an introduction to delta sigma converters.mht

Intro to Delta Sigma and PWM

welcome=20
consequence on alias effects: Only input signal frequencies close to the =

sampling frequency will be folded back and can cause alias signals as =
you can=20
see in the graphic below:</P>
<P>
<CENTER><IMG height=3D309=20
src=3D"http://www.beis.de/Elektronik/DeltaSigma/DeltaSigmaAliasFilter.GIF=
"=20
width=3D535 align=3Dbottom border=3D0 NATURALSIZEFLAG=3D"3"></CENTER>
<P></P>
<P>
<CENTER><B>Figure 16 - Distances of Desired and Alias Frequency=20
Bands</B></CENTER>
<P></P>
<P>Thus it becomes obvious that conventional ADCs need expensive low =
pass=20
filters in order to obtain a bandwidth close to the theoretical Nyquist =
limit.=20
Delta sigma converters require simple RC low pass filters only and with =
a little=20
more expense for a 2<SUP>nd</SUP> order filter one will get a virtually =
ideal=20
behaviour. On the other hand an output low pass filter preceeding the =
decimator=20
is required, which again can be realized more precisely, easily and =
cheap in=20
digital techniques. Note that in practice the proportions are much more =
extreme=20
than in the graphic above as due to limited space an oversampling rate =
of=20
approx. 16 only is shown there.</P>
<P>DACs: The input signals of DACs are bandwidth limited by nature, so =
an input=20
low pass filter is not necessary (it already had to be present when the =
digital=20
signal was produced). An analog output filter is required anyway to =
suppress=20
high frequency noise.</P>
<P><B>Infinite resolution of the bitstream</B>: In analogue modulators =
the=20
bitstream is sampled, but not quantized. It still has an infinite =
resolution=20
just like the analogue signal has. It is superimposed by noise of =
course, but=20
the more noise you filter out (the lower the low pass filter's frequency =
limit=20
is), the more of the original resolution is usable - (theoretically) =
without=20
limitation. This fact is also exploited by:</P>
<P><B>Direct Stream Digital (DSD) based devices</B>: Traditionally =
digital=20
devices use numerical representations of analogue samples, PCM in case =
of a=20
serial signal. Delta sigma ADCs and DACs gain the PCM data out of the =
bitstream=20
data (and vice versa) which is already a digital signal by means of low =
pass=20
filters.</P>
<P>
<CENTER><IMG height=3D115=20
alt=3D"Complete Delta Sigma Based PCM System: 2 Delta Sigma Converters"=20
src=3D"http://www.beis.de/Elektronik/DeltaSigma/DeltaSigmaADDAC.GIF" =
width=3D963=20
align=3Dbottom border=3D0 NATURALSIZEFLAG=3D"3"></CENTER>
<P></P>
<P>
<CENTER><B>Figure 17 - Complete Delta Sigma Based PCM System: 2 Delta =
Sigma=20
Converters</B></CENTER>
<P></P>
<P>Why not record the bitstream directly? Conversion in delta sigma ADCs =
and=20
DACs is executed in two steps each and as always each step has negative =
effects=20
on the signal quality. Leaving out half of these steps - the filter in =
the ADC=20
and the modulator in the DACs - should improve the performance of the =
complete=20
system. Both, the quantization noise due to the limited number of =
recorded PCM=20
bits and the conversion noise of the digital modulator would be =
dropped.</P>
<P>
<CENTER><IMG height=3D75=20
alt=3D"Complete Delta Sigma Based DSD System: 1 Delta Sigma Converter =
only"=20
src=3D"http://www.beis.de/Elektronik/DeltaSigma/DeltaSigmaAAC.GIF" =
width=3D962=20
align=3Dbottom border=3D0 NATURALSIZEFLAG=3D"3"></CENTER>
<P></P>
<P>
<CENTER><B>Figure 18 - Complete Delta Sigma Based DSD System: 1 Delta =
Sigma=20
Converter only</B></CENTER>
<P></P>
<P>This is actually done on super audio CDs (SACDs). The whole system =
from the=20
analogue input to the analogue output now requires only one modulator =
and one=20
low pass filter instead of two of both required with conventional =
digital=20
recording. Please remember: The bitstream of modern, high quality ADCs =
and DACs=20
use an oversampling rate of 64, e.g. the amount of data is 64 bits for =
each=20
audio sample - compared to 16 or up to 20 or 24 of conventional bits =
required=20
for a comparable quality. Technically, SACDs are DVDs and based on a =
sampling=20
frequency of 2.8224&nbsp;MHz (=3D 2.8224&nbsp;MBits net per channel). =
Not much=20
that more than on audio CDs (0.7056&nbsp;MBits net per channel), and no =
problem=20
at all for a DVD with its high capcity.</P>
<P><B>Class-D Power Amplifiers</B>:</P>
<P>
<CENTER><IMG height=3D171=20
src=3D"http://www.beis.de/Elektronik/DeltaSigma/DeltaSigmaPower.GIF" =
width=3D683=20
align=3Dbottom border=3D0 NATURALSIZEFLAG=3D"3"></CENTER>
<P></P>
<P>
<CENTER><B>Figure 19 - Power Amplifiers using a Digital Output=20
Stage</B></CENTER>
<P></P>
<P>Both output transistors operate in push-pull mode, i. e., =
alternatingly one=20
of both is conducting while the other one is switched off. Thus the =
bitstream is=20
amplified to the high level of the power supply and is available at the =
output=20
with low impedance. In order to regain the bitstream's mean value a =
simple=20
LC-low-pass filter is sufficient in practice. A typical representative =
of this=20
kind of amplifier is the <A =
href=3D"http://www.national.com/pf/LM/LM4670.html"=20
target=3D_blank>LM4670</A>, a simple and cheap low power amplifier with =
an=20
analogue input, so simple that even the LC-low-pass filter is omitted =
and only=20
the speaker's parasitic inductance remains as "low-pass filter". In =
contrast to=20
that the <A =
href=3D"http://focus.ti.com/docs/prod/folders/print/tpa3200d1.html"=20
target=3D_blank>TPA3200D1</A> is more complex, has higher output power =
and=20
includes a digital (IIS-)input.</P>
<P>For the sake of completeness it shall be mentioned that for the =
operation of=20
a class-D amplifier an analogue pulse width modulated (PWM) signal with =
a=20
sufficiently high frequency can be used instead of the bitstream =
produced by a=20
Delta Sigma converter. In contrast to digital pulse width modulated =
signals the=20
pulse width ratios of analogue pulse width modulated signals are not =
quantized.=20
With digital sources PWM operation does not suggest itself much, but =
with=20
anlogue sources both techniques can be found in practice. In this case =
the pulse=20
width modulator consists of a comparator comparing a triangle wave of e. =
g. a=20
couple of MHz with the analogue input signal. An example is the <A=20
href=3D"http://www.st.com/stonline/products/literature/ds/6871/tda7490.ht=
m"=20
target=3D_blank>TDA7490</A>.</P>
<P>Compared to a conventional analogue class-AB amplifier, which =
advantages and=20
disadvantages does such a class-D amplifier show?</P>
<UL>
  <LI><B>Advantage</B>: Its efficiency can theoretically become 100%. In =

