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Today • Course overview and information 09/16/2010 © 2010 NTUST Comparators Comparator • Op-amps can be used to compare the amplitude of one voltage with another. Although general-purpose op-amps can be used as comparators, special op-amps are available to optimize speed and add features. +V • An example of a comparison circuit is shown. The input is compared with a reference set by the voltage-divider. Notice that there is no feedback; the op-amp is operated in open-loop, so the output will be in saturation. R1 Vin + R2 Vout Examples Sketch the output of the comparator in relationship to the input; assume the maximum output is ±13 V. The threshold is +4.2 V. The output is in positive saturation when Vin > +4.2 V V = +15 V R1 10 kW Vin +10 V +4.2 V Vin 0V -10 V +13 V + R2 3.9 kW Vout 0V -13 V Examples Show the output of the comparator for the last example if the inputs to the op-amp are reversed. The threshold is still +4.2 V but now the output is in negative saturation +10 V when Vin > +4.2 V. +4.2 V Vin 0V V = +15 V R1 10 kW -10 V +13 V + - Vin R2 3.9 kW Vout 0V -13 V Summing Amplifier • There are a number of useful applications for the basic inverting amplifier configuration. One is the summing amplifier that uses two or more inputs and one output. • The virtual ground isolates R1 Rf VIN1 the inputs from each other. R2 Input current from each input VIN2 R3 is passed to Rf, which VIN3 + develops an output voltage Rn that is proportional to the VINn algebraic sum of the inputs. Virtual ground VOUT Summing Amplifiers Averaging Amplifier • An averaging amplifier is a variation of the summing amplifier in which all input resistors are equal. The feedback resistor is the reciprocal of the number of inputs times the input resistor value. • For example, if there are three input resistors, each with a value of 10 kW, then Rf = 3.3 kW to form an averaging amplifier. VIN1 VIN2 VIN3 R1 Rf 10 kW R2 3.3 kW 10 kW R3 10 kW + VOUT Averaging Amplifiers Scaling Adder Scalingadder adder • A scaling is another variation of the summing amplifier in which the input resistors are adjusted to weight inputs differently. The input “weight” is proportional to the current from that input. • Larger resistors will allow R1 Rf less current for a given VIN1 10 kW 10 kW input voltage, so they R2 VIN2 have less “weight” than VOUT 5.0 kW + smaller resistors. In the R3 VIN3 case shown, VIN3 is 2.5 kW “weighted” 2 times more than VIN2, which is 2 times more than VIN1. Scaling Adder What is VOUT for the scaling adder if all inputs are + 1.0 V? By Ohm’s law, the currents into Rf are I1 = 0.1 mA, I2 = 0.2 mA and I3 = 0.4 mA. Using the superposition theorem, the current in Rf is 0.7 mA. From Ohm’s law, VOUT = 7 V VIN1 VIN2 VIN3 R1 Rf 10 kW R2 10 kW 5.0 kW R3 2.5 kW + VOUT Integrators Integratorsintegration is basically a summing process. • Mathematical Within certain limitations, an integrator circuit simulates this process. • The ideal integrator is essentially a summing amplifier with a capacitor in place of the feedback resistor. Vin Rf C In practical circuits, a large value resistor is usually in parallel with the capacitor to prevent the output from drifting into saturation. R + Vout Integrators • ForIntegrators the ideal integrator, the rate of change of the output is Vout Vin given by t Ri C • The minus sign in the equation is due to the inverting amplifier. If the input is a square wave centered about 0 V, the output is a negative triangular wave (provided saturation is not reached). C Vin Vin 0V R + Vout 0V Vout Integrator Example A 5 kHz square wave with 10 Vpp is applied to a practical integrator. Show the output waveform voltages. During the positive input (½ the period), the change in the output is V 5V Vout - in t 100 μs = 5.6 V Ri C 2.7 kW 33 nF Rf 270 kW C Vin R 2.7 kW 33 nF + Vout The feedback resistor (Rf) is large compared to R, so has little effect on the shape of the waveform. In a practical circuit, it will cause the output waveform to center on zero as shown on the following slide. Example continued… The results of a computer