# Analog Circuits

## Introduction

Analog circuits operate on real world electrical signals, voltage and current. Its primary job is to transform and condition signals. We will focus on fundamental building block of analog devices namely, Op-Amps.

## Background

Purpose:

slow moving signal amplification

perform basic add, subtract, multiple and divide mathematics operations.

Ideal Characteristics of an Op-Amp

infinite open loop gain

infinite input impedance

infinite bandwidth

this means 0 rise time or fall time (i.e infinite slew rate)

zero output impedance

zero input offset

perfect linear

V+ = V-

This is only true in when opamp is used with negative feedback network. The infinite open loop gain drives V+ = V-.

Non Ideal Characteristics of an Op-Amp

Finite open loop gain (~60 to 80 dB)

Finite input impedance ( 100 kΩ to 100 MΩ )

Non zero output impedance (50 to 200 ohms)

Limited Bandwidth (1M GPBM)

finite rise time or fall time (i.e finite slew rate)

Note: rise or fall time is depended on voltage level but the slew rate is the same regardless of the power supply voltage.

Finite input offset voltage

This offset is due to process variation that introduce imbalance between Op-amp input terminals.. This is offsett voltage is modeled as the positive voltage across V=+terminal.

Voltage drift

Factor of temperature change

Amplifier Topology

Single Ended Amplifier

Amplification is based on the voltage placed on negative terminal terminal of the Op-Amp

Inverting amplifier

General Eq. Vout=(-Vin)*Gain

Non-inverting amplifier

General Eq. Vout=(Vin)*Gain

Differential Amplifier

Amplification is based on the voltage differential between positive and negative terminal of the Op-Amp

General differential amplifier Eq. Vdiff=(V+-V-)*Gain

Instrumentation Amplifier

special type of differential amplifier with very high amplification and common mode rejection.

it is used for measuring very low signal levels such as heart beat, earth quake ,etc.

Comparator

a special type of singled ended amplifier that detects whether or not input voltage at negative terminal is higher or less than the reference voltage set on positive terminal. If V- > V+, Vout = 0V, else Vout = VDD.

Power Supply Topology

Single power supply

Op-AMP is powered by a single + VDD suppy

This is common on electronic system due to most of the circuit operate between 0 to VDD

Split power supply

Op-AMP is powered by a dual power supply +VDD and -VDD

This requires both positive and negative power supplies.

## Practical Design Examples

Practical amplifier has following

Full output swing from ground to VDD power supply

Singled rail power supply

Inverting amplifier is designed based on differential amplifier topology with the signal input on the V- terminal with a fixed reference signal VCC applied on V+ terminal.

General differential amplifier equation: Vdiff=(V+-V-)*Gain

Inverting Transfer function

Vdiff=(VDD-Vin)*Gain

Non-inverting amplifier is designed based on differential amplifier topology with the signal input on the V- terminal with a fixed reference signal 0V on V- terminal on the op-amp

General differential amplifier equation: Vdiff=(V+-V-)*Gain

Non-inverting Transfer function

Vdiff=(Vin-0V)*Gain

Minimal input offset

Chopper circuit minimizes input offset

Trimming resistor minimizes input offset

Programmable gain amplifier (PGA)

Adjustable gain setting removes excessive external resistor feedback network

Amplifier can be used as a comparator when used in open loop condition (i.e no feedback network)

Often a non-inverting comparator is design where the V- voltage is the reference level that makes sets the logic high trigger level.

this reference voltage can be set by a resistor divider, voltage source (DAC, reference diode).

Application

Differential amp are used to measure voltage across a sense resistor for current sensing

Schmidt trigger uses comparator for logic level detection

## Q&A

What is the importance of high input impedance and low output impedance?

High input impedance provides isolation between weak signal source and the load.

Low output impedance provides strong signal drive strength to the load.

What causes voltage difference between V+ and V- equals to 0?

It's an effect of negative feedback and infinite open loop gain.

What contributes to temperature drift?

The feedback resistor has temperature coefficients. If these coefficients are not perpectly matched, then there will be additional gain error due to resistor deviation.

## Summary & Conclusion

Op-AMP are used for amplifier and comparator design

Inverting Amplifier has the opposite polarity of the input signal

Non-Inverting Amplifier has the same polarity of the input signal

Single rail supply design is common in practical design

Non Ideal Op-AMP has output errors due to input offset voltage, temperature drift, non-linearity, etc.

Op-AMP is the predominant choice for analog design due to low cost, robustness, and ease of design.

## Further Reading;

"Op Amps For Everyone", https://web.mit.edu/6.101/www/reference/op_amps_everyone.pdf