The RS DAC0800 used in the basic voltage output DAC system of Fig. 7.9 has the following error data: zero scale current (all bits off, Izs) = 2 μA; non-linearity = ±0.19 % FS; full-scale temperature coefficient (TCIFS)= ±50 ppm/°C; power supply sensitivity (PSSIFS+ , PSSIFS_) = 0.01 %/%. The 777

Question

The RS DAC0800 used in the basic voltage output DAC system of Fig. 7.9 has the following error data: zero scale current (all bits off, [latex]I_{zs}[/latex] ) = 2 μA; non-linearity = ±0.19 % FS; full-scale temperature coefficient [latex](TCI_{FS})= ±50[/latex] ppm/°C; power supply sensitivity ([latex]PSSI_{FS+}, PSSI_{FS-} ) = 0.01[/latex] %/%. The 777 type operational amplifier has the following data: [latex]V_{io} = 5[/latex] mV; [latex]\Delta V_{io}/\Delta T= 30[/latex] μV/°C; [latex]I_{os} = 40[/latex] nA and [latex] \Delta I_{os}/ \Delta T=10.3[/latex] nA/°C. The reference voltage of 10V has a tolerance of ± 1 % and a temperature coefficient [latex](TCV_{ref})[/latex] of ± 25 ppm/°C. The resistors have tolerances of 0.5% and both [latex]R_{L}[/latex] and [latex]R_{REF}[/latex] are 4.7 kΩ. Calculate the worst case errors before and after calibration. Assume that the maximum change in temperature is from 25 °C to 70 °C.

Accepted Answer

FSR

[latex]V_{x}= \frac{255}{256}\frac{V_{REF} }{R_{REF} } imes R_{L}\simeq \frac{10 imes 4.7 imes 10^{3} }{4.7 imes 10^{3}}= 10[/latex] V

Worst case initial offset error

=[latex]\pm V_{io} \pm I_{os}R_{L} \pm I_{zs}R_{L}[/latex]

=[latex] \pm 5 imes 10^{-3} \pm 40 imes 10^{-9} imes 4.7 imes 10^{3} \pm 2 imes 10^{-6} imes 4.7 imes 10^{3}= \pm 14.6[/latex] mV

[latex]=\pm \frac{14.6 imes 10^{-3} imes 100 }{10} = \pm 0.146 \%[/latex] of FS

The gain or scale factor is given by the ratio of the output voltage to the numerical fraction determined by digital input code.

[latex]\frac{V_{x} }{(\frac{1}{2}+...\frac{1}{2^{8} } )} = I_{FS} R_{l} \cdot \frac{1}{\frac{255}{256} }[/latex]

[latex]=\frac{255}{256} \cdot \frac{V_{REF} }{R_{REF}}\cdot R_{L}\cdot \frac{256}{255}= \frac{V_{REF} }{R_{REF}} imes R_{L}[/latex].

Thus the initial gain error comprises [latex]V_{REF}[/latex] tolerance, ± 1 % [latex]R_{REF}s[/latex] and [latex]R_{L}s[/latex] tolerances of ± 0.5% each, thus giving a worst case initial gain error ± 2%.

Linearity error is specified as ±0.19% of FS. Thus the worst case error without calibration

= ±0.146 ± 2 ± 0.19 = ±2.34 %.

After initial offset and gain errors are nulled to zero, the offset drift over the maximum temperature change of 45 °C (70° — 25°) [note: no data available for zero scale current-variation with temperature]

[latex]= \pm \frac{\Delta V_{io} }{\Delta T} imes 45 \pm \frac{\Delta I_{os} }{\Delta T}R_{L} imes 45[/latex]

[latex]= \pm 30 imes 10^{-6} imes 45\pm 10.3 imes 10^{-9} imes 4.7 imes 10^{3} imes 45 = \pm 0.00352[/latex] V

[latex]= \pm 0.035\%[/latex] FS

The gain error over temperature change

[latex]\pm TCI_{FS} imes 100 imes 45 \pm TCV_{ref} imes 100 imes 45[/latex]

[latex]= \pm \frac{50}{10^{6}} imes 100 imes 45 \pm \frac{25}{10^{6}} imes 100 imes 45 \simeq \pm 0.34 \%[/latex]

Linearity over temperature remains constant at 0.19%. Error over power supply variation = ±0.01 ±0.01 =0.02%. Thus the total worst case error after calibration
[latex]= \pm 0.035\% \pm 0.34\% \pm 0.19\% \pm 0.02\% =0.59\%[/latex].

Question 7.10: The RS DAC0800 used in the basic voltage output DAC system o...

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