Waveform Generators and Non-linear Circuits

Abstract

In this chapter, we consider circuits that involve non-linear operation of the operational amplifier. These can be used to realize waveform generators which are circuits that produce a variety of non-sinusoidal waveforms. They are fundamentally instrumentation building blocks used for signal generation and test and measurement. Typically, waveform generators produce square waves, triangular waves, pulses and in some cases arbitrary waveforms over a range of frequencies with constant amplitude. Here we discuss comparators, op-amp-based free-running (astable) and one-shot (monostable) multivibrator circuits as well as precision rectifiers and other non-linear circuits. At the end of the chapter, the student will be able to:

Problems

• 1. An op-amp is connected as a comparator with the inverting terminal held at 3 V. Describe the action of the circuit when the non-inverting input is below and above 3 V.

• 2. An op-amp is connected as a comparator with the non-inverting terminal held at 2 V. Describe the action of the circuit when the inverting input is below and above 2 V.

• 3. Using the basic circuit shown in Fig. 13.4, design a system to turn on an alarm when the ambient temperature in a room exceeds 70 °C.

• 4. Investigate the use of a thermistor for temperature control.

• 5. Design a Schmitt trigger circuit with a switching threshold of ±7.5 V using an op-amp powered by ±15 V supplies. For the op-amp, assume |V_omx| = |V_omn| = 13.2 V and A_d = 150, 000.

• 6. Using an op-amp, design a square-wave oscillator to have an oscillation frequency of 25 kHz, with an output of ±9 V using a ±15 V split supply.

• 7. For the Schmitt trigger circuit shown in Fig. 13.57 determine its threshold voltages and sketch its transfer characteristic. You may assume the output voltage is limited to the range V_omn ≤ V_o ≤ V_omx. What are the differences between this circuit and the one shown in Fig. 13.58?

• 8. If an input voltage V_ref is now applied to the inverting input, repeat Question 7.

• 9. For the collection of circuits in Fig. 13.59, determine their threshold voltages and sketch their transfer characteristics. The output level of the comparator is ±10 V. For Fig. 13.59, you may assume α = 0.3, 0.5 and 0.8.

• 10. In the circuit of Fig. 13.60, let R₁ = 220 kΩ, C₁ = 2.2 nF, R_a = 10 kΩ, R_b = 20 kΩ and the circuit be supplied with ±15 V supplies. For this circuit determine f_osc.

• 11. An alternative method of duty cycle control for the free-running multivibrator is shown in Fig. 13.61. Determine an expression for f_osc and the duty cycle, D, expressed as $D=\frac{T_1}{T_1+{T}_2}\times 100\%$ in terms of v_ctrl.

• 12. Design a square-wave/sawtooth oscillator that oscillates at a frequency of 1 kHz.

• 13. Design a triangular wave generator to generate a positive-going sawtooth wave of 8 V pk-pk amplitude with a frequency of 500 Hz with a ±15 V supply.

• 14. Describe the operation of a square/triangular voltage-controlled oscillator and derive an expression for the frequency of operation.

• 15. The variable frequency oscillator of Fig. 13.62 is set up using a TL082 op-amp and two multipliers (AD534) whose K₁ = K₂ = 0.2. You may assume that C₁ = C₂ = 0.003 μF and R₂ = 2.5 k. Determine the frequency of oscillation if V_c is varied from 1 to 0.4 V.

• 16. A monostable multivibrator is constructed using the circuit of Fig. 13.63. The values chosen were R₁ = 2 k, R₂ = 3 k, R = 1 k, C = 0.3 μF and V_cc = 15 V. Determine the period of this multivibrator if the voltage of each Zener diode is V_Z = 8.2 V.

• 17. Show how a JFET can be used to improve the operation of the monostable multivibrator in Fig. 13.63.

• 18. Describe the operation of the 555 timer and its use as an astable multivibrator. Hence design an astable multivibrator using the 555 to oscillate at 10 kHz. Show how a diode can be used to achieve 50% duty cycle.

• 19. An astable 555 oscillator is constructed using R_a = 5 k, R_b = 5 k and capacitor C = 0.01 μF. Calculate the output frequency of the square wave delivered by the 555 oscillator and the duty cycle of the output waveform.

• 20. Discuss the use of the 555 timer as a monostable multivibrator.

• 21. A monostable 555 timer is required to produce a specified time delay in a circuit. If a 3.3 μF timing capacitor is used, calculate the value of the resistor required to produce a minimum output time delay of 120 ms.

• 22. Explain the operation of the half-wave rectifier shown in Fig. 13.64, and determine the polarity of the output signal.

• 23. For the precision full-wave rectifier shown in Fig. 13.65, describe the operation of the system and determine the polarity of the output signal.

• 24. Using the circuit in Fig. 13.65, design a precision full-wave rectifier to operate at 10 kHz and below.

• 25. Using the circuit in Fig. 13.66, design a high input impedance precision full-wave rectifier.

• 26. Using the circuit in Fig. 13.67, design a precision full-wave rectifier.

Fig. 13.57

Circuit for Question 7

Fig. 13.58

Circuit for Question 7

Fig. 13.59

Circuits for Question 9

Fig. 13.60

Circuit for Question 10

Fig. 13.61

Circuit for Question 11

Fig. 13.62

Circuit for Question 15

Fig. 13.63

Circuit for Question 16

Fig. 13.64

Circuit for Question 22

Fig. 13.65

Circuit for Question 23

Fig. 13.66

Circuit for Question 25

Fig. 13.67

Circuit for Question 26