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Modeling Analog Non linearitiesfor Delta Sigma Modulator
Behavioral system level understanding &
simulations
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Common Biomedical Signals
Low frequency and low amplitude signals
Detection difficult as coupled with flicker noise, Common mode noise and electrode offset
voltage.
Electrodes eliminate common mode gain.
DC component eliminated - choppers
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Bio Signal sensing and processing system
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Input Signal BW=05 Hz to 1KHz
OSR= 1024
Order of Modulator= 2
LP or BP= LP
DR= 70dB
ENOB= 18
QUANTIZATION BITS=1
System Level Specifications
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For OSR=1024
L=2B=1
DR(dB)=115
ENOB=18
Performance Parameters
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The calculation of these coefficients is based
on the fact that the pulse response of filter is
weighted response of the all the pulses
generated by each feedback in DSM
architecture. This yields us with a system of
linear equations ..
The output matrix
System of linear
equations
Solution to the system of linear
equations gives us the required
coefficients
Calculating coefficients
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non-idealities
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Variations from ideal clock edges vary the feedback pulse length
Clock jitter causes error sequence in CT :
e(z) = { y(n) y(n-1) } * bn /Ts
Adds additional noise in DAC through feedback which is NOT shaped by loop filter
Simulation show NRZ codes & multi bit quantization are less sensitive to jitter
Modeling Clock Jitter
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Modeling Integrator Noise
thermal noise - caused by random fluctuations of carriers due to thermal energy
white spectrum and wide band, limited the BW of the operational amplifiers
Flicker noise - 1/f noise decrease with frequency increase
Time domain emulated sources of both noises are sum of N sine waves with randomphase
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Ideally infinite but actually limited by circuit constraints & op amp open loop gain
pole of integrator is pushed from dc to a / (Ao + 1)
TF of finite GBW & gain is:
Ideal TF is replaced by this eq. in simulink model
Modeling Finite Gain & GBW
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Modeling Slew Rate
Rate at which the output changes with the change in input