Baker's Best; Painless reduction of analogue filter noise

October 29, 2014 // By Bonnie Baker, Texas Instruments
They say a low-pass filter will rid you of noise in the higher frequencies. Well, this is not entirely true. It will succeed to a certain degree, but let’s take a closer look.

The classical approach to arranging an odd-order, low-pass active filter is to place the single pole of the odd-ordered filter at the front-end of the circuit. Following this first stage there are the remaining second-order stages. Figure 1 illustrates this fifth-order low-pass filter example.

Figure 1 Fifth-order, Sallen-Key, 1 kHz low-pass filter with a Butterworth approximation.

As shown in Figure 1, the first stage is in an active first-order configuration. This first-order stage uses an RC pair at the input followed by a buffered amplifier. Following this simple first-order stage are two second-order stages.

It is curious to look at the cumulative noise above the corner frequency of this fifth-order filter. With an operational amplifier (op amp) like the OPA350, the cumulative output noise from these three amplifiers and five resistors becomes approximately 3.9 µVrms at 10 kHz. If you use this circuit as an anti-aliasing filter, it reduces higher frequency signals above 1 kHz. However, some of the noise continues to sing through.

The 10 kHz noise density of this op amp is 7 nV / √Hz. The resistor's noise density at 10 kHz is equal to √(4 * k * T * R) (where k = 1.38 e-23, T = temperature in Kelvin, and R = resistance in Ohms).

next; re-arrange the circuit...