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Circuits for sensors Ideal OP Amps Basic OP Amp Circuit Blocks Analog Computation Nonlinear OP Amp Applications OP Amp Considerations Guarding Passive Filters Active Filters VCO(Voltage Controlled Oscillator) Function of Amplifiers Amplifiers provides GAIN Filtering, Signal processing, Correction for Nonlinearities Temperature Pressure Flow Motion …. Chap 0 Sensor Signal Conditioning Circuitry Digital Computer 2 Ideal OP Amps Transfer Function = Output / Input Voltage Amp TF (Gain): Av vo vi Av 1 OP Amp is preferred Usually Easy to use in circuit designed compared to discrete Transistor circuits Chap 0 3 Ideal OP Amps (Cont.) Assumptions Open loop Gain = Infinity Input Impedance Rd = Infinity Output Impedance Ro = 0 Bandwidth = Infinity Infinite vo=0 when v1 = v2 No Chap 0 Frequency Response Offset Voltage 4 Ideal OP Amps (Cont.) Note v0 = A(v2 – v1) If v0 = , A = (Typically 100,000) • Then v2 – v1 = 0 v2 = v1 Since v2 = v1 and Rd = • We can neglect the current in Rd Rule 1 Rule 2 Chap 0 When the OP Amp is in linear range the two inputs are at the same voltage No Current flows into either terminal of the OP Amp 5 Basic OP Amp Circuit Blocks Chap 0 Inverting Amplifier Noninverting Amplifier Unity-Gain Amplifier Differential Amplifier Instrumental Amplifier The Electrocardiogram Amplifier 6 Inverting Amplifier Inverting Amp with Gain = - Rf / Ri From Rule 1 v- = v+ = 0 From Rule 2 & KCL + if = 0 ii = -if From Ohm’s law ii ii vi = vi / Ri , , if = vo / Rf / R i = - v o / Rf vo Virtual Ground Chap 0 / vi = -Rf / Ri Inverting Amp Gain -Rf / Ri 7 Inverting Amplifier (Cont.) Linear Range By Power Supply Voltage Input Impedance Low (Ri) Increasing Ri Decreasing Gain Increasing Gain by increasing Rf • But there is practical limit Saturation Chap 0 8 Noninverting Amplifiers Noninverting Amp By Rule 2 Vo = If (Rf + Ri) Vi = If Ri Vo = Vi (Rf + Ri)/Ri Gain = (Rf + Ri) / Rf Gain: Vo/Vi = 1 + Rf / Ri Gain 1, Always Input Impedance Very Large (Infinite) By Rule 1 Vi Chap 0 9 Unity-Gain Amplifier Verify that the Gain of Unity-Gain Amp is 1 Vo = Vi Applications Buffer amplifier Impedance converter Chap 0 Isolate one circuit from the loading effects of a following stage Data conversion System (ADC or DAC) where constant impedance or high impedance is required 10 Differential Amplifiers Combination of Inverting and Noninverting Amp Can reject 60Hz interference Electrocardiogram amplifier Instrumentation Differential Chap 0 Noninverting 11 Differential Amplifiers (Cont.) Gain of Differential Amp By Rule 2 V5 = I2 * R2 V2 = I2 * R1 + V5 = V5 * R1 /R2 + V5 V5 = R2 * V2 / (R1 + R2) By Rule 1 V1 = R1 * I1 + V5 V5 = R2 * I1 + V6 V6 = (V2 – V1) * R2 / R1 Chap 0 12 Differential Amplifiers (Cont.) CMV (Common Mode Voltage) CMG (Common Mode Gain) = 0 DG(Differential voltage Gain) If V1 = V2, then V6 = 0 If V1 V2, then V6 = (V2-V1)*(R2/R1) In practice, CMG 0 CMRR (Common Mode Rejection Ratio) Measure of the ability to reject CMV CMRR = DG / CMG The Higher CMRR, the better quality Typically, 100 ~ 10,000 60Hz noise common to V1 and V2 can be rejected Chap 0 13 Instrumentation Amplifiers One OP Amp Differential Amplifier Input Impedance is not so High Good for Low impedance source • Strain gage Bridge Bad for High impedance source Instrumentation Amplifier Differential Amp with High Input Impedance and Low Output Impedance Two Noninvering Amp + One Differential Amp Chap 0 14 Instrumentation Amplifiers (Cont.) Instrumentation Amp = Noninverting Amp + Differential Amp We have: DG = (V1-V2) / (V3-V4) = (2*R4 + R3) / R3 V6 = (V3-V4)*DG*R2 / R1 