Basics of DACs

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BLOCK DIAGRAM OF A DIGITAL-ANALOG CONVERTER

b1 is the most significant bit (MSB)

The MSB is the bit that has the most (largest) influence on the analog output

bNis the least significant bit (LSB)

The LSB is the bit that has the least (smallest) influence on the analog output


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Chapter 10 - DA and AD Converters (6/4/01) _ P.E. Allen, 2001

10.1 - CHARACTERIZATION OF DIGITAL-ANALOG CONVERTERS

STATIC CHARACTERISTICS

OUTPUT-INPUT CHARACTERISTICS

Ideal input-output characteristics of a 3-bit DAC


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DEFINITIONS

Resolutionof the DAC is equal to the number of bits in the applied digital input word.

The full scale (FS):

FS = Analog output when all bits are 1 - Analog output all bits are 0VREF

FS = (VREF- 2N) - 0 = VREF 1 - 12N

Full scale range(FSR) is defined as

FSR =lim

N FS =

Quantization Noiseis the inherent uncertainty in digitizing an analog value with a finite resolution converter.


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max

max FSR

/2

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EVEN MORE DEFINITIONS

Effective number of bits (ENOB)can be defined from the above as

ENOB=SNRActual-1.76

6.02where SNRActualis the actual SNRof the converter.

Comment:

TheDR is the amplitude range necessary to resolveNbits regardless of the amplitude of the output voltage.

However, when referenced to a given output analog signal amplitude, theDR required must include 1.76 dB more

to acount for the presence of quantization noise.

Thus, for a 10-bit DAC, theDRis 60.2dB and for a full-scale, rmsoutput voltage, the signal must be approximately

62dB above whatever noise floor is present in the output of the DAC.


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OFFSET AND GAIN ERRORS

An offset erroris a constant difference between the actual finite resolution characteristic and the infinite

resolution characteristic measured at any vertical jump.

Again erroris the difference between the slope of an actual finite resolution and an infinite resolution

characteristic measured at the right-most vertical jump.


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Chapter 10 - DA and AD Converters(6/4/01) _ P.E. Allen, 2001


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Chapter 10 - DA and AD Converters(6/4/01) __ P.E. Allen, 2001


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Chapter 10 - DA and ADConverters (6/4/01) __ P.E. Allen, 2001

INFLUENCE OF THE OP AMP GAINBANDWIDTH

Single-pole response:

vout(t) =ACL[1 - e-Ht]vin(t)

whereACL= closed-loop gain

R 1 C2 H= GB R1+R2 or GB

C1+C2

To avoid errors in DACs (and ADCs), vout(t)must be within 0.5LSBof the final value by the end of the conversion

time.

Multiple-pole response:

Typically the response is underdamped like the following (see Appendix C of text).


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Chapter 10 - DA and AD Converters(6/4/01) __ P.E. Allen, 2001

=

2) = 0.693

3.141 0.693 = 1.986

- 2

GB

Assume that a DAC uses a switched capacitor noninverting amplifier with = and = 1MHz. Find the

conversion time of an 8-bit DAC if is 1V.

From the analysis in Secs. 9.2 and 9.3, we know that

+ = (2(0.5)(10 ) =3.141x10

and = 1. Assume that the ideal output is equal to .Therefore the value of the output voltage which is

0.5LSB of is

= 1 - - H

or

2 = H

Solving for gives

=


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TESTING OF DACs

INPUT-OUTPUT TEST

Test setup:

Comments:

Sweep the digital input word from 000...0 to 111...1.

The ADC should have more resolution by at least 2 bits and be more accurate than the errors of the DAC

INL will show up in the output as the presence of 1s in any bit.

If there is a 1 in the Nth bit, theINLis greater than 0.5LSB

DNLwill show up as a change between each successive digital error output.

The bits which are greater thanNin the digital error output can be used to resolve the errors to less than 0.5LSB


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SPECTRAL TEST

Test setup:

Comments:

Digital input pattern is selected to have a fundamental frequency which has a magnitude of at least 6NdB above its

harmonics.

Length of the digital sequence determines the spectral purity of the fundamental frequency.

All nonlinearities of the DAC (i.e.INLandDNL) will cause harmonics of the fundamental frequency

The THD can be used to determine the SNR dB range between the magnitude of the fundamental and the THD. ThisSNR should be at least 6NdB to have anINLof less than 0.5LSBfor an ENOB ofN-bits.

Note that the noise contribution of VREFmust be less than the noise floor due to nonlinearities.

If the period of the digital pattern is increased, the frequency dependence ofINLcan be measured.

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Basics of DACs