I am little confused over what the signal to noise ratio refer to and what is it actually used for. Is higher SNR better or Lower SNR better for your circuitry? Does infinite signal to noise ratio mean that you have no noise in the signal?
SNR as you know means Signal-to-Noise ratio. So it's \$20 log(\$\$V_S\over V_N\$), where \$V_S\$ is signal voltage and \$V_N\$ is noise voltage. So, if noise (\$V_N\$) is really small (compared to signal), then SNR gets really big.
It's quite possible to have systems with negative SNR (where the signal level is less than the noise), where you need synchronous demodulation or a lock-in amplifier to pull the signal out of the noise. In that case, you could write Noise-to-Signal ratio \$20 log(\$\$V_N\over V_S\$), which would be equal to - \$20 log(\$\$V_S\over V_N\$).
GNSS systems such as GPS have a negative SNR before processing.