How many averages are needed to achieve a 2:1 SNR if the signal amplitude is 5 uV and the noise amplitude is 20 uV?

To determine the number of averages needed to achieve a 2:1 signal-to-noise ratio (SNR), you can use the formula for calculating SNR based on the number of averages. The SNR improves as you average more samples, and the relationship is given by:

[ \text{SNR}{\text{after averaging}} = \text{SNR}{\text{before averaging}} \times \sqrt{N} ]

where (N) is the number of averages.

Initially, the signal amplitude is 5 µV and the noise amplitude is 20 µV. The initial SNR can be calculated as follows:

[ \text{SNR} = \frac{\text{Signal Amplitude}}{\text{Noise Amplitude}} = \frac{5 , \mu V}{20 , \mu V} = 0.25 ]

To achieve a 2:1 SNR, we want:

[ 2 = 0.25 \times \sqrt{N} ]

Rearranging gives:

[ \sqrt{N} = \frac{2}{0.25} = 8 ]

Squaring both sides results in:

[ N = 8^