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

- Inverting amplifier

**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

- 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.
- 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).

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

**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