SBOS849B December 2017 – February 2019 LMH5401-SP
PRODUCTION DATA.
The signal-to-noise ratio (SNR) of the amplifier and filter can be calculated from the amplitude of the signal and the bandwidth of the filter. The noise from the amplifier is band-limited by the filter with the equivalent brick-wall filter bandwidth. The amplifier and filter noise can be calculated using Equation 12:
where
For example, with a first-order (N = 1) band-pass or low-pass filter with a 30-MHz cutoff, the ENB is 1.57 × f–3dB = 1.57 × 30 MHz = 47.1 MHz. For second-order (N = 2) filters, the ENB is 1.22 × f–3dB. When filter order increases, the ENB approaches f–3dB (N = 3 → ENB = 1.15 × f–3dB; N = 4 → ENB = 1.13 × f–3dB). Both VO and eFILTEROUT are in RMS voltages. For example, with a 2-VPP (0.707 VRMS) output signal and a 30-MHz first-order filter, the SNR of the amplifier and filter is 70.7 dB with eFILTEROUT = 5.81 nV/√Hz × √47.1 MHz = 39.9 μVRMS.
The SNR of the amplifier, filter, and ADC sum in RMS fashion is as shown in Equation 13 (SNR values in dB):
This formula shows that if the SNR of the amplifier and filter equals the SNR of the ADC, the combined SNR is 3 dB lower (worse). Thus, for minimal degradation (< 1 dB) on the ADC SNR, the SNR of the amplifier and filter must be ≥ 10 dB greater than the ADC SNR. The combined SNR calculated in this manner is usually accurate to within ±1 dB of the actual implementation.