  practice typical values of 90% are achieved. The efficiency of =
class-AB=20
  amplifiers theoretically is 50% only. Moreover, the efficieny of =
class-AB=20
  amplifiers decreases much more at lower output levels than that of=20
  class-D-amplifiers. E. g. for battery equipped applications the saved =
energy=20
  may be the decisive reason for class-D amplifiers. But particularly =
with high=20
  power amplifiers the fact of 1/5 of exhaust heat is an enomous =
advantage:=20
  Class-D amplifieres can be built much smaller and much more =
lightweight.=20
  <LI><B>Disadvantage</B>: The speaker's voltage does not only depend on =
the=20
  bitstream (or its mean value resp.), but in the same amount on the =
supply=20
  voltage, too. (Actually it is the product of the bitstream's mean =
value and=20
  the supply voltage.) Thus the supply voltage has to be kept extra =
stable.=20
  <LI><B>Disadvantage</B>: The amplifier's output impedance results from =
the=20
  switching transistor's, the inductance's and the supply's resistances. =
In=20
  pratice it will be distinctly higher than the output impedance of a=20
  degenerative amplifier. A low output impedance is preferred because =
speakers=20
  are thereby much more damped, i. e,. they can perform less =
uncontrolled proper=20
  motion and follow the original signal more precisely. </LI></UL>
<P>In order to reduce both these disadvantages the supply voltage =
dependency as=20
well as the output impedance can principally be lowered by degenerative=20
feedback. But, if at all, this is by far not feasible in an amount as it =
is in=20
analogue amplifieres as phase shifts inside the modulator and the low =
pass=20
filter in conjunction with a degenerative feedback very soon lead to=20
instabilities. Usually Delta Sigma amplifiers do not include =
degenerative=20
feedback (as far as I experienced, at least). Once more, for the sake of =

