Electronics Primer • ohms law • Kirchhoff's current node rule • define resistor • define capacitor • high/low pass RC filters • s = jtti2ifjw notation, w = 2pi 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 • 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 input res is tance: R d = Ro 0 • output resistance: 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-bdidthdt(GB)bandwidth product (GB): practica l 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 2f 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 / jCf ) -3dB frequency Vo ( j) Zf [(1/ jCf ) Rf ] 1 V ( j) Z R 0 i i i R f C f R R 1 f f =2f s (1 jRf Cf )Ri Ri 1 0 V ( j) R 1 o f Vi ( j) Ri 1 jR f C f ECE 445: Biomedical Instrumentation Ch3 Amplifier Basics. p. 18 Active Filters • Active high pass filter V ( j) R jR C o f i i Vi ( j) Ri 1 jRiCi 1 0 RiCi ECE 445: Biomedical Instrumentation Ch3 Amplifier Basics. p. 19 Active Filters Band Pass Filter V ( j) R jR C o f f i Vi ( j) Ri (1 jR f C f )(1 jRiCi ) 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.