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Principle

Each DAC circuit has a specific purpose based on its use within the system but the general purpose of all DACs is to provide an analogue signal output based on the digital value represented in the digital computer. This analogue signal is either a voltage or current output but the principles involved are essentially the same.

The basic principle of a DAC converter is to divide the analogue output into a series of small steps. The number of steps depends on the number of bits used in the data to be converted. If the data consists of 8 bits then the output is divided into 256 (2⁸) steps. The size of each step would be 0.0195 volts (5v/256 steps). If an 8 bit, 5 volt converter is driven by a simple counter then the output of the converter would be a series of 256 steps of 0.0195 volts. As the counter progress from 0 to 255, the converter output increases from 0 volts to 4.98v then drops to zero when the counter rolls over. Also, note that the maximum output voltage is not 5 volts.

This is due a fact that each digital input bit is weighted according to its position within the binary input. The least significant bit (LSB) has a weight of 5v/256

= 0.0195 volts, the next most significant bit has a weight of 5v/128 = 0.039 volts, the next has a weight of 5v/64 = 0.078 volts, and so on, with the most significant bit (MSB) having a weight of 5v/2 = 2.5 volts. If you add all the individual bit weights, you get a 4.98 volt maximum output when the DAC input is 1111 1111.

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Binary Weighted Ladder

Starting from V1 and going through V3, this would give each input voltage exactly half the effect on the output as the voltage before it. In other words, input voltage V₁ has a 1:1 effect on the output voltage (gain of 1), while input voltage V₂ has half that much effect on the output (a gain of 1/2), and V₃ half of that (a gain of 1/4). These ratios are the same ratios corresponding to position weights in the binary system.

The op-amp is used as a summation device, to sum the weighted inputs of the digital information.

If we drive the inputs of this circuit with digital gates so that each input is either 0 volts or full supply voltage, the output voltage will be an analogue representation of the binary value of these three bits.

The disadvantage of this circuit is that a high precision is required of the resistors, especially the higher values (± 0.5%). This makes it difficult to mass produce.

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R-2R Ladder

The R-2R ladder network is another type of DAC. Each bit of the binary input controls a solid state switch which connects either a reference voltage or a ground to the resistors. The ladder is constructed of resistors of only two values, R or 2R rather than binary weighted. In this type of network the actual resistor values are not as critical as in the binary weighted ladder. Also since the resistance values can be small; it is much easier to implement this in a solid state device.

The inverting input of the op-amp is at virtual earth. Current flowing in the elements of the ladder network is therefore unaffected by switch positions. The selected resistor values ensure that the relationship:

The current ITOTAL, is the sum of the currents switched to the inverting input of the op-amp from the R-2R ladder by the digitally controlled switches Do - D3. ITOTAL is given by the relationship:

The output voltage V_OUT is the voltage across the op-amp feedback resistor which is by Ohms law:

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Some uses of DACs

Waveform Generators

The analogue output required from a digital computer which is not always a steady output level. Sometimes a particular wave form is required, such as a sawtooth or ramp. A ramp or sawtooth wave can be easily implemented by using simple R-2R ladder and a counter.

A binary counter used to drive a R-2R ladder causes the ladder to output a sequence of steps of different voltage levels. As the counter reaches its maximum value, it returns to zero or is said to "roll over'. When the input word rolls over to zero the output also returns to zero. While this output is not a pure ramp due to the fact that the binary words generate steps, most analogue systems are slow enough in their reaction times that they react the same as if the signal was continuous. High quality R-2R ladders have relatively short response times (2 microseconds typical). For an 8 bit device this makes the rise time from 0 to 10 volts in the order of 0.5 microseconds or a frequency of 2 MHz.

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Programmable Gain Amplifiers

DACs can also be used to provide gain control of an analogue signal. This arrangement may be required, for example, to control the speed of an AC motor by varying the input voltage level to the motor. This can be accomplished quite simply by applying an AC voltage as VR to a ladder network.

A simple-motor controller is shown. A 5 volt AC reference signal is applied as VR to an 8-bit DAC. The data word is generated by the computer to select the desired motor speed by setting the output level. Remember for an 8-bit device this output can be divided into 256 steps, so very fine control can be established with this simple method. One minor problem with this simple motor control is the fact that the computer does not know if the motor speed is correct. To check this, there must be a feedback from the motor. This feedback would be analogue so we need an analogue to digital converter.

Almost all "real world" applications are analogue in nature. Therefore, analogue to digital converters (ADCs) are quite common in computer systems, and especially in those systems dedicated to monitoring or controlling "real world" events. An ADC converts a continuous voltage signal, or analogue signal into a multi-bit digital word.

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5.3.5.2 Analogue to Digital Converters (ADCs)