CHAPTER 5

Chopping: a technique for noise and offset reduction

5.4. Noise modulation

From the previous paragraph we have seen the modulation effects of chopping on a input process x(t). It is important to notice the difference between a narrow-band process and a broadband process after chopper modulation. The input stationary random process x(t) can be white noise or 1/f noise applied to the amplifier A(f) which has a band limiting effect on the noise.

5.4.1. White noise modulation

For the beginning, assume that x(t) is a broadband random process white noise like with a power spectral density Swhite. In order to simplify the analysis, the gain of the amplifier is taken to be 0dB and the frequency transfer has a first order behavior:

(5.12)

The power spectral density of the noise at the output can be found from (5.11) with assumption that Sxx(f)=Swhite:

(5.13)

The series from (5.13) can be computed by using Poisson summation rule [9]. For large values of fLPT (fLPT>>1) we get:

(5.14)

In conclusion, the chopper modulator has a small influence on the white noise when the bandwidth of the amplifier is larger than the chopping frequency. This is not the case for sampling where undersampling phenomena actually increases the noise in the baseband [1]. The power spectral density of the white noise will be unchanged as long as the bandwidth of the amplifier is larger than the chopping frequency. Chopping at frequencies higher than fLP will reduce the power spectral density of the white noise as explained in reference [4]. Although white noise is a fundamental limitation it can be reduced by chopping. Oversampling in D/A and A/D converters has about the same effect on the baseband white noise.

5.4.2. 1/f noise modulation

When narrow band random processes are applied at the input of the chopper modulator the situation will change. The input power spectral density of 1/f noise is:

(5.15)

In the constant c we have included the 1/f noise constant k1/f process dependent and the geometry factor, dependent on the dimensions of the transistors. After chopping the PSD of the modulated 1/f noise becomes:

(5.16)

Fig.5.5 shows the normalized PSD of the flicker noise after chopping when fLPT>>1. The effect of chopper modulation on the flicker noise will be the reduction of the PSD of the output noise at low frequencies. At odd multiples of the chopper frequency the

 Fig.5.5: PSD of 1/f noise after chopper modulation

PSD of the flicker noise increases. Thus, under the same condition fLPT>>1 the PSD of the white noise after chopping remains the same and the PSD of the flicker noise at low frequencies will be reduced.

Featured Video
Jobs
Associate Packaging Engineer for Unilever at Englewood Cliffs, New Jersey
Vice President, GIS Business Unit for RAMTeCH Software Solutions, Inc. at Stillwater, Minnesota
Senior Account Manager, Utilities for RAMTeCH Software Solutions, Inc. at Stillwater, Minnesota
GIS Analyst for Institute for Children and Poverty at New York, California
GIS Engineer III for Nebraska State Government at Lincoln|, Nebraska
Upcoming Events
COMSOL Conference 2018 Lausanne at SwissTech Convention Center Quartier Nord EPFL, Route Louis-Favre 2, 1024 Ecublens Switzerland - Oct 22 - 24, 2018
6th OpenFOAM Conference 2018 at Radisson Blu Hotel, Hamburg Airport Flughafenstraße 1-3 Hamburg Germany - Oct 23 - 25, 2018
ASSESS 2018 CONGRESS at Chateau Elan Winery & Resort 100 Rue Charlemagne, Braselton GA - Oct 28 - 30, 2018
MEMS & Sensors Executive Congress—MSEC 2018 at Silverado Resort and Spa 1600 Atlas Peak Road Napa CA - Oct 28 - 30, 2018