Basic Noise Spectral Density Conversions for Sensor Front Ends
Root sum square integration of spot noise spectral density across effective noise bandwidth determines actual sensor resolution and achievable effective bits.
Noise Floor Integration
Spectral Compilation
Quantifying the total noise power in a measurement system requires summing the noise spectral density across the active bandwidth. This process of noise floor integration yields the root mean square noise voltage that limits the minimum detectable signal of the instrument. The integration is performed mathematically by taking the square root of the integral of the noise power density over the frequency range.
Frequency Boundary
The limits of the integration are defined by the low pass and high pass filters in the signal chain. Choosing these boundaries correctly prevents out of band noise from inflating the total noise estimate. For DC coupled systems, the integration must extend down to the sub hertz region to capture flicker noise.
Sensor Interference
External disturbances and electromagnetic pickup can introduce discrete spikes in the frequency spectrum of the system. These interfering signals are integrated along with the random noise, artificially raising the reported noise floor of the sensor. Adequate shielding and differential routing are necessary to minimize these external contributions.
Calibration Assay
Validating the noise performance of an instrument involves measuring the integrated noise while the input is terminated with a shielded resistor. Special test software acquires millions of samples to compute the power spectral density and perform the required integration. If the calculated root mean square noise exceeds the design tolerance, the circuit board is inspected for layout errors or faulty components, and the test is repeated under controlled temperature conditions.