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Mixed-Signal-Electronics<br />
Dr.-Ing. Henzler<br />
Dipl.-Ing. Cenk Yilmaz<br />
Prof. Dr. Schmitt-Landsiedel<br />
<strong>Lehrstuhl</strong> <strong>für</strong> <strong>Technische</strong> <strong>Elektronik</strong><br />
<strong>Technische</strong> Universität München<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
1
Prof. Dr. Schmitt-Landsiedel<br />
dsl@tum.de<br />
Mixed-Signal-Team<br />
PD Dr. Henzler<br />
henzler@tum.de<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
Dipl.-Ing. Yilmaz<br />
yilmaz@tum.de<br />
2
Course and Online Material<br />
Lecture notes<br />
available in the Fachschaft EI (<strong>TUM</strong>), handout (GIST <strong>TUM</strong> Asia)<br />
Online material comprising<br />
– annotated <strong>slides</strong><br />
– video stream of past lectures<br />
www.lte.ei.tum.de/homes/henzler<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
3
Administratives<br />
Lecture: Stephan Henzler<br />
henzler@tum.de<br />
office hours: online consultation<br />
Tutorial: Cenk Yilmaz<br />
yilmaz@tum.de<br />
office hours online & by arrangement<br />
Exam: in written form,<br />
preliminary date February, 15th 2011, 14:00 (<strong>TUM</strong>)<br />
Credits: 4.5 ECTS credits (<strong>TUM</strong>)<br />
Language: english<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
4
The Macroscopic World is Purely Analog<br />
motion/acceleration<br />
mechanical force<br />
sound waves<br />
light<br />
electromagnetic<br />
field<br />
temperature<br />
Digital System, e.g.<br />
- digital communication<br />
(DSL, GSM, …, LTE)<br />
- computer equipment<br />
- multimedia<br />
(DVD, mp3, camera… )<br />
- control application<br />
(e.g. automotive)<br />
discrete sequence of<br />
numbers from a discrete set<br />
continuous time<br />
Our environment is always analog … and values<br />
You just have to investigate the system in-depth!<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
sense organs<br />
sensors/<br />
actuators<br />
time<br />
even ‘digital’<br />
signals on a<br />
transmission<br />
channel<br />
5
The Macroscopic World is Purely Analog<br />
motion/acceleration<br />
mechanical force<br />
sound waves<br />
light<br />
electromagnetic<br />
field<br />
ADC<br />
DAC<br />
Digital System, e.g.<br />
- digital communication<br />
(DSL, GSM, …, LTE)<br />
- computer equipment<br />
- multimedia<br />
(DVD, mp3, camera… )<br />
- control application<br />
(e.g. automotive)<br />
discrete sequence of<br />
numbers from a discrete set<br />
The mixed-signal shell is a bridge between<br />
temperature sense organs<br />
– the analog environment and the digital signal processing<br />
– the physical representation (voltage/current) and a mathematical abstraction<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
sensors/<br />
actuators<br />
time<br />
even ‘digital’<br />
signals on a<br />
transmission<br />
channel<br />
6
Generic Mixed Signal System<br />
What means mixed-signal?<br />
Mixed-signal refers to a system which processes both analog<br />
and digital signals and which contains converter blocks that<br />
enable interaction between the two domains.<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
7
Topics of MSE Course<br />
Structure of mixed signal systems and mathematical<br />
representation of discrete time signals.<br />
ADC<br />
discrete time<br />
discrete states<br />
discrete time (step function)<br />
