Noise Reduction

Noise reduction strategies

Although noise is a serious problem for the designer, especially when low signal levels are present, a number of commonsense approaches can be used to minimize the effects of noise on a system. In this section we will examine several of these methods. For example:

1. Keep the source resistance and the amplifier input resistance as low as possible. Using high value resistances will increase thermal noise proportionally.

2. Total thermal noise is also a function of the bandwidth of the circuit. Therefore, reducing the bandwidth of the circuit to a minimum will also minimize noise. But this job must be done mindfully because signals have a Fourier spectrum that must be preserved for faithful reproduction or accurate measurement. The
solution is to match the bandwidth to the frequency response required for the input signal.

3. Prevent external noise from affecting the performance of the system by appropriate use of grounding, shielding, and filtering.

4. Use a low-noise amplifier in the input stage of the system.

5. For some semiconductor circuits, use the lowest DC power supply potentials that will do the job.

Using feedback to reduce noise

Negative feedback is well known for reducing amplitude and phase errors, thereby reducing the distortion of an amplifier. Judicious use of feedback can also reduce the output noise of a signal conditioning amplifier.

Consider Figure 5-18. This circuit model shows gain distributed into two blocks, G1 and G2. The total gain of the circuit (G) is the product G1G2. A noise source produces a noise signal, V_n, and injects it into a summation junction between G1 and G2. A feedback network with a transfer function b produces a signal bV_o that is summed with input signal V_in. By inspection of Figure 5-18 we know:

and

Substituting Equation 5-30 into Equation 5-31:

which, when rearranged, leads to:

and finally:
The result shown in Equation 5-35 is consistent with Black's equation for feedback amplifiers [G_o = G/(1-bG)], and demonstrates that the noise is reduced by the gain factor (G1). This result is also consistent with the design philosophy inherent in the Friis equation.

If a signal is either periodic or repetitive, or can be made so, then it is possible to enhance signal-to-noise ratio (S_n) by signal averaging. The basis for this simple signal processing technique is the assumption that noise meets the definition of either random or chaotic processes. If so, then noise tends to integrate to zero or near zero over time. If time-averaging integration is performed in a coherent manner, then a repetitive signal tends to build in value, while noise levels (being decorrelated) decrease. If we assume that the signal-to-noise ratio is:Then, for systems in which V_i < V_n, the noise reduction by time averaging is:

where

is the time-averaged SNR
S_n is the unprocessed SNR
N is the number of repetitions of the signal

Example ______________________
An EEG system processes a 5-µV signal in the presence of a lOO-µV random noise level. Calculate the unprocessed SNR, the processed SNR for 1000 repetitions of the signal, and the processing gain.

Solution
The effect of time averaging is to increase the time required to collect data, so (by F = 1/T), time averaging is effectively a means of decreasing the bandwidth of the system.

Coherency is maintained in a system by ensuring that repetitive data points are processed in a consistent time relationship with respect to each other. The averager will be triggered by a repetitive event, and that action starts the process. Data points are always matched to other data points taken at the same elapsed time after the trigger for previous iterations. For example, the ith data point following a current sweep is paired with all other ith points from previous sweeps, and none other.

An example of signal averaging used to extract weak signals from larger noise signals is found in evoked potential studies of EEG waveforms (Chapter 13).

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