First Stage CMRR CMRR Overall CMG = 0 High Chap 0 = DG / CMG = DG CMRR High Input Impedance Gain is adjustable by changing R3 15 The Electrocardiogram Amplifier Low Pass Filter < 100Hz < 0.2 V Gain = 40 Gain = 32 Maximize CMRR Chap 0 High Pass Filter >0.05Hz 16 Analog Computation Circuit Digital Signal Processing is preferred Flexibility Easy to Change Elimination of hardware However, Analog Signal Processing Is preferred when DSP consumes too much time Chap 0 17 Inverter and Scale Changer Inverting Amp with Gain = - Rf / Ri Inverter Inverter and Scale Changer Proper choice of Rf / Ri Application Chap 0 Rf / Ri = 1 Use of inverter to scale the output of DAC 18 Adders (Summing Amplifiers) Adder Inverter with Several inputs If = I1 + I2 + In I1 = V1/R1, … Vo = -If * Rf Chap 0 Vo = -Rf(V1/R1 + V2/R2 +… + Vn/Rn) Rf determines overall Gain Ri determines weighting factor and input impedance 19 Integrator Drawbacks 1 t1 v0 vi dt vic 0 RC Vo will reach saturation voltage, if Vi is left connected indefinitely Chap 0 Integrator operates as an open-loop amplifier for DC inputs 20 Practical Integrator Reset S1 Controlled By Relay or Solid State Switch or Analog Switch Open, S0 Closed Hold S1 Open, S0 Open Keeps Vo constant Chap 0 Inverter C is initialized to Vr Integrate S1 Closed, S0 Open Read and Process 21 Differentiators Drawbacks v0 RC dvi dt Practical Differentiator Chap 0 Instability at High frequencies To Stable Ri R A0 0 C 22 Comparators Compare Two Inputs Vi > Vr Vi < Vr Chap 0 Vo = -Vs Drawbacks If Vi = Vr + small noise Rapid fluctuation between Vs Vo = Vs 23 Comparators with Hysteresis Positive Feedback Hysteresis loop Can remove the effect of Small Noise Chap 0 Reduce Fluctuation (VS Vr ) R1 Vr Vr Vr R1 R2 (VS Vr ) R1 Vr Vr Vr R1 R2 24 Rectifiers Chap 0 Precision Half Wave Rectifier Precision Full Wave Rectifier Limiters 25 OP Amp Considerations Effects of Nonlinear characteristics Compensation Undesirable Oscillation at High frequency • Add external Capacitance according to Spec sheet GBW (Gain Bandwidth Product) Gain Bandwidth = Constant (Typically 1MHz) • For Noninverting Amp: Bandwidth = GBW / Gain Input Offset Voltage Practical OP Amp • Zero input Does NOT give Zero output Input Offset Voltage • Applied input voltage to obtain Zero output Nulling the offset Voltage • Adding External Resister according to Spec sheet Chap 0 26 OP Amp Considerations (Cont.) Input Bias Current Practical OP amp • Current flowing into the terminal is NOT Zero • To keep the input Tr of OP amp turned on • Causes errors proportional to feedback network R To minimize errors • feedback R should be low (<10K) Slew Rate Maximal rate of change of amplifier output voltage • Ex: Slew rate of 741 = 0.5 V / s – Time to output change from –5V to 5V = 20 s To Minimize slew rate problem • Use OP amp with smaller external compensating C Chap 0 27 OP Amp Considerations (Cont.) Power Supply Usually 15V • Linear Range 13V Reducing power supply voltage • Results reduced linear range • Device does not work < 4V Different OP Amps Bipolar Op Amps • Good input offset stability • Moderate input bias current and Input resistances FET • Very Low input bias current and Very High Input resistances • Poor Input offset voltage stability Chap 0 28 Guarding Elimination of Surface Leakage Currents Elimination of Common Mode Signals Very important in practice But Chap 0 skip in this course 29 Passive Filters Passive Circuits Contains only passive elements Registers, Capacitors and Inductors Examples Bridge Circuit Voltage Divider Filters Filters Eliminate unwanted signal from the loop Low Pass, High Pass, Band