continuous states<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
digital discrete time (step function)<br />
discrete values (states)<br />
8
Sample & hold circuits<br />
Topics of MSE Course<br />
Switched-capacitor circuits<br />
Data converter fundamentals (ADC, DAC)<br />
converter parameters and characteristics<br />
Nyquist rate D/A Converters<br />
Nyquist rate A/D Converters<br />
Oversampling Converters<br />
Outlook: More mixed signal building blocks<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
9
Recommended Literature<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
Relevant chapters:<br />
Chapter 7:<br />
Comparators.<br />
Chapter 8:<br />
Sample-and-Holds<br />
Chapter 9:<br />
Discrete Time Signals<br />
Chapter 10:<br />
Switched Capacitor Circuits<br />
Chapter 11:<br />
Data Converter Fundamentals<br />
Chapter 12:<br />
Nyquist-Rate D/A Converters<br />
Chapter 13:<br />
Nyquist-Rate A/D Converters<br />
Chapter 14:<br />
Oversampling Converters<br />
10
Additional Literature & References<br />
Razavi. Principles of Data Conversion System Design.<br />
Wiley, 1994.<br />
Allen, Holberg. CMOS Analog Circuit Design. Oxford, 2010.<br />
Baker, Li, Boyce. CMOS Circuit Desig, Layout, Simulation.<br />
Wiley, 1997.<br />
Gregorian, Temes. Analog MOS Integrated Circuits for<br />
Signal Processing. Wiley 1986.<br />
Oppenheim. Zeitdiskrete Signalverarbeitung. Oldenbourg<br />
1999.<br />
Norsworthy, Schreier, Temes. Delta-Sigma Data<br />
Converters. IEEE Press, 1997.<br />
Schreier, Temes. Understanding Delta Sigma Data<br />
Converters. IEEE Press 2005.<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
11
Constraints of Mixed Signal Circuits in SoC<br />
PROS CONS<br />
• Cheap implementation of complex<br />
signal processing tasks<br />
• System-on-chip (SOC)<br />
Small pcb footprint<br />
• Fast time reference/clock<br />
• Digitally assisted analog<br />
• All advantages of digital<br />
systems, e.g. robustness, noise<br />
immunity, data storage,<br />
reconfigurability, efficient highly<br />
automated design and test<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
• Need to build analog circuits in<br />
digital process, i.e.<br />
• Devices optimized for high<br />
switching speed not for analog,<br />
(e.g. small gm/gds)<br />
• Transistors with high field<br />
and short channel effects<br />
µ(V G), V th(W,L,V DS,V BS), I gate, I DB<br />
• Signal contamination due to digital<br />
switching noise, e.g. cross talk,<br />
supply noise substrate coupling<br />
• several 100mA digital currents<br />
• V analog signals<br />
12
Generic Structure of Mixed-Signal Systems<br />
System Perspective<br />
Circuit Perspective<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
13
Representation of Discrete Time Signals and<br />
Spectral Transformation<br />
xs(t) = xc(t) X<br />
= X<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
n<br />
n<br />
±(t ¡ nT )<br />
x(nT )±(t ¡ nT )<br />
= X<br />
x[n]±(t ¡ nT )<br />
n<br />
14
Representation of Discrete Time Signals and<br />
Spectral Transformation<br />
Fourier Transformation<br />
X(!) =<br />
generalization<br />
s = j<br />
+1<br />
Z<br />
¡1<br />
x(t) = 1<br />
2¼<br />
x(t)e ¡j!t dt<br />
+1<br />
Z<br />
¡1<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
X(!)e j!t d!<br />
X(s) =<br />
+1<br />
Z<br />
¡1<br />
x(t)e ¡st dt<br />
Laplace Transformation<br />
15
Spectral Transformation of Discrete Time Signal<br />
Insertion of sampled signal in Fourier formula:<br />
