Weighted resistor digital to analog Converter is a very basic D/A converter. By using simple resistor network we can easily build that. As we discuss earlier about how digital to analog converters works you may refer that first. Let us consider a N-bit straight binary resistor network, which produces a current I corresponding to logic 1 at the most significant bit, I/2 corresponding to logic 1 at the next lower bit, I/22 for the next lower bit and so on, and I/ 2N–1 for logic 1 at the least significant bit position. Now the total current thus produced by that resistive network will be proportional to the digital inputs, which we want to convert in equivalent analog signal. Farther this current can be converted to voltage with the help of a converter circuit by an using operational amplifier (OP AMP). Finally then we get the produced voltage is analog in nature and will be proportional to the digital inputs.
Now see the circuit bellow
It may be observed in the circuit diagram that different values of resistances are used at the digital inputs and the resistance values are the multiple of the resistance corresponding to the most significant digital input to produce the currents I, I/2, I/22, …. I/ 2N–1. Since the resistance values are weighted in accordance with the binary weights of the digital inputs, this circuit is referred to as a weighted-resistor D/A converter.
Now question is how it converts digital to analog signal?
If we consider the above picture shows the ideal op-amp amplifier then the output current (Io) will be
Io = I1+I2+I3+……..+In
= (V(1)/21R)*B1 + (V(1)/22R)*B2 + (V(1)/23R)*B3 +……….+ (V(1)/2NR)*Bn
= (V(1)/R)[B1*2-1 + B2*2-2 + B3*2-3 + …………………… + Bn*2-n]
Then the output voltage will be
VO=IO*Rf = (V(1)/Rf)[B1*2-1 + B2*2-2 + B3*2-3 + …………………… + Bn*2-n] * Rf
So by using above relation the equivalent analog voltage will be produce foe any corresponding digital inputs. And as we can see that the out put is totally depend on the weight of register by power of 2. that is why it is called weighted resistor digital to analog converter In bellow see the diagram of analog output of corresponding input signal.