Primer

• ohms law • Kirchhoff's current node rule

• define • define

• high/low pass RC filters • s = jtti2ifjw notation, w = 2pi f • filter transfer functions

Amplifiers and Analog Processing

• Most bioelectric are small • in micro-volts range • currents in pA and nA range common

• Small signals require amplification and filtering • op-amp, and • integrated circuit and surface-mount technology

• Most modern tasks (filtering) are performed on a digital signal processor. • little change in amplification/filtering requirements over last 40 years • but new interest in putting DSP algorithms into analog circuits • due to demand for low power portable/implantable instruments

ECE 445: Biomedical Instrumentation Ch3 Amplifier Basics. p. 2 Ideal Op-Amp

• (op-amp) is a high-DC-gain differential amplifier

• Design circuits assuming op-amps are ideal ideal op-amp • then verify/modify using simulations/prototyping A  

vo  0 • Ideal op-amp model R   • “open loop” gain: A =  d

• differen tia l i nput resi st ance: R d =  Ro  0 • output resistance: Ro = 0 • input current = 0 • output :

• vo = 0 when v1-v2 = 0

ideal op-amp small signal model

ECE 445: Biomedical Instrumentation Ch3 Amplifier Basics. p. 3

Op-Amp Properties

• Properties • open-loop gain: ideally infinite: practical values 20k-200k • high open-loop gain  virtual short between + and - inputs • input impedance: ideally infinite: CMOS opamps are close to ideal • output impedance: ideally zero: practical values 20-100 • zero output offset: ideally zero: practical value <1mV • gain-bdidthdt(GB)bandwidth product (GB): practical val ues ~MH z • frequency where open-loop gain drops to 1 V/V

• Commercial opamps provide many different properties • low noise • low input current • low power • high bandwidth • low/high supply voltage • special purpose: comparator, instrumentation amplifier

ECE 445: Biomedical Instrumentation Ch3 Amplifier Basics. p. 4 Basic Op-Amp Principles

typical op-amp schematic symbol

vo, v1, v2 referenced to ground

• Open loop gain: vo = A (v2-v1) • since A is very large, v1-v2 must be very small • When the op-amp output is in its linear range • two input terminals are at (essentially) the same voltage • i.e., “virtual ground” between op-amp inputs • relthifDC/billtily on this for DC/bias calculations

• Single vs. Dual Supply Voltage • most modern ICs use single supply • “d”dllb“ground” in a dual supply becomes VDD/ 2 in singl le suppl y • mid way between VDD and Ground

ECE 445: Biomedical Instrumentation Ch3 Amplifier Basics. p. 5

Basic Opamp Configuration

• Voltage Comparator • digitize input • assumes veryyg high DC g ain • Vcc = supply voltage

Vref • Negative Feedback • output tied back into negative input Vout = Vcc (sign(Vin-Vref)) terminal • generally avoid positive feedback

• Voltage Follower • buffer • prevents input signal from being loaded down by a low-resistance load Rin = 

ECE 445: Biomedical Instrumentation Ch3 Amplifier Basics. p. 6 Inverting/Non-Inverting Configurations

• Inverting Amplifier (uses negative feedback)

v  R A  o  f vi Ri

• Non-Inver ting Amplifi er ( al so uses negati ve f eedb ack)

v R R  R A  o 1 f  i f vi Ri R f

ECE 445: Biomedical Instrumentation Ch3 Amplifier Basics. p. 7

Transfer Function Derivation

• Ideal op-amp conditions (simplify derivation) • virtual short at inputs (voltage at + same as at - ) • no current into input terminals • Inverting amplifier gain transfer function • write equations of operation from schematic using Ohms law • Vx–Vin = R1 * i1 • Vout – Vx = R2 * i2 i • apply ideal op-amp conditions 2 • virtual short  Vx = 0

• no input current  i1 = i2 = i Vx

• thus i1 • -Vin = R1 * i  i= -Vin/R1 • Vout = R2 * i  i = Vout/R2 • and setting i = i… •  -Vin/R1 = Vout/R2  Vout= -Vin (R2/R1) More Opamp Configurations • Summing Amp • weighted sum of multippple inputs • inverting or non??

• Differential Amp • match R1s and R2s • inverting or non??

