Digital to Analog Converter using Binary Weighted Resistors R 2R

The R-2R ladder DAC which is a binary-weighted DAC that uses a repeating cascaded structure of resistor values R and 2R. This improves the precision due to the relative ease of producing equal valued-matched resistors (or current sources). However, wide converters perform slowly due to increasingly large RC-constants for each added R-2R link. The D/A converter using binary-weighted resistors is shown in the figure below. In the circuit, the op-amp is connected in the inverting mode. The op-amp can also be connected in the non-inverting mode. The circuit diagram represents a 4-digit converter. Thus, the number of binary inputs is four.

Circuit Diagram

Fig. 1

We know that, a 4-bit converter will have 2⁴ = 16 combinations of output. Thus, a corresponding 16 outputs of analog will also be present for the binary inputs.

Four switches from b0 to b3 are available to simulate the binary inputs: in practice, a 4-bit binary counter such as a 7493 can also be used.

Working

The circuit is basically working as a current to voltage converter.

1. b0 is closed
It will be connected directly  to the +5V.
Thus, voltage across R = 5V
Current through R = 5V/10kohm = 0.5mA
Current through feedback resistor, Rf = 0.5mA (Since, Input bias current, IB is negligible)
Thus, output voltage = -(1kohm)*(0.5mA) = -0.5V

2. b1 is closed, b0 is open
R/2 will be connected to the positive supply of the +5V.
Current through R will become twice the value of current (1mA) to flow through Rf.
Thus, output voltage also doubles.

3. b0 and b1 are closed
Current through Rf = 1.5mA
Output voltage = -(1kohm)*(1.5mA) = -1.5V

Thus, according to the position (ON/OFF) of the switches (bo-b3), the corresponding “binary-weighted” currents will be obtained in the input resistor. The current through Rf will be the sum of these currents. This overall current is then converted to its proportional output voltage. Naturally, the output will be maximum if the switches (b0-b3) are closed,

V0 = -Rf *([b0/R][b1/(R/2)][b2/(R/4)][b3/(R/8)]) 

Where each of the inputs b3, b2, b1, and b0 may either be HIGH (+5V) or LOW (0V).

The graph with the analog outputs versus possible combinations of inputs is shown below.

Fig. 2

The output is a negative going staircase waveform with 15 steps of -).5V each. In practice, due to the variations in the logic HIGH voltage levels, all the steps will not have the same size. The value of the feedback resistor Rf changes the size of the steps. Thus, a desired size for a step can be obtained by connecting the appropriate feedback resistor. The only condition to look out for is that the maximum output voltage should not exceed the saturation levels of the op-amp. Metal-film resistors are more preferred for obtaining accurate outputs.

Disadvantages

If the number of inputs (>4) or combinations (>16) is more, the binary-weighted resistors may not be readily available. This is why; R and 2R method is more preferred as it requires only two sets of precision resistance values.