Biopotential and Neural Interface Circuits - 5XCC0

5XCC0 Biopotential and Neural Interface Circuits

• Area: Electronics
• Topics: Filters · MOSFET · Operational Amplifiers · Data Converters · Systems Engineering
• Related courses: Electronics II - 5ECC0 · Electronics I - 5ECB0 · Electronic Systems Engineering - 5XIC0

Schedule

Health Applications

5XCC0-01 Health Applications.pdf

Formulas

Electrode Capacitance

Impedance of a Capacitor

Amplifier Gain (AC Coupling)

Cut-off Frequency (AC Coupling)

Input Impedance (Capacitive)

Signal Attenuation due to Impedance

CMRR (Common-Mode Rejection Ratio)

CMRR due to Electrode Mismatch (Approx.)

Dynamic Range

1/f Noise Trend

Voltage Divider for Interference Sensitivity

Transfer Function for Capacitive Coupling Interference

IRN
Adding them in RMS: After amplifier the filter and ADC see factor of 10 from amplifier.

Other

Electrode types

Gel: galvanic connection: lowest and reliable impedance → skin prep.
Dry: higher less reliable impedance → no skin prep
Capacitive: galvanic isolated electrode (capacitive coupling): highest impedance but best comfort.

Measurement challenges: small signal amplitudes, large ETI impedances, large disturbances, close to DC information needed

Dealing with small signal: high gain required for amplification, since the signal of interest is usually (). But filters and ADCs most efficient when signals large (). We need a trade-off:

• Minimum signal amplitude should be detectable by the system. (at ADC).
• Maximum signal, interference, DC, etc., should not saturate the system.

• electronics add random noise (thermal noise, 1/f noise, quantization noise).
• ETI, environment and tissue add noise.
• IRN (input-referred noise): sensitivity of system: should be smaller than smallest signal you want to detect.

ETI Impedance: where

maximizing without saturation of amplifier (accounting for interference and disturbances):

Common-mode Rejection Ratio (CMRR):

There are various (slight) differences in CMRR definitions.
CMRR looks at small signal behavior. If CM disturbance is large, amplifier might saturate, and the small signal model does not hold.

EEG signal (differential):
Power-line interference (common-mode):

So we need enough dynamic range to accommodate both the signal/disturbance without saturation.

large dynamic range needed, spatial discrimination, frequency-domain filtering, time selection, advanced dsp.

dynamic range: the voltages must be same unit!

to make sure that the voltages are same unit.

CMRR to Common-Mode Gain - Multiple differential contibutions

common-mode interference: and CMRR given.
eg:
since we care about input voltage contribution we don’t need exact gain values.
CM suppression factor = 1000
if then

if we have multiple differential contributions like EEG signal, disturbance signal, converted CM interference:

AC coupling & DC Coupling

AC coupling should be before amplification, otherwise saturation:

• Gain:
• Cut-off frequency:
• 
  signal attenuation:

Trade-off:

• For large small
• For low , high gain large

Assume we have a DC coupled amplifier. Due to electrode mismatch, the half-cell potentials result in a differential DC level of up to 100mV. The signal of interest is 400µV. The amplifier has a 1V output range.

• 1/f noise (flicker noise) has a power-spectral density (PSD) that is inversely proportional to the frequency
• ExG signals are at low frequencies too
• Often the 1/f noise is dominant compared to white noise sources

Can look at slides for example details of health applications

Low-Power System Design

Summary

5XCC0-02 Low-Power System Design.pdf

Formulas

Power vs bandwidth and noise for analog (amp):

Noise Efficiency Factor (NEF):

Power vs DR for ADC (mixed-signal):

Schreier Figure of Merit (FOMS):

Dynamic Range (general):

DR due to quantization (digital):

Effective Number of Bits (ENOB):

Quantization noise (uniform distribution):

Input/Output referred noise:

Total input-referred noise (cascaded blocks):

Input-referred quantization noise (ADC):

FOMS estimation rearrangement:

Least significant bit

RMS→

V model, Risk, Optimization

Topic: Systems Engineering

requirements: what can product do.
specification: how design meet requirements.
verification: whether circuits/blocks system meet specifications/requirements.
validation: overall solution meets needs.


IRN: input referred noise level, BW: bandwidth, P: power consumption.

Analog, mixed-signal, and digital circuits

System Analysis Example

Signal → Amplifier (gain = 100) → Filter (gain = 1) → ADC

.

input range of the system would be the most severe limit: in this case would be .

ENOB is the effective number of bits (or effective resolution) including the effects of quantization noise and circuit noise: ideally equal to N, but in practice smaller.

