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R 2R Ladder Type DAC

The R-2R Digital-to-Analog Converter (DAC) utilizes a ladder network of two resistor values, R and 2R, to convert digital binary numbers into proportional analog signals. The output voltage can be calculated based on the binary input and reference voltage, allowing for easy scaling to any number of bits. Advantages include the simplicity of using only two resistor types and a consistent output impedance.

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Kavida A
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28 views22 pages

R 2R Ladder Type DAC

The R-2R Digital-to-Analog Converter (DAC) utilizes a ladder network of two resistor values, R and 2R, to convert digital binary numbers into proportional analog signals. The output voltage can be calculated based on the binary input and reference voltage, allowing for easy scaling to any number of bits. Advantages include the simplicity of using only two resistor types and a consistent output impedance.

Uploaded by

Kavida A
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PPTX, PDF, TXT or read online on Scribd
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R-2R ladder type Digital to

Analog Converter
R-2R DAC

 R-2R Digital-to-Analogue Converter, or DAC,


is a data converter which use two precision
resistor to convert a digital binary number
into an analogue output signal proportional
to the value of the digital number
 The R-2R resistive ladder network uses just
two resistive values. One resistor has the
base value “R”, and the second resistor has
twice the value of the first resistor, “2R”, no
matter how many bits are used to make up
the ladder network.
R-2R DAC
R-2R DAC
R-2R DAC
R-2R DAC
R-2R DAC
R-2R DAC
R-2R DAC
R-2R DAC
R-2R DAC
 For n bit DAC
R-2R DAC
 Let’s assume a 3 bit DAC using R-2R ladder
network.
 B B B are the 3 bits of the binary input.
2 1 0
When B0 = 1, B1 & B2 = 0. Then the
equivalent circuit would be;
R-2R DAC
 Replacing the 1st stage with its Vth & Rth;
 Vth = Vref/2 & Rth = R
R-2R DAC
 Now the 2nd stage Vth & Rth;
 Vth = Vref/4 & Rth = R
R-2R DAC
 Now the 3rd stage V­th & Rth
 Vth = Vref/8 & Rth = R

So the output voltage in this case


would become
Vout = -Vth (Rf/R) = -(Vref/8) (R/R) = -
(Vref/8)
R-2R DAC
 When B1 = 1, B0 & B2 = 0. Then the
equivalent circuit would be;
R-2R DAC
Applying the same process the output
voltage will be
V
out = -(Vref/4)
R-2R DAC
 When B2 = 1, B0 & B1 = 0. Then the
equivalent circuit would be;
R-2R DAC
Applying the same process the output
voltage will be
V
out = -(Vref/2)
R-2R DAC
As we know the output of the opamp is the
sum of individual inputs where each bit is
V
out = -{ B0 (Vref/8) + B1 (Vref/4) + B2 (Vref/2)}

 Vout = – Vref { B0(1/8) + B1 (1/4) + B2 (1/2)}


 Vout = – Vref { B0(1/23) + B1 (1/22) + B2 (1/21)}
We can generalize this formula for an N bit
binary number as;
V
out = – Vref {B0(1/2 ) + B1(1/2 ) + B2(1/2N-2)
N N-1

+…+ BN-2(1/22) + BN-1(1/21)}


R-2R DAC
 Example:
 Convert a binary number of 10110 into an analog
output where the vref = 12v
 The number of bit N = 5
 Vout = – Vref {B0(1/2N) + B1(1/2N-1) + B2(1/2N-2) +…+ BN-
2(1/2 ) + BN-1(1/2 )}
2 1

 Vout = – Vref {B0(1/25) + B1(1/24) + B2(1/23) + B3(1/22) +


B4(1/21)}
 Vout = – (12) {(0)(1/25) + (1)(1/24) + (1)(1/23) + (0)
(1/22) + (1)(1/21)}
 Vout = – (12) {(1/24) + (1/23) + (1/21)}
 Vout = – (12) {(1/16) + (1/8) + (1/2)}
 Vout = – 8.25 v
R-2R DAC
 Advantages of R-2R Ladder DAC;
 Uses only two types of resistors

 Easiliy scalable to any number of bits

 Output impedance is always R

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