Tutorial for learning AVR assembly language
for AVR single chip controllers AT90S, ATtiny, ATmega and ATxmega
from ATMEL using practical examples
Simple 8-bit-Digital-to-Analog-Converter with a R/2R Network Calculation basics of a R/2R network
Calculation basics R/2R net work
Here, it is demonstrated stepwise how a R/2R network functions and how it can be
This is a simple One-Bit-DAC.
Depending from the state on the input on bit 0 the DAC generates two different
If bit 0 is zero or low, the resulting output voltage is half the operating
voltage is 0.
If bit 0 is one or high, the output voltage is half of the operating voltage
The operating voltage UB is the operating voltage of the AVR driving
the output port, e.g. 5.0 V. The half operating voltage results from the
resistor divider, which consists of the two 2R resistors. This voltage is divided:
Uout = UB * 2R / (2R + 2R) = UB * 0.5
The upper half of the operating voltage is consumed by the upper resistor.
For the starter three additional notes:
Why "2*R" and not simply "R" is shown below, when more
bits are added. If that occurs, additional resistors with half the value of
"2*R" play an essential role. So be patient.
The horizontal line in the lower part of the second resistor means "
connected to zero Volt" or ground or GND. In our case, the minus pole of the
It makes no difference which type of or value of resistors are used. They
should not be too small because if the portpin would have to drive a too
large current, its output voltage is higher than 0.0 Volt or smaller than
the operating voltage. Currents of a few mA are ok. The resistors should
not be too large, too, because the added load on the output can reduce the
R/2R voltage or capacitive loads can speed down any voltage changes.
Now we add two more resistors, to have a 2-Bit-DAC.
Depending from the state of the two bits not only two different but four
voltages result. The states 00, 01, 10 and 11 on the two inputs generate
this. Here, the "2R" on the inputs (and on the lower part) and
the connection of the lower with the upper bit via a R, half the resistance
of the 2R. That causes the name R/2R network.
The same principle can be continued to construct 4-, a 8- or a 10-bit DAC.
How it works that the two input pins 0 and 1 contribute so differently to
the resulting voltage at UR1 can only be understood by looking
at all the currents in the network.
The current in the lower part divides into two tracks: one part flows
to the input pin Bit 0 via 2R, the other part to minus, also via 2R.
This current equals the current that flows from the output pin to
the lower part, through R.
And finally this current equals the current that flows from the
input pin Bit 1 to the output pin.
The calculation of all those currents is a bit more complicated and requires
some algebra, but comes to a simple result. Here is the complete calculation.
The result of all those calculations in equation (18) is rather simple, all
resistors and currents have disappered and the result is nice: both bits
contribute to the output voltage by their binary part. Bit 1 one half, bit
0 one fourth.
Equation (19) writes this as a general formula for n bits. Without having
to write down douzends of currents through 9 times 2R and 7 times R. That
would not fit to a HTML screen, and especially not onto the screen of a
The maximum voltage that a R/2R network provides is not the operating
voltage but slightly smaller (due to the lowest 2R to ground). It rather
UMax = UB * (2n - 1) / 2n
In case of an 8-bit network and 5.0 V the maximum is 4.98 V.