
# Amplifier Noise Matching: Choose the Right Source Impedance
Noise matching chooses the source impedance presented to an amplifier to optimize a stated noise-performance metric. In a simple voltage/current-noise model, source resistance trades the amplifier’s voltage-noise contribution against the voltage generated by its input current noise. The impedance that minimizes noise figure need not match the amplifier’s input impedance for maximum power transfer.
## 1. Follow the noise through the source
*Simplified high-input-impedance voltage amplifier. The drawing shows one equivalent voltage-noise source and one equivalent current-noise source. The resistor’s thermal generator is omitted from the schematic but included in the equation. The model neglects noise correlation, loading and feedback-network noise.*
For an ideal resistive source Rs at temperature T, uncorrelated white amplifier voltage noise en and current noise in give the source-inclusive input voltage power density Stotal = en² + in² Rs² + 4 kB T Rs. The first term is voltage noise, the second is current noise converted through the source resistance, and the last is source thermal noise.
At low source resistance, amplifier voltage noise often dominates its added noise. At high resistance, current noise can become decisive. Choosing the smallest data-sheet voltage-noise number alone can therefore select the wrong amplifier for a high-impedance sensor.
## 2. Define what is being minimized
*Analytical single-frequency example, not measured data or product performance. The noise-factor calculation uses source temperature 300 K consistently. Standard noise-figure specifications normally use a stated reference temperature, commonly 290 K; use that convention when comparing specifications.*
Under the model above, the noise factor at the specified source temperature is F = 1 + [en² + in² Rs²]/(4 kB T Rs), and noise figure is NF = 10 log₁₀ F in decibels. Differentiating the added-to-source-noise ratio gives Ropt = en/in for positive, finite en and in. At that resistance, en and in Rs have equal amplitude density.
For en = 3 nV/√Hz and in = 1 pA/√Hz, Ropt = 3 kilohms. At 300 K, Fmin is about 1.362, corresponding to NF ≈ 1.34 dB. This optimum minimizes degradation relative to the source’s own thermal noise. It does not minimize absolute input voltage noise: all terms in Stotal are constant or increase with Rs in this simplified model.
The actual signal also matters. Changing source impedance can change signal amplitude, loading and available power. Optimize the signal-to-noise ratio of the complete sensor and amplifier arrangement, with the source model held physically consistent.
## 3. Distinguish noise matching from power matching
| Objective | What is optimized | Information required |
|---|---|---|
| Minimum absolute input noise | Noise voltage or current in a stated band | Source model, transfer paths and bandwidth |
| Minimum noise factor | SNR degradation relative to source thermal noise | Source temperature and amplifier noise model |
| Maximum power transfer | Delivered signal power | Source/load impedances and frequency |
| Complete receiver performance | Sensitivity with gain and linearity constraints | Matching-network loss, stability and system budget |
An RF amplifier can have correlated voltage/current noise and a complex optimum source impedance. RF noise parameters such as minimum noise factor, optimum source reflection coefficient and noise resistance characterize that behavior. The simple real-valued en/in rule does not replace those data.
A passive matching network transforms impedance and signal together. Its loss can add thermal noise and reduce available signal before amplification. A resistive pad inserted ahead of an LNA to improve a match can worsen overall receiver noise figure, so include the network in the calculation.
## 4. Verify the practical interface
Use noise parameters at the intended frequency, bias and temperature. Include the sensor’s frequency-dependent impedance, input capacitance, bias components, feedback resistors and matching-network loss. If voltage and current noise are correlated, retain the appropriate cross term instead of adding independent powers only.
Compare input-referred noise using the same reference plane and bandwidth. Integrate the full output or input-referred spectrum for broadband signals; a single-frequency optimum may not be best over the required band. Check stability, signal gain, distortion and overload behavior after changing the impedance transformation.
The useful result is a source/amplifier interface with a defined signal and noise model, an explicit optimization target, and verified performance under the intended operating conditions.
## References
- [Analog Devices: Low Noise Amplifier Selection Guide](https://www.analog.com/en/resources/app-notes/an-940.html) — voltage noise, current noise and source resistance.
- [Analog Devices: LNA Matching Techniques for Optimizing Noise Figures](https://www.analog.com/en/resources/technical-articles/lownoise-amplifier-lna-matching-techniques-for-optimizing-noise-figures.html) — correlated noise and optimum RF source impedance.
- [Analog Devices: Ask the Applications Engineer — Op-Amp Noise](https://www.analog.com/en/resources/analog-dialogue/articles/what-should-i-know-about-opamp-noise.html) — amplifier selection across source impedances.