3 Digital-to-Analog Conversion

 

(1) Weighted Resistor Digital-to-Analog Converter

            The type described for the case of a voltage-output DAC where a digital input results in a discrete voltage level at the output.

3.1 Weighted Resistor Digital-to-Analog Converter

Figure 1 illustrates 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. From the diagram it can be noticed that each switch has it own binary bit of the digital input word which controls it.  The switch is closed when the binary bit is 1 and open when the binary bit is 0. When the binary bit is 1 (switch is closed) 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. 

Since the currents sum together and go through Rf where the inverting input is 0V and Vout = IfRf.  The input resistors are inversely proportional to the binary weights of the input bits.  The lowest-value resistor (R) corresponds to the highest binary-weighted input (2³ = 8).  The other resistors are multiples of R (i.e. 2R, 4R, and 8R) and the equivalent binary weight is 2², 2¹, and 2⁰, respectively. The input current is proportional to the binary weights and the output voltage is proportional to the sum of the binary weights.  This is  because the sum of all the input current is through Rf. 

The disadvantage of the weighted resistor DAC is the numerous resistor values.  For instance, if we take an 8-bit converter, the 8 resistors will range from R to 128R in binary weighted steps.  This type of 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. 

 

3.2 Performance Characteristics of Digital-to-Analog Converters

Resolution

    The resolution of a DAC is the reciprocal of the number of discrete steps in the DAC.  This is independent of the number of bits. Resolution can also be shown as the number of bits converted.

Accuracy

    This is the comparison of the actual output of a DAC with the expected output. This is expressed as a percentage of a full scale, or maximum output voltage.

Linearity

    A linear error is a deviation from the ideal straight-line output of a DAC.

Monotonicity

    A DAC is monotonic if it does not take any reverse steps then it is sequenced over its entire rage of input bits.

Setting Time

    This is the time it takes a DAC to settle within +/- 1/2 of a least significant bit of its final value when a change occurs in the input code.