Analog Function Circuits

Fundamentals, Principles, Design and Applications

K. C. Selvam

• Publisher: CRC Press
• Year: 2021
• Print ISBN: 9781032081601
• eBook ISBN: 9781000484311
• Topic: Technology & Engineering
• Subtopic: Electrical Engineering & Telecommunications
• Index: Technology & Engineering

This textbook comprehensively presents different types of analog function circuits and outlines the function circuit types implemented with lowpass filters, peak detectors, and sample and hold circuits. The text analyzes the complete architecture of a function circuit, identifies the applications of op-amps for performing a function circuit, and explores new ways of deriving function circuits using a sawtooth wave generator and a triangular wave generator. It covers important topics including waveform generators, analog dividers, time division multipliers-cum-dividers (MCDs), peak responding MCDs, vector magnitude circuits, multifunction converters, and phase sensitive detector circuits. The textbook will serve as an ideal study material for senior undergraduate and graduate students in the fields of electrical, electronics, and communications engineering. The textbook is accompanied by teaching resources, including a solutions manual for instructors.

Part C Design of Function Circuits

11 Design of Analog Multipliers – Multiplexing

DOI: 10.1201/9781003221449-14

If the width of a pulse train is made proportional to one voltage and the amplitude of the same pulse train to a second voltage, then the average value of this pulse train is proportional to the product of two voltages, and it is called “time division multiplier,” “pulse averaging multiplier,” or “sigma delta multiplier.” The time division multiplier (TDM) can be implemented using a (1) triangular wave, (2) sawtooth wave, and (3) without using any reference wave.

Peak responding multipliers are classified into (i) peak detecting multipliers and (ii) peak sampling multipliers. A short pulse/sawtooth waveform is generated whose time period ‘T’ is proportional to one voltage. Another input voltage is integrated during the time period ‘T’. The peak value of the integrated voltage is proportional to the product of the two input voltages. This is called “double single slope peak responding multiplier.” A square/triangular waveform whose time period ‘T’ is proportional to one voltage is generated. Another input voltage is integrated during the time period ‘T’. The peak value of the integrated voltage is proportional to the product of the two input voltages. This is called “double dual slope peak responding multiplier.” A rectangular pulse waveform is generated whose OFF time is proportional to one voltage. Another voltage is integrated during this OFF time. The peak value of integrated output is proportional to the product of the two input voltages. This is called “pulse width integrated peak responding multiplier.” At the output stage of a peak responding multiplier, if peak detector is used, it is called “peak detecting multiplier,” and if sample and hold is used, it is called “peak sampling multiplier.”

A multiplier uses either analog switches or analog multiplexers for its operation. If analog switches are used, they are called “switching multipliers,” and if analog multiplexers are used, they are called “multiplexing multipliers.” Multiplexing multipliers are discussed in this chapter, and switching multipliers are described next in Chapter 12.

11.1 Triangular Wave–Based Time Division Multipliers

The circuit diagrams of triangular wave–based TDMs are shown in Figure 11.1, and their associated waveforms are shown in Figure 11.2. In Figure 11.1(a), a triangular wave V_T1 with ±V_T peak-to-peak value and time period ‘T’ is generated by the op-amp OA₁ and transistors Q₁ and Q₂. The value of V_T is given as

(11.1)$${\mathrm{V}}_{\mathrm{T}}=\mathrm{\beta }\left({\mathrm{V}}_{\mathrm{S}\mathrm{A}\mathrm{T}}\right)\approx \mathrm{\beta }\left(0.76\right)\left({\mathrm{V}}_{\mathrm{C}\mathrm{C}}\right)$$

Figure 11.1(a) Triangular wave–based time division multiplier – type I.

Figure 11.1(b) Triangular wave–based time division multiplier – type II.

Figure 11.2 Associated waveforms of Figure 11.1.

where β is given as $\mathrm{\beta }=\frac{{\mathrm{R}}_1}{{\mathrm{R}}_1+{\mathrm{R}}_2}$ and time period ‘T’ is given as

(11.2)$$\mathrm{T}=4{\mathrm{R}}_5{\mathrm{C}}_1\frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}$$

In Figure 11.1(b), op-amps OA₁ and OA₂ constitute a triangular/square wave generator. The output of op-amp OA₁ is a triangular wave V_T1 with ±V_T peak values and time period ‘T’. Let initially the comparator OA₂ output be LOW(−V_SAT), and the integrator ouput composed by op-amp OA₁, resistor R₁, and capacitor C₁ be given as

(11.3)$${\mathrm{V}}_{\mathrm{T}1}=-\frac{1}{{\mathrm{R}}_1{\mathrm{C}}_1}{\displaystyle \int -{\mathrm{V}}_{\mathrm{S}\mathrm{A}\mathrm{T}}}\mathrm{d}\mathrm{t}=\frac{{\mathrm{V}}_{\mathrm{S}\mathrm{A}\mathrm{T}}}{{\mathrm{R}}_1{\mathrm{C}}_1}\mathrm{t}$$

The integrator output is rising toward positive saturation, and when it reaches a value +V_T, the comparator output becomes HIGH(+V_SAT). The integrator output composed by op-amp OA₁, resistor R₁, and capacitor C₁ is given as

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Table of contents

• Cover
• Half Title Page
• Title Page
• Copyright Page
• Dedication
• Contents
• Preface
• Useful Notations
• Abbreviations
• Introduction
• Part A Fundamentals of Function Circuits
• Part B Principles of Function Circuits
• Part C Design of Function Circuits
• Part D General on Function Circuits
• Part E Miscellaneous Function Circuits
• Part F Applications of Function Circuits
• Appendix A Analog Function Circuits Tutorial Kit
• Index