slides - Lehrstuhl für Technische Elektronik - TUM

Mixed-Signal-Electronics 

Dr.-Ing. Henzler 

Dipl.-Ing. Cenk Yilmaz 

Prof. Dr. Schmitt-Landsiedel 

Lehrstuhl für Technische Elektronik 

Technische Universität München 

Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11 

1

Prof. Dr. Schmitt-Landsiedel 

dsl@tum.de 

Mixed-Signal-Team 

PD Dr. Henzler 

henzler@tum.de 


Dipl.-Ing. Yilmaz 

yilmaz@tum.de 

2

Course and Online Material 

Lecture notes 

available in the Fachschaft EI (TUM), handout (GIST TUM Asia) 

Online material comprising 

– annotated slides 

– video stream of past lectures 

www.lte.ei.tum.de/homes/henzler 


3

Administratives 

Lecture: Stephan Henzler 

henzler@tum.de 

office hours: online consultation 

Tutorial: Cenk Yilmaz 

yilmaz@tum.de 

office hours online & by arrangement 

Exam: in written form, 

preliminary date February, 15th 2011, 14:00 (TUM) 

Credits: 4.5 ECTS credits (TUM) 

Language: english 


4

The Macroscopic World is Purely Analog 

motion/acceleration 

mechanical force 

sound waves 

light 

electromagnetic 

field 

temperature 

Digital System, e.g. 

- digital communication 

(DSL, GSM, …, LTE) 

- computer equipment 

- multimedia 

(DVD, mp3, camera… ) 

- control application 

(e.g. automotive) 

discrete sequence of 

numbers from a discrete set 

continuous time 

Our environment is always analog … and values 

You just have to investigate the system in-depth! 


sense organs 

sensors/ 

actuators 

time 

even ‘digital’ 

signals on a 

transmission 

channel 

5

The Macroscopic World is Purely Analog 

motion/acceleration 

mechanical force 

sound waves 

light 

electromagnetic 

field 

ADC 

DAC 

Digital System, e.g. 

- digital communication 

(DSL, GSM, …, LTE) 

- computer equipment 

- multimedia 

(DVD, mp3, camera… ) 

- control application 

(e.g. automotive) 

discrete sequence of 

numbers from a discrete set 

The mixed-signal shell is a bridge between 

temperature sense organs 

– the analog environment and the digital signal processing 

– the physical representation (voltage/current) and a mathematical abstraction 


sensors/ 

actuators 

time 

even ‘digital’ 

signals on a 

transmission 

channel 

6

Generic Mixed Signal System 

What means mixed-signal? 

Mixed-signal refers to a system which processes both analog 

and digital signals and which contains converter blocks that 

enable interaction between the two domains. 


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Topics of MSE Course 

Structure of mixed signal systems and mathematical 

representation of discrete time signals. 

ADC 

discrete time 

discrete states 

discrete time (step function) 

continuous states 


digital discrete time (step function) 

discrete values (states) 

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Sample & hold circuits 

Topics of MSE Course 

Switched-capacitor circuits 

Data converter fundamentals (ADC, DAC) 

converter parameters and characteristics 

Nyquist rate D/A Converters 

Nyquist rate A/D Converters 

Oversampling Converters 

Outlook: More mixed signal building blocks 


9

Recommended Literature 


Relevant chapters: 

Chapter 7: 

Comparators. 

Chapter 8: 

Sample-and-Holds 

Chapter 9: 

Discrete Time Signals 

Chapter 10: 

Switched Capacitor Circuits 

Chapter 11: 

Data Converter Fundamentals 

Chapter 12: 

Nyquist-Rate D/A Converters 

Chapter 13: 

Nyquist-Rate A/D Converters 

Chapter 14: 

Oversampling Converters 

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Additional Literature & References 

Razavi. Principles of Data Conversion System Design. 

Wiley, 1994. 

Allen, Holberg. CMOS Analog Circuit Design. Oxford, 2010. 

Baker, Li, Boyce. CMOS Circuit Desig, Layout, Simulation. 

Wiley, 1997. 

Gregorian, Temes. Analog MOS Integrated Circuits for 

Signal Processing. Wiley 1986. 

