| 8-bit
Digital to Analog converter(DAC)
Using R/2R resistor network
By Ibrahim
Kamal
Last update:
5/5/08
Learn how to build an Analog to digital converter
using the same simple technique explained in this page. click
here.
|
 Overview
 |
| This
article aims to introduce to beginners and intermediate
readers a simple solution to build a digital to analog converter,
based on the famous r/2r resistors network. This article
also discuss a problem encountered by many beginners while
trying to build their own DAC, and proposes some very simple
solutions to that problem. |
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Through this article, I am going to explain how to build an 8-bit
digital to analog converter with parallel input. If you don't
know what this means, well its simply a circuit that will take
as input a digital 8-bit number from 0 (00000000) to 255 (11111111),
and output the relative value on a scale from 0 to 5v.
The maths that describe this process is very simple, an 8 bit
converter will divide the 5 volts into 255 steps, each step having
a value of:
5/255 = 0.019 V
Then the output voltage for the converter should be equal to the
binary input multiplied by the step value, e.g. for an input of
129 (1000 0001 in binary) the output voltage should be:
129 X 0.019 = 2.451V
Here is a simplified functional diagram of an 8-bit DAC.
|
 Some
vocabulary |
DAC:
Digital to Analog converter
D0, D1, D..: Data lines
Analog: Continuous electrical signals
Digital: Method of representing information
using "1" and "0" (usually 5v and
0V)
LSB: Less significant bit.
MSB: Most significant bit. |
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The
R/2R resistor network.
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| The digital
data entering thought the 8 lines (D0
to D7)
are going to be converted to an equivalent analog voltage
(V out) by
the mean of the R/2R resistor network. Actually a lot of
commercial Digital to Analog converter ICs are based on
this same principle. The R/2R network is build by a set
of resistors of 2 values, with one of them double the other
(example 10K and 20K), in on of my circuits I used 1M
ohm and 470K ohm resistors, which
is quite near to the R/2R ratio, and this
small difference didn't cause any detectable |
Follow the colors
on the schematic and on the description text respectively,
it can help! |
errors in most applications.
However, if you want to build a very precise DAC,
be precise when choosing the values of the resistors that will
exactly match the R/2R ratio.
Note that you can build a DAC with any number of bits you want,
simply by enlarging the resistor network, by adding more
R/2R branches (like
the one shaded in green), BUT
you must keep the 2R resistance connected to
ground (shaded in light red)
Going through the mathematical proof for the operation of
this converter can be a pain for some of us, and I am only intending
to keep things simple.
Now, in order to use this Resistor Network (also called R/2R
Ladder) for real applications, you will have to build a very
simple voltage buffer circuit, which will be explained in the
next section.
The applied circuit
|
Follow the colors
on the schematic and on the description text respectively, it
can help!
All the components are labeled on the circuit,
so i'll start directly to explain how it works. to simplify this
task, i'll split the circuit into 2 main stages: the Digital
to analog converter and the Voltage buffer stage.
 Stage
1: the Digital to analog converter (The R/2R network)
This part have been explained in detail
in the previous section, its purpose is to create the voltage
V1
which is equivalent to the weight of the binary number on the
lines (D0
to D7).
Now that this is a resistor network, if we apply any load on the
output of the first stage,
this load will be considered as an additional resistor in the
network, and thus will disturb the network which will no longer
provide the correct & desired output voltage. Therefore, to
overcome this problem, we need a voltage buffer, here is where
the next stage comes...
Stage
2: the voltage buffer
This stage will isolate the point V1
from the final output V2,
while always keeping the voltage V2
at the exact same value of V1.
This is what we call a voltage buffer. for the voltage buffer
we use an opamp with the output connected to the inverting input
(this special configuration of the Op Amp is also called Voltage
Follower). The most important things to note are:
1 No current
(almost 0A) will flow from the point V1
into the opamp, so we wont be disturbing the resistor network
configuration
2
V2 will always equal
V1 (theoretically,
see the rest of this document)
3
The current going out from the point V2
to any other stage is sourced from from
the power supply of the OpAmp.