Single-Enddded Ampl lfifier Representation noise signal V V V out in out Av  gnd gnd Vin Noise Amplification • even small interf erence at input gets ampl if ied at output

ECE 445: Biomedical Instrumentation Ch3 Amplifier Basics. p. 9

Differential vs. Common Mode Signal

• Define • x+ = input at + terminal • x- = input at – terminal • c = common mode signal on both inputs • Differential inputs   Vout  x  x

• Add common mo de inpu t • c rejected by differential amplifier (not amplified) • c must be small enough to keep op-amp biased in linear operation   Vout  (x  c)  (x  c)   x x x  x c  2

ECE 445: Biomedical Instrumentation Ch3 Amplifier Basics. p. 10 Noise in Differential Amplifiers

• Global interference (e.g., supply voltage variations) • assumed to be located far away from amp. input terminals • same interference on both the terminals • appear as common mode disturbance. • example: clock noise

• Differential amplifiers • amplify only the difference • reject the interference (common-mode)

  Vin + - Vout

 - +  Vin V common-mode gone at out input noise output

ECE 445: Biomedical Instrumentation Ch3 Amplifier Basics. p. 11

Desirable Properties of Amplifiers

• High differential gain, Av V  V    in + - out Vout  Vout Av     - +  Vin  Vin Vin Vout

• Low common mode gain, Acm = high “ common modjtide rejection”   Common-mode signal Vin  Vin   Vout  Vout 2 ACM      Vin  Vin Vin V + - out 2 - + A V  V  common mode rejection ratio: CMRR  v in out Acm

ECE 445: Biomedical Instrumentation Ch3 Amplifier Basics. p. 12 3-Op-Amp Instrumentation Amplifier

• Differential amplifiers • low common mode gain = Great! • lower than ideal input resistance – Bad!

• 3-op-amp structure • klkeeps low common mod die gain • provides very high input resistance • why? • call “instrumentation amp ” • will discuss in detail later

total differential gain 2R  R A  2 1 2R  R  R  R 2 1  4  1 Gd    R1  R3 

Acom 1

ECE 445: Biomedical Instrumentation Ch3 Amplifier Basics. p. 13

Comparator

• Compare an input voltage vi to a reference voltage vref • Output digital value (hi/low)

• liflow if vi > vref whlhy low and not thi? hi? • high if vi < vref • Output voltage = supply voltage • Op-amp comparator

• Add hysteresis to improve noise immunity • hyygpsteresis = rising transition point different that falling gp transition point • R3 controls hysteresis

ECE 445: Biomedical Instrumentation Ch3 Amplifier Basics. p. 14 Logarithmic Amplifiers

• Uses non-linear current-voltage relationship of BJT in feedback path  I   C  VBE  k log   I S  • Useful for computing logarithms and anti-logs • for compressing and multiplying/dividing signals

A10A=10

A=1

A1A=1

A=10

ECE 445: Biomedical Instrumentation Ch3 Amplifier Basics. p. 15

Integrating/Differentiating Configurations

• Integrating Amp 1 t v  i dt   2f C o

• Differentiating Amp

dv i  C dt

ECE 445: Biomedical Instrumentation Ch3 Amplifier Basics. p. 16 Converting Configuration

• Current-to-Voltage

• Voltage-to-Current

ECE 445: Biomedical Instrumentation Ch3 Amplifier Basics. p. 17

Active Filters

• Passive low pass filter

If Z1 is a resistor (R) and Z2 is a capacitor (1/sC) then

• Active low pass filter

(Rf / jCf ) -3dB frequency Vo ( j) Zf [(1/ jCf )  Rf ]     1 V ( j) Z R 0  i i i R f C f R R 1   f   f =2f s (1 jRf Cf )Ri Ri 1 0 V ( j) R 1 o   f Vi ( j) Ri 1 jR f C f

ECE 445: Biomedical Instrumentation Ch3 Amplifier Basics. p. 18 Active Filters

• Active high pass filter

V ( j) R jR C o   f i i Vi ( j) Ri 1 jRiCi 1 0  RiCi

ECE 445: Biomedical Instrumentation Ch3 Amplifier Basics. p. 19

Active Filters Band Pass Filter V ( j) R jR C o   f f i Vi ( j) Ri (1 jR f C f )(1 jRiCi )

2-stage Band Pass Filter

High Q (narrow frequency) Band Pass Filter

ECE 445: Biomedical Instrumentation Ch3 Amplifier Basics. p. 20 Non-ideal Characteristics

• Offset voltage • output not zero when the inputs to the amplifiers are equal • could be in order of millivolts • cancel offset voltage by adding an external “nulling” potentiometer

• Temperature Drift • offset voltage can drift by 0.1 microvolts over one degree variation

• Finite (lower than infinite) input impedance • can cause errors at input • High output impedance • limits load driving capabilities

• Noise • Thermal noise or high -frequency noise • Flicker noise: low-frequency noise

ECE 445: Biomedical Instrumentation Ch3 Amplifier Basics. p. 21