Pass, Notch, … Chap 0 30 Passive first-order Low pass Filter Pass desired Audio signal and reject undesired RF Order of Filter Chap 0 Number of C and L Vo 1 , RC Vi 1 j Plot Magnitude and Phase plot (Bode plot) Meaning of C 31 Passive first-order High pass Filter Chap 0 Pass desired High frequency signal and reject undesired low frequency signal Vo j , RC Vi 1 j Plot Magnitude and Phase plot (Bode plot) Meaning of C 32 Passive second-order Low pass Filter To increase the attenuation of transfer function Order of Filter Vo 1 Vi ( j / c ) 2 (2 j / c ) 1 c 1 R C , LC 2 L Meaning of Quality factor Number of C and L Q 1 c , 3dB BW 2 1 1 1 Chap 0 33 Passive second-order High pass Filter To increase the attenuation of transfer function Order of Filter Number of C and L Vo 2 Vi ( j / c ) 2 (2 j / c ) 1 c 1 R C , LC 2 L 1 1 Chap 0 1 34 Active First-order Low Pass Filter Inverting Amp + Feedback Capacitor Identical frequency response with Passive filter Very Low Output impedance Chap 0 Negligible Loading Effect 35 Active First-order High Pass Filter Inverting Amp + Input Capacitor Identical frequency response with Passive filter Very Low Output impedance Chap 0 Negligible Loading Effect 36 Active High-order Filters Chap 0 Low Pass Filters High Pass Filters 37 Bandpass and Band-reject Filters Butterworth Filters Maximally Flat Magnitude response in pass band High Attenuation Rate Chebyshev Filters Maximum Attenuation Rate Ripple in pass band Bessel Filters Maximally flat time delay in response to step input Attenuation Rate is very gradual Chap 0 38 Filter Design Table Chap 0 C when 0 = R0 = 1 39 Filter Design Example Low pass five-pole Butterworth filter with a corner frequency of 200Hz and input resistance of 50K Economic Solution = 3rd order + 2nd order Desired R and C ? C1A = (0 R0 C0 ) / ( R) = 1x1x1.753 / 2x200x50K = 27.9 nF C2A = 21.6 nF, C3A = 6.7 nF, C1B = 51.5 nF, C2B = 4.9 nF Chap 0 40 VCO(Voltage Controlled Oscillator) VCO = Voltage to Frequency(V/F) Converter VCO converts an input voltage to a series of output digital pulses whose frequency is proportional to the input voltage Applications ADC Digital Transmission Telemetry Digital Voltmeter Chap 0 41 VCO (Cont.) Module form Better linearity, Lower Gain drift, Higher full-scale frequencies than IC Monolithic IC form Less expensive, Small size Lower drift, Better flexibility of frequency range Examples LM331 Low cost VCO from National Semiconductor Maximum nonlinearity 0.01% over 1 ~ 100KHz CD4046B PLL contains VCO Maximum nonlinearity 1.0% over 1 ~ 400MHz Chap 0 42 PLL(Phase Locked Loop) VCO is commonly used in PLL Applications Communications Radar Time and frequency control Instrumentation system Control loop Goal Chap 0 Minimize z(t) s(t) = r(t) Change r(t) until z(t)=0 s(t) can be obtained By reading r(t) 43 VCO Interfacing Output of VCO Digital pulses whose frequency is proportional to input voltage # of pulse / Duration Duration # of Pulse Chap 0 Controlled by Sampling Gate Counted in Counter 44 Divider Circuit Convert Register Variations to Voltage Variations Output Voltage Vo = {R2 / (R1 + R2)} Vs Vs R1 Vo R2 Chap 0 45 Divider Circuit: Drawbacks Vo is not linearly changed Ex: Vs = 5V, R1 = 1K, R2 = 0 ~ 1K(Sensor) Vo Vs/2 Vs/3 R2 500 Chap 0 1K Output Impedance(R1 || R2) is not so High Large Power Consumption 46 Divider Circuit: Example R1 = 10K, R2 = (4K ~ 12K), Vs = 5V Maximum Vo = 5 {12 / (10+12)} = 2.73V Minimum Vo = 5 { 4 / (10 + 4)} = 1.43V Maximum Z = (10K || 12K) = 120/22 K Minimum Z = (10K || 4K) = 40/14 K Maximum Power = (Vo)2/R2 = (2.73)2/12K = 0.62mW Minimum Power = (1.43)2/4K = 0.51mW Chap 0 47