Electronics Primer • ohms law • Kirchhoff's current node rule • define resistor • define capacitor • high/low pass RC filters • s = jw j notation, t ti w=2 2pii f • filter transfer functions Amplifiers and Analog Signal Processing • Most bioelectric signals are small • voltages in micro-volts range • currents in pA and nA range common • Small signals require amplification and filtering • op-amp, resistors and capacitors • integrated circuit and surface-mount technology • Most modern signal processing 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 • Operational amplifier (op-amp) is a high-DC-gain differential amplifier ideal op-amp • Design circuits assuming op-amps are ideal A vo 0 • then verify/modify using simulations/prototyping • Ideal op-amp model Rd • “open loop” gain: A = • differential diff ti l input i t resistance: i t Rd = • output resistance: Ro = 0 Ro 0 • input current = 0 • output voltage: • 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-bandwidth i b d idth product d t (GB): (GB) practical ti l values l ~MHz MH • 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 • rely l on this thi for f DC/bias DC/bi calculations l l ti • Single vs. Dual Supply Voltage • most modern ICs use single supply • “ground” “ d” in a d duall supply l becomes b VDD/2 / in single l supply l • mid way between VDD and Ground ECE 445: Biomedical Instrumentation Ch3 Amplifier Basics. p. 5 Basic Opamp Configuration • Voltage Comparator • digitize input g DC gain g • assumes veryy high • Vcc = supply voltage Vref • Negative Feedback • output tied back into negative input terminal • generally avoid positive feedback Vout = Vcc (sign(Vin-Vref)) • 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) A vo R f vi Ri • Non-Inverting N I ti A Amplifier lifi (also ( l uses negative ti feedback) f db k) A R f Ri R f vo 1 vi Ri Rf 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 • V Vx – Vin = R1 * i1 • Vout – Vx = R2 * i2 i2 • apply ideal op-amp conditions • virtual short Vx = 0 • no input current i1 = i2 = i • thus • -Vin = R1 * i i = -Vin/R1 • Vout = R2 * i i = Vout/R2 • and setting i = i… • -Vin/R1 = Vout/R2 Vout= -Vin (R2/R1) Vx i1 More Opamp Configurations • Summing Amp • weighted sum of p inputs p multiple • inverting or non?? • Differential Amp • match R1s and R2s • inverting or non?? Single-Ended l d d Amplifier l f Representation signal noise V in V out gnd gnd Av Noise Amplification Vout Vin • even smallll interference f at input gets amplified l f d 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 d iinputt • Add common mode • c rejected by differential amplifier (not amplified) • c must be small enough to keep op-amp biased in linear operation x x Vout ( x c) ( x c) 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 Vin + - - + Vout Vout g gone at output common-mode input noise ECE 445: Biomedical Instrumentation Ch3 Amplifier Basics. p. 11 Desirable Properties of Amplifiers • High differential gain, Av Vin Vout + - + Vin Vout Vout Vout Av Vin Vin • Low common mode gain, Acm = high hi h “common “ mode d rejection” j ti ” Common-mode signal in V Vin + - + Vin Vin 2 ACM Vout Vout Vout Vout Vin Vin 2 common mode rejection ratio: ECE 445: Biomedical Instrumentation CMRR Av Acm 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 • keeps k llow common mode d gain i • provides very high input resistance • why? • call “instrumentation instrumentation amp amp” • will discuss in detail later total differential gain 2 R R1 R4 Gd 2 R1 R3 A 2 R2 R1 R1 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) • llow if vi > vref why h low l and d nott hi? • high if vi < vref • Output voltage = supply voltage • Op-amp comparator • Add hysteresis to improve noise immunity • hysteresis y = rising g transition point p different that falling g transition point p • 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 IC VBE k log IS • Useful for computing logarithms and anti-logs • for compressing and multiplying/dividing signals A 10 A=10 A=1 A 1 A=1 A=10 ECE 445: Biomedical Instrumentation Ch3 Amplifier Basics. p. 15 Integrating/Differentiating Configurations • Integrating Amp t 1 v i dt Co 2f • Differentiating Amp iC dv 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 / jCf ) Vo ( j ) Z [(1 / jCf ) Rf ] f Ri Vi ( j ) Zi Rf R 1 f (1 jRf Cf ) Ri Ri 1 s -3dB 3dB frequency 0 1 R C f f =2f 0 Rf Vo ( j ) 1 Vi ( j ) Ri 1 jR f C f ECE 445: Biomedical Instrumentation Ch3 Amplifier Basics. p. 18 Active Filters • Active high pass filter R f jRi Ci Vo ( j ) Vi ( j ) Ri 1 jRi Ci 0 1 R C i i ECE 445: Biomedical Instrumentation Ch3 Amplifier Basics. p. 19 Active Filters Band Pass Filter Rf jR f Ci Vo ( j ) Vi ( j ) Ri (1 jR f C f )(1 jRi Ci ) 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 high-frequency frequency noise • Flicker noise: low-frequency noise ECE 445: Biomedical Instrumentation Ch3 Amplifier Basics. p. 21