ADC Resolution and DR

levels/codes:

gain of ADC from input voltage to output code: .

where RMS value quantization noise

The lower the NEF (closer to unity) the better.
Noise Efficiency Factor (NEF):

Models of power and performance in amplitude/frequency
Frequency: analog & digital scale similar
Amplitude: analog favorable for low DR, digital favorable for high DR

Electronics Fundamentals

Topic: MOSFET
5XCC0-03 Electronics Fundamentals.pdf

Formulas

Sub-threshold region (MOSFET):

Above-threshold, Linear mode (MOSFET):

Above-threshold, Saturation mode (MOSFET):

Thermal voltage:

Transconductance (gm):
Sub-threshold:

Above-threshold:

Efficiency ratio:
Sub-threshold:

Above-threshold:

Shot noise (current):

Thermal noise (resistor):
Current PSD:

Voltage PSD:

Noise power (bandwidth ):
Current noise:

Voltage noise:

Integrated noise amplitude:

Noise at MOS input (sub-threshold):

Noise at MOS input (above-threshold):

1/f noise:
Sub-threshold:

Above-threshold:

General:

Voltage divider ratio:

Effective resistance:

Low-pass filter cutoff frequency:

Sampled noise power (switched capacitor):

SNR (in dB):

Small signal gain of differential pair:

Noise output of differential amplifier:

Input-referred noise:

other

diffusion current:
drift current:

.
In saturation the current is constant since no longer depends on

• trans-conductance efficiency: the ration of trans-conductance to drain current, tells how much gain you get per unit of current. Which is power efficiency.
• It is constant in sub-threshold → why that mode operation is great for low power electronics.
• Increasing improves performance in strong inversion mode.

signal power:


not rms values

noise power spectral density:
total integrated noise power:

Amplifiers and Filters

Topic: Filters
5XCC0-04 Amplifiers and Filters.pdf

Formulas

• Voltage amplifier:
• Transconductance amplifier:
• Current amplifier:
• Transimpedance amplifier:
• TIA transfer function (ideal):
• TIA with op-amp gain :
• Transconductance amplifier: ,
• Input-referred noise OTA:
• CS voltage amplifier gain:
• Inverter-based voltage amplifier gain:
• Input-referred noise CS VA:
• Input-referred noise INV VA:
• Positive feedback gain:
• Condition for stability:
• Input impedance with positive feedback: when
• Capacitive amplifier gain:
• Gm-C filter time constant:
• Gm-C 1st-order LPF:
• Gm-C 2nd-order LPF:
• Gm from bias current (subthreshold):
• Noise in Gm-C filters:

Amplifier Types

Topic: Operational Amplifiers

Concepts to be familiar with

• Differential pair
• Current mirror
• Common-mode, differential-mode
• Common-mode feedback
• Open-loop, closed-loop, stability, phase margin

Transimpedance Amplifiers

Transconductance Amplifiers

Voltage Amplifiers

The reason for small signal model not having is because in small signal model so so there is no current, so there is no gain. The top part basically just acts as a resistor in small signal model, so we only consider .

More gain (about 2x) and lower input-referred noise power spectral density (about 4x) compared to CS VA.

Advanced Amplifier Techniques

Low-Voltage Analog Design

• Each transistor needs a certain
  • Minimize number of stacked transistors
  • Use sub-threshold biasing (lower )
• Use cascaded stages rather than cascoded transistors to increase gain.
• Increase DC gain by positive feedback.

negative feedback: and positive feedback:

Positive vs Negative Feedback Amplification

• Positive feedback entails adding the output of a function or process to its input. Negative feedback is subtracted from the input instead of being added.
• The effect, generally, is that positive feedback causes the output, or its amplitude, to grow without bound or until a saturation level is reached.
• Another purpose for positive amplification is to enhance impedance. So either increase gain or enhance impedance.

With positive feedback, can be increased… theoretically can be increased to infinity but that’s impractical. for :

Chopper (electronics) - Wikipedia
*A chopper circuit is used to break up the input signal so that it can be processed as if it were an AC signal, then integrated back to a DC signal at the output. In this way, extremely small DC signals can be amplified.

Filters

• Passive RLC for high requires very large passive RLC values so cant be used on integrated circuits.
• Opamp-RC
• OPAMP-Switched-capacitor
• Mosfet-RC

Digital. ADCs, and Layout

Topic: Data Converters
5XCC0-07 Digital, ADCs, and Layout.pdf

Formulas

Dynamic Power Consumption

Quantization noise (rms):

Total Power Consumption

Average Power from Simulation

Dynamic IR Drop

ADC Parameters

ADC Resolution / Dynamic Range

Nyquist Criterion

SAR ADC Voltage Step

Capacitor Array for SAR ADC

Parasitic Impact on Full-Scale Range

Sampling Noise
(single-ended)
(differential)

Signal Power and SNR

Power Consumption of DAC

MIM Capacitor

Random Mismatch

Systematic Gradient Offset

Wire Resistance and Capacitance

Static IR Drop

Thermal noise

Acquisition of neural signals

5XCC0-05 Acquisition of neural signals.pdf

Formulas

High-pass filter cutoff frequency (from AC coupling):

Amplifier Gain (capacitive feedback amplifier):

Low-pass cutoff frequency (in capacitive feedback):

Input-Referred Noise (IRN):

Input Impedance (for capacitive input):

Pseudo-Resistor Effective Resistance:

Noise corner shift due to increased bias current:
(not a formula, but remember that increasing bias shifts to a higher frequency)

Chopping Requirement:
Chopping frequency

Chopping Duty Cycle Requirement:
Must be exactly to avoid DC offset in modulated signal

Stimulation of neural tissues

5XCC0-06 Stimulation of neural tissues.pdf

Formulas

• Nernst Equation:
• Butler–Volmer Equation:
• Electrode Current Density:
• Overpotential:
• Safe Stimulation Limit (Shannon equation):
• Strength-Duration Relationship (Weiss Law):
• Charge:
• Charge Density per Phase:
• Charge Transfer Resistance (ideally): for safe implanted electrodes
• Power Dissipation:
• DC current avoidance (concept): ensure over time to avoid electrolysis