Oppenheim. Zeitdiskrete Signalverarbeitung. Oldenbourg 

1999. 

Norsworthy, Schreier, Temes. Delta-Sigma Data 

Converters. IEEE Press, 1997. 

Schreier, Temes. Understanding Delta Sigma Data 

Converters. IEEE Press 2005. 


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Constraints of Mixed Signal Circuits in SoC 

PROS CONS 

• Cheap implementation of complex 

signal processing tasks 

• System-on-chip (SOC) 

Small pcb footprint 

• Fast time reference/clock 

• Digitally assisted analog 

• All advantages of digital 

systems, e.g. robustness, noise 

immunity, data storage, 

reconfigurability, efficient highly 

automated design and test 


• Need to build analog circuits in 

digital process, i.e. 

• Devices optimized for high 

switching speed not for analog, 

(e.g. small gm/gds) 

• Transistors with high field 

and short channel effects 

µ(V G), V th(W,L,V DS,V BS), I gate, I DB 

• Signal contamination due to digital 

switching noise, e.g. cross talk, 

supply noise substrate coupling 

• several 100mA digital currents 

• V analog signals 

12

Generic Structure of Mixed-Signal Systems 

System Perspective 

Circuit Perspective 


13

Representation of Discrete Time Signals and 

Spectral Transformation 

xs(t) = xc(t) X 

= X 


n 

n 

±(t ¡ nT ) 

x(nT )±(t ¡ nT ) 

= X 

x[n]±(t ¡ nT ) 

n 

14



Fourier Transformation 

X(!) = 

generalization 

s = j 

+1 

Z 

¡1 

x(t) = 1 

2¼ 

x(t)e ¡j!t dt 

+1 

Z 

¡1 


X(!)e j!t d! 

X(s) = 

+1 

Z 

¡1 

x(t)e ¡st dt 

Laplace Transformation 

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Spectral Transformation of Discrete Time Signal 

Insertion of sampled signal in Fourier formula: 

X(!) = 

+1 Z 

X 

¡1 

= X 

Normalization of frequency to sampling frequency: 


n 

n 

x(nT ) 

x(nT )±(t ¡ nT )e ¡j!t dt 

+1 

Z 

¡1 

= X 

x(nT )e ¡j!nT 

n 

e ¡j!t ±(t ¡ nT )dt 

X() = X 

x[n]e ¡jn X(z) = X 

x[n]z ¡n 

n 

FT of discrete sequence 


z = e j = e j!T 

FT of sampled signal 

= !T = 2¼f 

n 

z-Transformation 

fs 

16



Meaning of frequency: oscillations per second. 

What is meaning of normalized frequency Ω? 


Ω = angular change from sample to sample 

17



Spectrum of a sampled signal: 

s(t) = X 

±(t ¡ nT ) $ S(!) = 2¼ 

T 

n 

xs(t) = xc(t) ¢ s(t) $ 

Sampling means multiplication 

of continuous time signal with 

pulse train 

X 


k 

±(! ¡ k!s) !s = 2¼ 

T 

Xs(!) = 1 

2¼ Xc(!) ¤ S(!) 

= 1 

T Xc(!) ¤ X 

= 1 

T 

X 

k 

In frequency domain this translates 

into convolution of signal spectrum 

with spectrum of pulse train. 

This is simply a copy and shift of 

the spectrum to multiples of the 

sampling frequency 

k 

Xc(! ¡ k!s) 

±(! ¡ k!s) 

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Aliasing occurs if mirror spectra overlap 

19

amplitude fsampling = 1 f signal,1 = 0.22 

1 

0.8 

0.6 

0.4 

0.2 

0 

-0.2 

-0.4 

-0.6 

-0.8 

-1 

Sampling and Aliasing 1 

0 5 10 15 

samples 


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amplitude fsampling = 1 f signal,2 = 0.22 + fsampling 

1 

0.8 

0.6 

0.4 

0.2 

0 

-0.2 

-0.4 

-0.6 

-0.8 

-1 


0 5 10 15 

samples 


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amplitude 

1 

0.8 

0.6 

0.4 

0.2 

0 

-0.2 

-0.4 

-0.6 

-0.8 

-1 


Only with the Nyquist criterion it is assured that the samples 

represent the signal unambiguously 

0 5 10 15 

samples 


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low-pass 

low-pass 

low-pass 

Aliasing in the Frequency Domain 

low-pass filtering 


t 

t 

t 

t 

t 

t 

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Practical Sampling: Sample & Hold 