The
most encourted problem & some solutions
|
A
quick look on those 2 graphs can be sufficient to understand
the problem: the output of the op-amp is not linear on the
full 0-to-Vcc scale. actually an OpAmp, depending on its
type, will deliver a maximum voltage of (Vcc - 0.5V), where
Vcc is the supply voltage of the OpAmp. So, in our application,
the OpAmp will only deliver 4.5V even if theoretically it
should deliver 5V.
You may think this caused by the resistor network, but it's
not! this is a limitation in the op-amp itself.
Lets get a little deeper into the problem, the actual
output curve in red
should be linear, but actually it begins loosing its linearity
beginning from 3.9 volt. (Again this depends on the
type of OpAmp, those results a based on my own tests on
a LM350 OpAmp) The red 'Error zone' is where the output
of the DAC no longer math the relative binary input.
This is the error we will be trying to overcome in the next
part, through 2 very simple solutions. |
 |
Solution
1 :
The first solutions - shown
in the red shading - is to increase the supply voltage
of the Op-Amp, as shown in the schematic. this will totally solve
the problem, and, whether you are supplying 6.5 volts or more,
you will get neat linear output from 0V to 5V.
Solution
2 :
The second solutions - shown
in the red shading - is to reduce the range of the input
to [0 to 127] from the original range of [0 to 255]. This will
result on a voltage swing of 0 to 2.5 volt at the output, which
will be in the linear operating area of the Op-Amp (this done
by attaching the MSB line to ground, this way you only control
the 7 other lines, and a 7 bit value can swing from 0 to 127).
I hope this introduction was interesting, and that it will help
you to build simple but reliable DACs to suit your application.
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Related
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Analog to digital conversion, using an R/2R DAC.
Preview of the last 15
messages discussing this page. Messages are sorted from the newest to
the oldest. |
Posted
by:
ikalogic
on:
28 Aug 2008 |
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Re: R-2R based DAC |
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Quoting randykayc: hey Ika
just wondering if you can help with the finding how the Thevenin theorem applies here.
randykayc |
It should... why don't you try out and tell us? 
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Posted
by:
randykayc
on:
27 Aug 2008 |
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R-2R based DAC |
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hey Ika
just wondering if you can help with the finding how the Thevenin theorem applies here.
randykayc
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Posted
by:
wand23
on:
23 Aug 2008 |
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Re: R-2R based DAC |
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yes..i already read that article...i'll try to design first..thanks a lot ika...
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Posted
by:
ikalogic
on:
22 Aug 2008 |
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Re: R-2R based DAC |
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| Quoting wand23: hello ika..i'm new member at this forum...i need your help and also your opinion..my final project title is to design 12-bit DAC..i need to design the schematic diagram and then continue with layout design..so can u help me how to design the schematic diagram of 12-bit DAC? |
Welcome to ikalogic,
i guess you've read this article right? http://www.ikalogic.com/dac08.php
It explains how to build any N-bit DAC... jest add as many branches as you want..
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Posted
by:
wand23
on:
21 Aug 2008 |
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R-2R based DAC |
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hello ika..i'm new member at this forum...i need your help and also your opinion..my final project title is to design 12-bit DAC..i need to design the schematic diagram and then continue with layout design..so can u help me how to design the schematic diagram of 12-bit DAC?
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Posted
by:
ikalogic
on:
27 May 2008 |
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Re: R-2R based DAC |
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Quoting ias_aca: very good explanation..gud job,ibrahim!
if u dont mind, please make the same article about 8 bit ADC...would u?
thanks a lot |
It is already there: [link]
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Posted
by:
ias_aca
on:
27 May 2008 |
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R-2R based DAC |
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very good explanation..gud job,ibrahim!
if u dont mind, please make the same article about 8 bit ADC...would u?
thanks a lot
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Posted
by:
winnie
on:
09 May 2008 |
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Posted
by:
boobka
on:
09 May 2008 |
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R-2R based DAC |
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Nice article.
BUt I would suggest that for beginners it would be of help
if you could give some hints of the Thevenin equivalent of the network
..and thereafter discuss how the LM358 act as the voltage follower I guess... 