X(!) =<br />
+1 Z<br />
X<br />
¡1<br />
= X<br />
Normalization of frequency to sampling frequency:<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
n<br />
n<br />
x(nT )<br />
x(nT )±(t ¡ nT )e ¡j!t dt<br />
+1<br />
Z<br />
¡1<br />
= X<br />
x(nT )e ¡j!nT<br />
n<br />
e ¡j!t ±(t ¡ nT )dt<br />
X() = X<br />
x[n]e ¡jn X(z) = X<br />
x[n]z ¡n<br />
n<br />
FT of discrete sequence<br />
generalization<br />
z = e j = e j!T<br />
FT of sampled signal<br />
= !T = 2¼f<br />
n<br />
z-Transformation<br />
fs<br />
16
Representation of Discrete Time Signals and<br />
Spectral Transformation<br />
Meaning of frequency: oscillations per second.<br />
What is meaning of normalized frequency Ω?<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
Ω = angular change from sample to sample<br />
17
Representation of Discrete Time Signals and<br />
Spectral Transformation<br />
Spectrum of a sampled signal:<br />
s(t) = X<br />
±(t ¡ nT ) $ S(!) = 2¼<br />
T<br />
n<br />
xs(t) = xc(t) ¢ s(t) $<br />
Sampling means multiplication<br />
of continuous time signal with<br />
pulse train<br />
X<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
k<br />
±(! ¡ k!s) !s = 2¼<br />
T<br />
Xs(!) = 1<br />
2¼ Xc(!) ¤ S(!)<br />
= 1<br />
T Xc(!) ¤ X<br />
= 1<br />
T<br />
X<br />
k<br />
In frequency domain this translates<br />
into convolution of signal spectrum<br />
with spectrum of pulse train.<br />
This is simply a copy and shift of<br />
the spectrum to multiples of the<br />
sampling frequency<br />
k<br />
Xc(! ¡ k!s)<br />
±(! ¡ k!s)<br />
18
Representation of Discrete Time Signals and<br />
Spectral Transformation<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
Aliasing occurs if mirror spectra overlap<br />
19
amplitude fsampling = 1 f signal,1 = 0.22<br />
1<br />
0.8<br />
0.6<br />
0.4<br />
0.2<br />
0<br />
-0.2<br />
-0.4<br />
-0.6<br />
-0.8<br />
-1<br />
Sampling and Aliasing 1<br />
0 5 10 15<br />
samples<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
20
amplitude fsampling = 1 f signal,2 = 0.22 + fsampling<br />
1<br />
0.8<br />
0.6<br />
0.4<br />
0.2<br />
0<br />
-0.2<br />
-0.4<br />
-0.6<br />
-0.8<br />
-1<br />
Sampling and Aliasing 2<br />
0 5 10 15<br />
samples<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
21
amplitude<br />
1<br />
0.8<br />
0.6<br />
0.4<br />
0.2<br />
0<br />
-0.2<br />
-0.4<br />
-0.6<br />
-0.8<br />
-1<br />
Sampling and Aliasing 3<br />
Only with the Nyquist criterion it is assured that the samples<br />
represent the signal unambiguously<br />
0 5 10 15<br />
samples<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
22
low-pass<br />
low-pass<br />
low-pass<br />
Aliasing in the Frequency Domain<br />
low-pass filtering<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
t<br />
t<br />
t<br />
t<br />
t<br />
t<br />
23
Practical Sampling: Sample & Hold<br />
Remember: All realizable signals have<br />
– finite slope (dx/dt)<br />
– finite pulse width, i.e. finite bandwidth<br />
– finite value<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
t<br />
t<br />
t<br />
ideal sampling<br />
step function<br />
alternative solution<br />
24
Practical Sampling: Sample & Hold<br />
Remember: All realizable signals have<br />
– finite slope<br />
– finite pulse width<br />
– finite bandwidth<br />
– finite value<br />
Hence sampling means always SAMPLE & HOLD<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
25
Sampling with Finite Pulse Width<br />
x sh(t) = xs(t) ¤ h(t)<br />