completeness it shall be mentioned that PWM amplifiers do not =
incorporate phase=20
shifting modulators so that degenerative feedback is much easier or much =
more=20
efficient to achieve.</P>
<P>In analogue Delta Sigma based power amplifiers another trick is =
possible to=20
drastically improve the signal quality:</P>
<P>
<CENTER><IMG height=3D252=20
src=3D"http://www.beis.de/Elektronik/DeltaSigma/DeltaSigmaImprovedPower.G=
IF"=20
width=3D784 align=3Dbottom border=3D0 NATURALSIZEFLAG=3D"3"></CENTER>
<P></P>
<P>
<CENTER><B>Figure 20 - Power Output Stage as Part of the Delta Sigma=20
Modulator</B></CENTER>
<P></P>
<P>Compare to Figure 2: Instead of feeding back the bitstream via a =
1-bit DAC to=20
build the difference in this case a portion of the power transistor's =
output is=20
directly fed back. Thus it is guaranteed that independent of all =
parasitic=20
effects like supply voltage variations or the transistor's resistances =
the mean=20
value at the low-pass input is always exactly proportional to the =
analogue input=20
signal. Excellent performance is feasible by this concept. An example =
for that=20
is the <A href=3D"http://www.analog.com/en/prod/0,2877,AD1992,00.html"=20
target=3D_blank>AD1996</A>. Unfortunately, this trick works for =
amplifiers with=20
analogue inputs only.</P>
<P>Conclusion: Class-D power amplifiers offer a much higher efficiency =
and less=20
exhaust heat at the expense of their signal quality. Thus they are =
favourable=20
for generic public address systems, where high power, small size and =
probably=20
portability too, are required. They are less predestinated for =
high-quality=20
audio amplifiers. Constructively the most critical elements are the =
output=20
transistors: The faster they switch, the less the losses are or the =
higher the=20
switching frequency may be. The latter, on the other hand, allows low =
pass=20
filters with higher frequencies, which due to their less phase shifts =
within the=20
signal band allow stronger degenerative feedback, so that the signal =
quality can=20
be improved. With the advancing semiconductor technology class-D =
amplifiers will=20
be increasingly utilizable for high-quality audio amplifiers.</P>
<P><B>Delta Sigma Converters or <A=20
href=3D"http://www.beis.de/Elektronik/DeltaSigma/SigmaDelta.html">Sigma =
Delta=20
Converters</A>?</B> Mankind does not seem to agree on one notation. Both =

notations are used equally often when you search via Google. I decided =
to stay=20
with that guy who told he is living in the Mississippi Delta, so deltas =
mean=20
something to him - and for him only the Sigma River may have a Sigma =
Delta...=20
good point. Later I found out that the original name "Delta Sigma" was =
coined by=20
the inventors Inose and Yasuda and "Sigma Delta" is actually not =
correct. I was=20
lucky...</P>
<P>