# Mixed Signal Circuits

## Introduction

Mixed signal circuits brings both analog and digital functionality under one circuit/chip (e.g.integrated circuit). it is commonly used to convert information from analog world to digital world, and vice versa such as on sensors and transducers.

## Background

Mixed signal circuit: a circuit that contains both analog and digital circuits on the same chip (integrated circuit).

Resolution

- The minimum amount of
**input voltage**variation between**two****measurements change**for ADC (i.e step size of analog input) - The minimum amount of
**output voltage**variation between**two quantization level****change**for DAC (i.e step size of analog output)- Resolution is typically represented in number of bits, n. Another parameter known as effective number of bits
**ENOB**in ADC, tells the real resolution of an ADC, which is smaller than the reported bit depth due to noise and errors.

- Resolution is typically represented in number of bits, n. Another parameter known as effective number of bits

ADC Process (Sampling ->Quantization-> Encoding/Conversion)

- Sampling: An analog signal is sampled at a fixed time interval.
- Quantization: it's the signal processing technique that transforms
**an infinite precise and continuous**analog signal to**a finite and discrete levels**(quantization levels). - Encoding/Conversion: It's a process of represent each quantization levels with binary bits (0s &1s)

Dynamic Range

- It's the maximum ADC input range swing characterized by the relative difference between max signal to the minimum signal.
- Typically this value is represented in dB.

Linearity error

- The linearity parameter characterizes deviation between ADC/DAC analog input to its digital output relationship, and vice versa.
- Typically this value is represented in % of maximum deviation away from a perfect input to output linear relationship.
- For ADC
- Differential non-linearity (
**DNL**) reports the**deviation in step size**between actual**analog input**and ideal step size,1 LSB. ADC datasheet often report this as the maximum error per step. - Integral non-linearity (INL) reports the
**deviation in ADC transfer function**between actual curve to a straight line fit approximation using the end points of ADC actual curve. It's calculated as the difference between actual analog input transition edge and best fitted transition edge at**each digital output transition**. ADC datasheet report this as the maximum transfer function error.

- Differential non-linearity (
- For ADC
- Differential non-linearity (
**DNL**) reports deviation in step size between actual**analog output**and ideal step size, 1 LSB. DAC datasheet often report this as the maximum error per step. - Integral non-linearity (INL) reports the
**deviation in transfer function**between actual curve to a straight line fit approximation using the end points of DAC actual curve. It's calculated as the difference between actual analog output and best fitted analog output at**each digital input step**. DAC datasheet often report INL as the maximum transfer function error.

- Differential non-linearity (

Absolute/Maximum Error

- Maximum deviation between actual curve and ideal ADC/DAC curve .
**Note:**The ideal curve differs from best straight fitted line curve in that idea curve is independent when of ADC/DAC end points start or ends. The ideal curve has no offset, ideal step size of LSB, and is perfectly stair case curve.

Alternative way to characterize Linearity

- Another way to characterize linearity is to evaluate how close the data is to the best fitted line.
- R^2 value of the best fitted regression line

## Overview

**ADC**

Common Architecture

Flash ADC

- up to 12 bits
- up to GHz bandwidth (fastest speed)
- high cost

Application

- communication system such software radio processing, fiber optics, etc.

Successive Approximate Register (SAR)

Main features

- up to 16 bit resolution
- up to of MHz bandwidth (Medium speed)
- low cost

Application

- Data acquisition, Instrumentation and control systems.

Sigma-Delta

Main features

- up to 24 bit resolution
- up to 10s of kHz bandwidth

Application

- Commonly used in sensor application where high precision is needed such as pressure measurement on weight scales.
- Often you these on MEMS sensor that has integrated ADC.

**DAC**

Common Architecture

Binary Weighted Resistor

- Fast conversion
- Need to control resistor precision
- Typ. resolution is limited to 8 bit

R-2R Ladder

- Two only two combination of resistor values (R&2R) needed
- No need to have high resistor precision
- Lower conversion speed

Digital Amplifier

- It' takes a digital signal such as digital PCM audio and outputs a pulse width modulated signal (i.e high frequency analog pulses) that is immediately pass through a analog low pass filter to recover the analog representation of PCM audio.
**Note:**it's built using a Class-D amplifier, which also have benefit of high efficiency.

Application

- Speaker driver in audio system (DAC or Digital Amplifier)
- Voltage control in motor controllers
- Signal generator

CODEC (En**co**de and **De**code)

In hardware world, CODEC a **special hardware** that contains both ADC and DAC functionalities that converts signal between analog to digital data stream and vice versa.

- Example, a audio digital data stream (PCM format) is
**decoded by a DAC**to an analog data stream for a line out speaker. - Example, a microphone audio analog data stream is
**encoded by a ADC**to a PCM audio digital stream for digital processor.

**Note:** Don't confuse this with codec terms that is commonly heard as audio codec using in digital audio world. In software world, CODEC is a **special software program** that does encoding or decoding of a digital data stream between different data stream formats.

- Example, a MP3 CODEC can encode a raw audio format PCM to a compressed audio format MPEG3, and vice versa.

## Example Design

Define the effective number of bit (ENOB) for a Digital MEMS Microphone

## Q&A

*What reports the maximum measurement error for ADC and DAC?*

For ADC and DAC, on datasheet, there is a absolute accuracy error (total error). This total error includes the non-zero offset, differences in slope (gain error), and quantization error that can be used on the single value error parameter for a quick evaluation.

## Summary & Conclusion

- ADC converts analog signal to digital signal.
- DAC converts digital signal to analog signal.
- CODEC contains both ADC and DAC functionalities
- Inherent non-linearity of mixed signal electronic components contributes measurement errors which degrades signal integrity.

Electronic system engineer must understand the fundamentals of mix signal circuits and apply them to highly digitized electronic system today. It's essential to make tradeoffs between sampling rate, precision, and cost in choosing a right mixed signal technology chip.

## Further reading:

- " Analog to Digital Conversion", http://hyperphysics.phy-astr.gsu.edu/hbase/Electronic/adc.html#c1
- "Understanding Data Converter" http://www.ti.com/lit/an/slaa013/slaa013.pdf?ts=1588289792537