There are a number of situations when digital signals have to be converted to analogue ones. For example, a digital computer often needs to produce a graphical display on the screen; this involves using a D/A converter to change the two-level digital output voltage from the computer, into a continuously varying analogue voltage for the input to the cathode ray tube, so that it can deflect the electron beam to produce screen graphics.

A binary weighted resistor D/A converter is shown in figure for a four-bit input. The values of the resistors, R, 2R, 4R, 8R increase according to the binary scale – hence the name of the converter. The circuit uses an op amp as a summing amplifier with a feedback resistor R_{f}. Digitally controlled electronic switches are shown as S_{1} to S_{4}.

Each switch connects the resistor in series with it to a fixed reference voltage V_{REF} when the input bit controlling it is a 1 and to ground (0V) when it is a 0. The input voltages V_{1} to V_{4} applied to the op amp by the four-bit input via the resistors therefore have one of two values, i.e. either V_{REF} or 0V.

The analogue output voltage Vo is given by:

V_{\mathrm{o}}=-\left(\frac{R_{\mathrm{f}}}{R} V_1+\frac{R_{\mathrm{f}}}{2 R} V_2+\frac{R_{\mathrm{f}}}{4 R} V_3+\frac{R_{\mathrm{f}}}{8 R} V_4\right)Let R_{f} = R = 1 kΩ, then:

With a four-bit input of 0001 (i.e. decimal 1), S_{4} connects 8R to V_{REF}, i.e. V_{3} = V_{REF}, and S_{1}, S_{2} and S_{3} connect R, 2R and 4R to 0V, making V_{1} = V_{2} = V_{3} = 0. Let V_{REF} = −8 V, then output voltage,

With a four-bit input of 0101 (i.e. decimal 5), S_{2} and S_{4} connects 2R and 8R to VREF, i.e. V_{2} = V_{4} = V_{REF}, and S_{1} and S_{3} connect R and 4R to 0V, making V_{1} = V_{3} = 0.

Again, if VREF = −8 V, then output voltage,

If the input is 0111 (i.e. decimal 7), the output voltage will be 7V, and so on. From these examples, it is seen that the analogue output voltage, V_{o}, is directly proportional to the digital input. V_{o} has a ‘stepped’ waveform, the waveform shape depending on the binary input. A typical waveform is shown in Fig.

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