=<br />
x sh(!) =<br />
=<br />
1X<br />
n=¡1<br />
+1<br />
Z<br />
¡1<br />
1X<br />
n=¡1<br />
= ¡ 1<br />
j!<br />
xc[n] [¾(t ¡ nT ) ¡ ¾(t ¡ nT ¡ ¿)]<br />
1X<br />
n=¡1<br />
xc[n]<br />
1X<br />
n=¡1<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
xc[n] [¾(t ¡ nT ) ¡ ¾(t ¡ nT ¡ ¿)] e ¡j!t dt<br />
nT +¿<br />
Z<br />
nT<br />
e ¡j!t dt<br />
xc[n] h<br />
e ¡j!ti nT +¿<br />
nT<br />
(t)<br />
t<br />
26
Sampling with Finite Pulse Width<br />
Xsh(!) = ¡ 1<br />
j!<br />
=<br />
1X<br />
n=¡1<br />
Distortion of base band and damping of mirror spectra<br />
– visible in DAC<br />
– not visible in ADC<br />
1X<br />
n=¡1<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
xc[n] ³<br />
e ¡j!nT e ¡j!¿ ´<br />
¡ e<br />
j!nT<br />
xc[n]e ¡j!nT<br />
1<br />
j!<br />
= Xs(!)e ¡1 2j!¿ ¿ ej 1 2 !¿ ¡ e ¡j 1 2 !¿<br />
2j 1 2 !¿<br />
= Xs(!)¿e ¡j 1 2 !¿ sin ³ 1<br />
2 !¿ ´<br />
³<br />
´<br />
1 ¡ e<br />
¡j!¿<br />
ideal sampling X S() impact of hold<br />
1<br />
2 !¿<br />
27
Representation of Discrete Time Signals and<br />
Spectral Transformation<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
28
generalization<br />
X(s) =<br />
Relation Between s- and z-Plain<br />
Fourier Transformation:<br />
+1 Z<br />
X(!) =<br />
¡1<br />
x(t)e ¡j!t dt<br />
LaPlace Transformation: z-Transformation:<br />
+1 Z<br />
1X<br />
j<br />
¡1<br />
x(t)e ¡st dt X(z) =<br />
s<br />
<br />
z = e j!T<br />
discrete<br />
signals<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
Im(z)<br />
1X<br />
n=¡1<br />
x(nT )e ¡j!nT<br />
normalization<br />
&<br />
generalization<br />
n=¡1<br />
z<br />
x[n]z ¡n<br />
Re(z)<br />
29
Downsampling<br />
Additional information: If there is noise beween the repeated signal spectra, an additional filtering is required (low pass).<br />
However, it is sufficient to compute one out of L samples.<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
30
Downsampling II<br />
Down-sampling requires, that there is no signal energy in<br />
between baseband and mirror spectra (e.g. noise)<br />
In general this is not the case, so down-sampling may cause<br />
aliasing<br />
To avoid aliasing a low pass filter is required in front of downsampling<br />
block Decimation Filter (Decimator)<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
31
Upsampling<br />
Additional information: Fractional sample rate conversion is up-sampling followed by subsequent down-sampling. Low-pass filters<br />
may be shared. Compute only what is necessary!<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
32
Upsampling II<br />
Zero padding results in higher sampling rate<br />
However, this does not mean that mirror spectra occur only<br />
at multiples of the sampling frequency<br />
Imaging, i.e. replica in between 0..2<br />
Low pass filter removes images: Interpolation filter<br />
– Result in frequency domain: Replica only at k x f s<br />
– Result in time domain: Zeros move on real signal curve<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
33
Fractional Sample Rate Conversion<br />
Purpose: Change sample rate by a non-integer factor L/M<br />
Two possibilities:<br />
– Up-sampling by L, downsampling by M<br />
– Down-sampling by M, than up-sampling by L<br />
The order of up- and down-sampling may be exchanged<br />
without any change in the input/output behavior if the<br />
decimation factor M and the interpolation factor L are<br />
relatively prime.<br />
Henzler, Schmitt-Landsiedel Mixed-Signal-Electronics 2010/11<br />
34