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Posted
by:
ikalogic
on:
08 May 2008 |
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Re: R-2R based DAC |
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Quoting nura100: Hello Ika,
Thanks alot for providing us with such a wonderful tutorial !
i want your opinion on the two kinds of DACs
1) Voltage output type
2) Current output type
Where will the Voltage type be used and where will be the current output type used
iam trying to reproduce some sound from 8051 using 8 bit Parallel DAC - but not sure which type to use volatge or current type .
Please Help
Arun |
The most natural, simple, and usable solution is voltage output type, like the one produced on that page good luck with your project, and let me know how it turns out.
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Posted
by:
nura100
on:
07 May 2008 |
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R-2R based DAC |
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Hello Ika,
Thanks alot for providing us with such a wonderful tutorial !
i want your opinion on the two kinds of DACs
1) Voltage output type
2) Current output type
Where will the Voltage type be used and where will be the current output type used
iam trying to reproduce some sound from 8051 using 8 bit Parallel DAC - but not sure which type to use volatge or current type .
Please Help
Arun
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Posted
by:
ikalogic
on:
28 Feb 2008 |
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Re: R-2R based DAC |
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Contribution from Chris :
Quote: Brill tutorial, but...
I think your circuit would divide the input voltage into 256 steps going from 00000000=0v to 11111111=4.98v (if input voltage is 5v). I don't think 5v is achievable.
Formula:
Vdigitalinput / 2^no of bits * digital value = Vout?
examples:
11111111 -> 5 / 2^8 * 255 = 4.98v (3sf)
10101010 -> 5 / 2^8 * 170 = 3.32v (3sf)
00000000 -> 5 / 2^8 * 0 = 0v
Okay, it's very close and is even less significant for more bits, but it might help someone if they've got a small error and can't figure out where it's coming from. (For a four bit DAC the output is about 4.7v; the error gets larger for less bits.)
Chris. |
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Posted
by:
ikalogic
on:
28 Feb 2008 |
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Re: R-2R based DAC |
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Quote: Thanks for this guide. I had a feeling this sort of solution was possible and this is exactly what I was looking for. Nice intro.
Two points you may like to improve:
1. Low end non linearity can be even more important than the top end that you explain well. Worth adding a comment.
2. The simplest most practicle solution is to use a more recent rail-to-rail op-amp like the LM2902. They are dirt cheap (0.20 euros for a quad op-amp package) and save the inconvenience of split suppies.
Finally a question. What is the cause of the minimum of 1k for R?
I have some digital outputs that already have 1k current limitting resistors. I would be great to have this as half the component count and use R=500 ohm. Looks like this would draw about 5mA for a 4 bit DAC which is fine by me.
Is the power drain the only reason for the limit ?
TIA.
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Exactly, the power drain IS the reason for the 1k limit.
Thanks a lot Ike for your contributions.
i'll work on the low end non linearity problem... i think it's time to update this article.. it hasen't changed for 5 monthes..
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Posted
by:
ikalogic
on:
28 Feb 2008 |
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Re: R-2R based DAC |
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Quote: i have a question regarding DAC. i am a student working on a project where i am using a microcontroller that creates a PWM signal as a function of a certain transfer function. normaly if i where to use an AC motor i would not need to do anything else since the engine would just take the average voltage of the PWM signal. but in my case i need to output a DC value (an average voltage value of the PWM voltage) since i have to make a battery emulator. as i said i am actually outputting the PWM on only one pin. how would you advise i do the DA conversion here so that i am outputing an average of voltage of the PWM?
i thank you for your time and hope to hear from you soon. |
Hello, You don't need DA conversion to control the speed of DC motors. changing the duty cycle of the PWM on one pin works perfectly to control DC motors. Actually in PWM, you do not want to send an average voltage, you let the motor do that as it acts as an inductor with it's coil...
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Posted
by:
ikalogic
on:
28 Feb 2008 |
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Re: R-2R based DAC |
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| Quote: If it's a volt reference source,and how can output current over 200 mA? |
A simple NPN transistor in common emitter configuration (emitter attached to groud)
a 2N2222 BJT will give you up to 800mA, a TIP122 will give you up to 5A.
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