Explain the working of Binary Weighted Resistor Digital to Analog converter with a neat diagram

Solution:

Binary Weighted Resistor Digital to Analog converter:

• The type described for the case of a voltage-output Digital to Analog converter where a digital input results in a discrete voltage level at the output.

• A weighted resistor Digital-to-Analog converter which has a reference voltage source a set of binary-weighted resistors an op-amp and a set of switches.

• The switch is closed when the binary bit is 1 and open when the binary bit is 0.

• When the binary bit is 1 the current flows through the resistor in series into the summing bus.
• When the current from all networks of resistors are summed in the amplifier, the total current is proportional to the output voltage of the amplifier.

• Show, the figure the currents sum together and go through Rf where the inverting input is 0V and Vout = IfRf.

• The lowest-value resistor (R) corresponds to, the highest binary-weighted input.

• The other resistors are multiples of 2R, 4R, and 8R and the equivalent binary weight is $2^2$, $2^1$, and $2^0$, respectively. This is because the sum of all the input current is through Rf.

• R = $2^3$ 2R = $2^2$

• 4R = $2^1$ 8R = $2^0$

• This type of Digital to Analog converter (DAC) is very difficult to mass produce due to the range of resistors required where the tolerance is less than 0.5% to accurately convert the input.