09/16/2010© 2010 NTUST Today Course overview and information

Comparators

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. 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. V in R1R1 V out +  R2R2 +V Comparator

Sketch the output of the comparator in relationship to the input; assume the maximum output is ±13 V. V in R1R1 V out +  R2R2 V = +15 V 10 k  3.9 k  The threshold is +4.2 V. The output is in positive saturation when V in > +4.2 V V in +10 V  10 V 0 V +4.2 V +13 V  13 V 0 V Examples

Show the output of the comparator for the last example if the inputs to the op-amp are reversed. V in R1R1 V out +  R2R2 V = +15 V 10 k  3.9 k  The threshold is still +4.2 V but now the output is in negative saturation when V in > +4.2 V. V in +10 V  10 V 0 V +4.2 V +13 V  13 V 0 V Examples

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. R1R1 V IN1 V IN2 V IN3 V INn R2R2 R3R3 RnRn RfRf +  V OUT The virtual ground isolates the inputs from each other. Input current from each input is passed to R f, which develops an output voltage that is proportional to the algebraic sum of the inputs. Virtual ground Summing Amplifier

Summing Amplifiers

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. R1R1 V IN1 V IN2 V IN3 R2R2 R3R3 RfRf +  V OUT For example, if there are three input resistors, each with a value of 10 k , then R f = 3.3 k  to form an averaging amplifier. 10 k  3.3 k  Averaging Amplifier

Averaging Amplifiers

Scaling adder A scaling adder 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. R1R1 V IN1 V IN2 V IN3 R2R2 R3R3 RfRf +  V OUT Larger resistors will allow less current for a given input voltage, so they have less “weight” than smaller resistors. In the case shown, V IN3 is “weighted” 2 times more than V IN2, which is 2 times more than V IN1. 10 k  5.0 k  2.5 k  10 k  Scaling Adder

R1R1 V IN1 V IN2 V IN3 R2R2 R3R3 RfRf +  V OUT 10 k  5.0 k  2.5 k  10 k  What is V OUT for the scaling adder if all inputs are V? By Ohm’s law, the currents into R f are I 1 = 0.1 mA, I 2 = 0.2 mA and I 3 = 0.4 mA. Using the superposition theorem, the current in R f is 0.7 mA. From Ohm’s law, V OUT = 7 V Scaling Adder

Integrators Mathematical integration is basically a summing process. 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. R C V in V out In practical circuits, a large value resistor is usually in parallel with the capacitor to prevent the output from drifting into saturation. RfRf +  Integrators

For the ideal integrator, the rate of change of the output is given by R C V in V out 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). V in V out 0 V +  Integrators

Integrator

R C V in V out A 5 kHz square wave with 10 V pp is applied to a practical integrator. Show the output waveform voltages. 33 nF 2.7 k  270 k  RfRf During the positive input (½ the period), the change in the output is 5.6 V The feedback resistor (R f ) 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

R C V in V out 33 nF 2.7 k  270 k  RfRf The results of a computer simulation on Multisim confirm the calculated change (5.6 V) in output voltage (blue line). continued… +  Example

Examples

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. +  C V in V out In practical circuits, a small value resistor is added in series with the input to prevent high frequency ringing. R in V in RfRf Differentiators

The output voltage for the ideal differentiator is given by +  RfRf C V in V out 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. V in V out Differentiator

A 1.0 kHz, 10 V pp 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 RfRf C V in 100 nF 2.7 k  120  +  V out R in V in +5.0 V  5.0 V 0 V  5.4 V By symmetry, when the input has a negative slope, the output will be +5.4 V. See next slide for waveforms… 0 1 ms 2 ms 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

Summing amplifier Averaging amplifier Scaling adder An amplifier with several inputs that produces an output voltage proportional to the algebraic sum of the inputs. A special type of summing amplifier with weighed inputs. An amplifier with several inputs that produces an output voltage that is the mathematical average of the input voltages. Selected Key Terms

Integrator Differentiator Active filter Series regulator A frequency selective circuit consisting of active devices such as transistors or op-amps combined with reactive (RC) circuits. A circuit that produces an inverted output that approaches the mathematical integral of the input. A circuit that produces an inverted output that approaches the mathematical derivative of the input, which is the rate of change. A type of voltage regulator with the control element in series between the input and output. Selected Key Terms

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 R1R1 V IN 1 V IN 2 V IN 3 R2R2 R3R3 RfRf +  V OUT 10 k  3.3 k  a.the average of the input voltages. b.the sum of the input voltages c.0 V d. Quiz

3. For the scaling adder shown, the input with the greatest weight is a. V IN1 b. V IN2 c. V IN3 d.they are all equal R1R1 V IN 1 V IN 2 V IN 3 R2R2 R3R3 RfRf +  V OUT 10 k  5.0 k  2.5 k  10 k  Quiz

4. In a practical integrator, the purpose of the feedback resistor (R f ) is to a. limit the gain. b. prevent drift. c. prevent oscillations. d. all of the above. R C V in V out +  RfRf Quiz

5. Assume the top waveform represents the input to a differentiator circuit. Which represents the expected output? VinVin 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. d. sawtooth and triangle waves. Comparato r Integrator +  +  R3R3 R2R2 R1R1 C V out 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. V OUT +  R3R3 R2R2 R1R1 V IN Q1Q1 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 2. c 3. c 4. b 5. c 6. b 7. a 8. b 9. d 10. a Quiz