simulation on Multisim confirm the calculated change (5.6 V) in output voltage (blue line). Rf 270 kW C Vin R 2.7 kW 33 nF + Vout Example Examples Examples Differentiators Differentiators • In mathematics, differentiation is the process of finding the rate of change. An idea differentiator circuit is shown. It produces an inverted output that is proportional to the rate of change of the input. In practical circuits, a small value resistor is added in series with the input to prevent high frequency ringing. Vin Rin Vin Rf C + Vout Differentiator Differentiators The output voltage for the ideal differentiator is given by Vout VC - t Rf C • The minus sign in the equation is due to the inverting amplifier. If the input is a ramp, the output is a negative dc level for the positive slope and a positive dc level for the negative slope. Rf Vin Vin Vout C + Vout Differentiator Examples A 1.0 kHz, 10 Vpp triangular wave is applied to a practical differentiator as shown. Show the output in relationship to the input. When the input has a positive slope, the output is V Vout - C t 10 V R C 2.7 kW 100 nF -5.4 V f 0.5 ms By symmetry, when the input has a negative slope, the Rf output will be +5.4 V. Rin Vin +5.0 V Vin 2.7 kW C 120 W 100 nF - Vout + 0V -5.0 V 0 1 ms 2 ms See next slide for waveforms… Examples continued… The results of a computer simulation on Multisim confirm the calculated output voltages (±5.4 V). The output voltage is the blue line. Examples Examples Examples Selected Key Terms Summing An amplifier with several inputs that amplifier produces an output voltage proportional to the algebraic sum of the inputs. Averaging An amplifier with several inputs that amplifier produces an output voltage that is the mathematical average of the input voltages. Scaling adder A special type of summing amplifier with weighed inputs. Selected Key Terms Integrator A circuit that produces an inverted output that approaches the mathematical integral of the input. Differentiator A circuit that produces an inverted output that approaches the mathematical derivative of the input, which is the rate of change. Active filter A frequency selective circuit consisting of active devices such as transistors or op-amps combined with reactive (RC) circuits. Series regulator A type of voltage regulator with the control element in series between the input and output. Quiz 1. When an op-amp is configured as a comparator, the gain is equal to a. 0. b. 1. c. a ratio of two resistors. d. the open-loop gain. Quiz 2. The approximate voltage at the inverting input of the op-amp shown is equal to a. the average of the input voltages. b. the sum of the input voltages c. 0 V d. VOUT 3 VIN 1 VIN 2 VIN 3 R1 Rf 10 kW R2 3.3 kW 10 kW R3 10 kW - + VOUT Quiz 3. For the scaling adder shown, the input with the greatest weight is R1 R f VIN a. VIN1 b. VIN2 c. VIN3 1 VIN 2 VIN 3 d. they are all equal 10 kW R2 5.0 kW R3 2.5 kW 10 kW + VOUT Quiz 4. In a practical integrator, the purpose of the feedback resistor (Rf) is to a. limit the gain. b. prevent drift. Rf c. prevent oscillations. C d. all of the above. Vin R + Vout Quiz 5. Assume the top waveform represents the input to a differentiator circuit. Which represents the expected output? V i n a. b. c. d. Quiz 6. The lead-lag network in a Wien bridge with equal value R’s and C’s attenuates the signal by a factor of a. 2 b. 3 c. 5 d. 10 Quiz 7. A Wien-bridge is used to produce a. sine waves. b. square waves. c. triangle waves. d. all of the above. Quiz 8. For the circuit shown, the two outputs (in red) produce a. sine and square waves. b. triangle and square waves. c. sine and triangle waves. C Vout waves. d. sawtooth and triangle + Comparato r R1 Vout R2 R3 + Integrator Quiz 9. The purpose of the op-amp in the series regulator is a. to sample the output. b. to establish a reference. c. as a control element. d. error detection. Q1 VIN VOUT R1 + - R2 R3 Quiz 10. An advantage of a shunt regulator is a. short circuit protection. b. efficiency. c. no need for a reference voltage. d. all of the above. Quiz Answers: 1. d 6. b 2. c 7. a 3. c 8. b 4. b 9. d 5. c 10. a