The accelerometer designed has piezoresistors at the edges of the beams to sense maximum stress.
The sensor has to be placed on the plane normal to the tremor affected area of the patient. Usually, the single axis accelerometer if placed normal to the surface of the skin mainly the dorsum of the hand, can sufficiently capture feeble tremor as majority of the nerve fibres are connected. Whenever acceleration is applied, there is proof-mass displacement, and the suspension beams deflect, and this causes strain on the piezoresistors. The effect of applied stress is to change the number and mobility of the charge carriers within a material. This causes large change in resistivity. All the eight piezoresistors are connected in a manner that they form the arms of a Wheatstone bridge with each arm having two piezoresistors. Thus, the change in output voltage of the bridge is directly proportional to the applied acceleration. This analog output obtained from the MEMS accelerometer with the Wheatstone bridge circuit is then taken and fed to a sigma-delta converter. Here basically oversampling, noise shaping using sigma delta modulator, digital filtering and decimation are the stages the analog signal goes through for reduction of noise.
Oversampling is the process of taking more samples per second than required on the basis of the Nyquist-Shannon criterion. When we change the sampling rate the signal power and total quantization noise power is not affected. Therefore, the signal to quantization noise ratio is not changed. However, the quantization noise is spread over a larger frequency range, reducing the spectral density of the
quantization noise. If now only the original Nyquist band is considered, the quantization noise power is reduced by 3 dB for every doubling of the oversampling ratio and the signal to quantization noise ratio is improved accordingly. In this manner we get an increased efficiency since now the quantization noise can be pushed to frequencies far from the signal band. This effect is illustrated in Fig. 6.2 for an oversampling ratio of 1, 2, and 4 times.
Noise shaping is applied as a second step to improve the signal to quantization noise ratio. In this
Figure 6.2: Illustration to show oversampling reduces noise spectral density
process the frequency distribution of the quantization noise is altered such that the quantization noise density reduces in the signal band. As a result the noise density increases at other frequencies where the noise is less harmful. This effect is depicted in Fig. 6.3 where low frequency noise is pushed to high frequencies. The amount of quantization noise is not changed by this process but the signal-to-noise ratio is increased in the low frequency area of the spectrum. In a sigma-delta modulator ( SDM ) the techniques of oversampling and noise shaping are combined, resulting in an increased efficiency since now the quantization noise can be pushed to frequencies far from the signal band. First, the sigma delta converter converts the analog signal into digital with a very low resolution analog to digital converter(ADC). The effective resolution is increased by using oversampling techniques in conjunction with noise shaping and digital filter. The digital filter is used to attenuate signals and noise that are outside the band of interest followed by decimation. During decimation the data rate is reduced from the oversampling rate without losing any necessary information. The proposed model for noise reduction is given in Fig. 6.4
Figure 6.3: Noise shaping where low frequency noise is pushed to high frequencies
Figure 6.4: Proposed Noise reduction model with desired frequency range
summing junction. The signal is then passed through the integrator so that there can be a low pass filtering effect and we can focus on our desired frequency of 40 Hz and then this signal of desired band is fed to a comparator. The comparator acts as a one bit quantizer. The comparator output is fed back to the input summing junction via a one-bit digital-to analog converter (DAC), and it also passes through the digital filter and decimator for high resolution. The feedback loop forces the average of the signal entering from the DAC to be equal to the signal fed. The key feature of these converters is that they are the only low cost conversion method which provides both high dynamic range and flexibility in converting low bandwidth input signals.
6.3.1 Dissipation mechanism
In order to evaluate the mechanical thermal noise we should take into consideration the sources of dissipation or energy loss. Dissipation is termed as the mechanism that allows energy to escape from the orderly motion of the sensor. These include mechanical damping in the spring and support, viscous
Figure 6.5: Sigma delta modulator for noise reduction
air damping, electrical leakage, magnetic eddy current damping etc. Damping determines the thermal fluctuations, hence in order to have an improvement in the signal to noise ratio the device design should have an effective and controlled damping mechanism. For the piezoresistive sensor having proof-mass and the top and bottom cover lids, damping is determined both by the spacing between them and the viscosity of the fluid used. This type of damping occurs when the proof-mass is pushed towards a fixed microstructure with the fluid in it. Squeeze film damping dominates the dissipation mechanism for gaps of several micrometers. In the present case the piezoresistive accelerometer senses the acceleration in the vertical z- axis therfore squeeze film damping is considered. The damping force arises from the squeeze film effect of the proof-mass and the air film trapped in the gap between the mass and the encapsulation. A large area to gap ratio results in higher squeeze number which results in greater damping. A small damping coefficient translates into lower energy loss, smaller damping ratio, and hence higher Q. We can improve the quality factors by reducing the operating pressure, improving the surface roughness, thermal annealing and by modifying the boundary conditions.