Noise characteristics of cascaded 2nd-order active filters

The absolute noise level at the output of single-amplifier, 2nd-order active filters, suitable for cascade connection, is derived in terms of the sensitivity of the filter response to the amplifier gain. A very simple expression is obtained, which is shown to be valid under practical conditions. A similar expression is obtained for cascaded 2nd-order sections, and a 4th-order example shows that the position of the sections in the cascade has a significant effect on the output noise level. The cascade positions giving lowest noise level are the opposite of those normally used to give maximum dynamic range.