Remember: All realizable signals have 

– finite slope (dx/dt) 

– finite pulse width, i.e. finite bandwidth 

– finite value 


t 

t 

t 

ideal sampling 

step function 

alternative solution 

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Practical Sampling: Sample & Hold 

Remember: All realizable signals have 

– finite slope 

– finite pulse width 

– finite bandwidth 

– finite value 

Hence sampling means always SAMPLE & HOLD 


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Sampling with Finite Pulse Width 

x sh(t) = xs(t) ¤ h(t) 

= 

x sh(!) = 

= 

1X 

n=¡1 

+1 

Z 

¡1 

1X 

n=¡1 

= ¡ 1 

j! 

xc[n] [¾(t ¡ nT ) ¡ ¾(t ¡ nT ¡ ¿)] 

1X 

n=¡1 

xc[n] 

1X 

n=¡1 


xc[n] [¾(t ¡ nT ) ¡ ¾(t ¡ nT ¡ ¿)] e ¡j!t dt 

nT +¿ 

Z 

nT 

e ¡j!t dt 

xc[n] h 

e ¡j!ti nT +¿ 

nT 

(t) 

t 

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Sampling with Finite Pulse Width 

Xsh(!) = ¡ 1 

j! 

= 

1X 

n=¡1 

Distortion of base band and damping of mirror spectra 

– visible in DAC 

– not visible in ADC 

1X 

n=¡1 


xc[n] ³ 

e ¡j!nT e ¡j!¿ ´ 

¡ e 

j!nT 

xc[n]e ¡j!nT 

1 

j! 

= Xs(!)e ¡1 2j!¿ ¿ ej 1 2 !¿ ¡ e ¡j 1 2 !¿ 

2j 1 2 !¿ 

= Xs(!)¿e ¡j 1 2 !¿ sin ³ 1 

2 !¿ ´ 

³ 

´ 

1 ¡ e 

¡j!¿ 

ideal sampling X S() impact of hold 

1 

2 !¿ 

27




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X(s) = 

Relation Between s- and z-Plain 

Fourier Transformation: 

+1 Z 

X(!) = 

¡1 

x(t)e ¡j!t dt 

LaPlace Transformation: z-Transformation: 

+1 Z 

1X 

j 

¡1 

x(t)e ¡st dt X(z) = 

s 

 

z = e j!T 

discrete 

signals 


Im(z) 

1X 

n=¡1 

x(nT )e ¡j!nT 

normalization 

& 


n=¡1 

z 

x[n]z ¡n 

Re(z) 

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Downsampling 

Additional information: If there is noise beween the repeated signal spectra, an additional filtering is required (low pass). 

However, it is sufficient to compute one out of L samples. 


30

Downsampling II 

Down-sampling requires, that there is no signal energy in 

between baseband and mirror spectra (e.g. noise) 

In general this is not the case, so down-sampling may cause 

aliasing 

To avoid aliasing a low pass filter is required in front of downsampling 

block Decimation Filter (Decimator) 


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Upsampling 

Additional information: Fractional sample rate conversion is up-sampling followed by subsequent down-sampling. Low-pass filters 

may be shared. Compute only what is necessary! 


32

Upsampling II 

Zero padding results in higher sampling rate 

However, this does not mean that mirror spectra occur only 

at multiples of the sampling frequency 

Imaging, i.e. replica in between 0..2 

Low pass filter removes images: Interpolation filter 

– Result in frequency domain: Replica only at k x f s 

– Result in time domain: Zeros move on real signal curve 


33

Fractional Sample Rate Conversion 

Purpose: Change sample rate by a non-integer factor L/M 

Two possibilities: 

– Up-sampling by L, downsampling by M 

– Down-sampling by M, than up-sampling by L 

The order of up- and down-sampling may be exchanged 

without any change in the input/output behavior if the 

decimation factor M and the interpolation factor L are 

relatively prime. 


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