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## LESSON 22. R& 2R ladder DAC-Advantages-performance

**R/2R Ladder DAC**

In this type, reference voltage is applied to one of the switch positions and other switch position is connected to ground, as shown in the fig.

** **

In general, the expression for V_{o} can be obtained as,

Let

I_{out} = Output current

R_{f} = feedback resistance of op-amp

@ V_{o} = - I_{out} R_{f}

Now I_{out} = current resolution x D

@ V_{o} = - (current resolution x D) R_{f}

@ V_{o} = - (current resolution x R_{f} ) D

The coefficient of D is the voltage resolution and can be called as simple resolution.

@ V_{o} = - resolution x D

In terms of actual circuit elements, output can be written as,

V_{o} =

The resolution of R/2R ladder type DAC with current output is,

1 V_{R}

resolution = ------- x ------

2^{n} R

While the resolution for R/2R ladder type DAC with voltage output is

resolution =

Example:

Suggest the values of resistors and reference voltage if resolution required is 0.5 V for 4 bit r/2R ladder type DAC.

Solution:

resolution

let V_{R } = 10 V, n = 4 and resolution = 0.5

@ 0.5 =

Advantages of R/2R ladder DACs:

1) Easier to build accurately as only two precision metal film resistors are required.

2) Number of bits can be expanded by adding more sections of same R/2R values.

3) In inverted R/2R ladder DAC, node voltages remain constant with changing input binary words. This avoids any slowdown effects by stray capacitances.

**Performance Parameters of DAC**

The various performance parameters of DAC are,

Resolution

Resolution is defined in two ways.

- Resolution is the number of different analog output values that can be provided by DAC. For an n-bit DAC.

resolution = 2^{n}

- Resolution is also defined as the ratio of a change in output voltage resulting from a change of 1 LSB at the digital inputs. For an n-bit DAC it can be given as

V_{oFS}

resolution = -------------

2^{n } - 1

Where, V_{oFS} = Full scale output voltage

From equation (2) we can say that, the resolution can be determined by the number of bits in the input binary word. For an 8 – bit DAC resolution can be given as

resolution = 2^{n} = 2^{8} = 256

If the full scale output voltage is 10.2 V then by second definition the resolution for an 8 –bit DAC can be given as

V_{oFS } 10.2 10.2

resolution = ------------- = ------------ = --------- = 40 mV/LSB

2^{n } - 1 2^{8} - 1 255

Therefore, we can say that an output change of 1 LSB causes the output equation for a DAC.

Thus V_{o} = resolution x D

where D = decimal value of the digital input

and V_{o} = output voltage

The resolution takes care of changes in the input.

Accuracy

It is a comparison of actual output voltage with expected output. It is expressed in percentage. Ideally the accuracy of DAC should be, at worst, ± ½ of its LSB. If the full scale output voltage is 10.2 V then for an 8-bit DAC accuracy can be given as

V_{oFS}

Accuracy = -------------

(2^{n } - 1) 2

10.2

Accuracy = ------------- = 20 mV

255 x 2

Monotonicity

A converter is said to have good monotonicity if it does not miss any step backward when stepped through its entire range by a counter.

Conversion Time

It is a time required for conversion of analog signal into its digital equivalent. It is also called as setting time. It depends on the response time of the switches and the output of the amplifier.

Setting Time

This is the time required for the output of the DAC to settle to within ± ½ LSB of the final value for a given digital input i.e., zero to full scale.

Stability

The performance of converter changes with temperature, age and power supply variations. So all the relevant parameters such as offset, gain, linearity error and monotonicity must be specified over the full temperature and power supply ranges. These parameters represent the stability of the converter.