Signal averaging can recover a good estimate of s(k) even when σn(k) is 60 dB larger than s(k). From Equation 9.145, it is possible to find the N required to give a specified SNRo, given σn2(k), σa2 and s(k)2.

9.8.7.3Discussion

Signal averaging is widely used in biomedical research and diagnosis. A periodic stimulus (e.g., noise, flash, electric shock, pin prick, etc.) is given to a subject. The response is generally electrophysiological, i.e., an evoked cortical potential (ECP), an electrocochleogram (ECoG), or an electroretinogram (ERG) — all richly contaminated with noise. By averaging, the noise is reduced (its sample mean tends to zero) as the number of averaging cycles, N, increases, while the signal remains the same. Thus, signal averaging increases the SNR in the averaged signal. However, as demonstrated, there are practical limits to the extent of SNR improvement.

9.9Some Low-Noise Amplifiers

TABLE 9.2

Partial Listing of Commercially Available Low-Noise Op Amps and Instrumentation Amplifiers with Low-Noise Characteristics Suitable for Biomedical Signal Conditioning Applications

© 2004 by CRC Press LLC

TABLE 9.2 (continued)

Partial Listing of Commercially Available Low-Noise Op Amps and Instrumentation Amplifiers with Low-Noise Characteristics Suitable for Biomedical Signal Conditioning Applications

aType refers to whether the amplifier is an op amp (OP) or an instrumentation amplifier (IA), and whether it has a BJT or FET headstage.

bena is given in nV RMS/ Hz measured at 1 kHz.

cina is given in picoamps (pA) or femtoamps (fA) RMS/ Hz measured at 1 kHz.

dLow freq. Vn is the equivalent peak-to-peak, short-circuit input noise measured over a standard 0.1- to 10-Hz bandwidth.

eRin is the input resistance.

ffT is the unity gain bandwidth in MHz, unless followed by (–3), in which case it is the highfrequency −3-dB frequency.

gAV0 for op amps is their open-loop dc gain; the useful gain range is given for IAs.

9.10The Art of Low-Noise Signal Conditioning System Design

9.10.1Introduction

Consider the scenario in which a physiological signal such as nerve action potentials (spikes) is to be recorded extracellularly from the brain with a metal microelectrode embedded in the cortex. The signal has a peak amplitude, vspk, generally in the tens of microvolts. The input signal is assumed to be accompanied by additive white noise and to be resolved above the total broadband noise at the preamplifier’s input. It has been shown previously that the MS input noise is:

where ena and ina are white root noise spectra that are properties of the amplifier used and ens is a white noise root power spectrum added to the recorded signal in the brain.

It is also assumed that the thermal noise in the source resistance, Rs, is white and B is the Hertz bandwidth over which the signal and input noises are considered. Low-noise amplifier design is particularly desired when vspk

< 3 [ena2 + ina2 R2s + 4kTRs]B V .

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The first step in designing a low-noise signal conditioning system is to choose a low-noise headstage amplifier that also meets other design criteria for parameters such as bandwidth, slew rate, input dc offset voltage (VOS) and bias current (IB), and VOS and IB tempcos. Modern low-noise IC amplifiers typically have enas < 7 nV/ Hz in the white region. Such amplifiers may use super beta BJT headstages that, unlike FET headstages, have higher values of IB and ina and a relatively lower Rin. See Table 9.2 for examples.

Because the noise performance of a multistage amplifier used for signal conditioning is set by the noise characteristics of the (input) headstage, it is necessary to give the low-noise headstage at least a gain of 5, preferably 10. Having done this, following amplifier stages need not be expensive lownoise types. Any resistance used in an input high-pass filter coupling the electrode to the headstage should be a low-noise metal film type, not carbon composition.

Finally, a band-pass filter with noise bandwidth B should follow the amplifier stages. The filter’s corner frequencies to pass nerve spikes and to exclude highand low-frequency noise should be at 30 Hz and 3 kHz. The noise Hertz BW, B, is generally close to but greater than the signal passband. For a simple two-real-pole BPF with low break frequency at flo = 1/(2πτ1) Hz and a high break frequency at fhi = 1/(2πτ2) Hz, the noise BW from Table 9.1 is:

The signal’s −3-dB Hz bandwidth is easily seen to be:

For example, if τ2 = 10−4 sec and τ1 = 10−2 sec then B = 2.475 ∞ 103 Hz for noise and the signal BW is SBW = 1.576 ∞ 103 Hz.

Section 9.4.3 described the use of an input transformer to maximize the SNR at the output of the analog signal conditioning system. It may be worthwhile to consider transformer coupling of the source to the headstage if the Thevenin source resistance of the electrode, Rs, is less than 1/10 of Rsopt = ena/ina Ω. Transformer coupling carries a price tag, however. Special expensive, low-loss, low-noise transformers are used that generally have extensive magnetic shielding to prevent the pick-up of unwanted, time-varying magnetic fields, such as those from power lines, etc. The author has never heard of SNRo-maximizing coupling transformers being used with metal microelectrodes. The Rs of a typical metal microelectrode is on the order of 15 kΩ with its tip platinized (Northrop and Guignon, 1970). If an instrumentation amplifier such as the AD624 is used as the headstage, its ena = 4 nV/ Hz and

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its ina = 0.4 pA/ Hz, so its Rsopt = ena/ina = 105 Ω. If a transformer were to be used, its turns ratio to maximize SNRout would be 2.58.

Experience indicates that, although SNRout improvement would occur, it would be too small to justify the expense of the transformer. (It would be only 1.08 times the SNR of the amplifier with no transformer.) On the other hand, if the same amplifier were to be used with a transducer having Rs = 10 Ω, the transformer turns ration would be no = 100 and the improvement in SNRout over an amplifier with no transformer would be:

Thus, the use of the transformer under the preceding conditions would lead to a significant improvement in the output MS SNR.

Section 9.7 and Section 9.8.2 examined the effect of negative feedback applied around an amplifier through a resistive voltage divider. A surprising result was found for a sinusoidal voltage source connected to a standard inverting, ideal op amp circuit with short-circuit equivalent input noise root power spectrum, ena (ina = 0 in this case) and noisy resistors. Namely, the amplifier’s SNRout increases monotonically with amplifier gain magnitude, RF/R1, to a best asymptotic value of:

Thus the output MS SNR depends on the absolute value of the input resistor and the amplifier’s overall closed-loop gain.

As a design example, examine the SNRout for an op amp used in the noninverting mode. Although both op amp inputs are properly characterized with their own ena and ina, it is common practice to assume infinite CMRR and combine the noises as one net ena and ina at the amplifier’s summing junction, as shown in Figure 9.22. Assume that the three resistors make thermal white noise and that the signal is sinusoidal. The MS output signal is:

The MS output noise has five independent components:

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