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INA823: INA823:

Part Number: INA823
Other Parts Discussed in Thread: ADS8689

Hi, team!

I want to calculate ADC823+ Amp8689 error.

offset voltage error:

INA823:        G=1, V(OS_RTI)=V_OSI+V_OSO∕G=(20+140∕1)uV=160.06uV  V(OS_INA)=G*V(OS_RTI)=160.06uV

ADS8689:     V(OS_ADC)=Eo=±0.2mV

                     V_OST=√((V(OS_INA))^2+(V(OS_ADC))^2 )≈256.16uV

Gain Error:

E_G=√((E(INA_G))^2+(E(ADC_G)^2+(E_R1)^2 )       R1 is sample resistor(50ohm,0.1% )

       = (0.01^2*2+0.1^2)

       ≈0.101%

Noise:

INA823:     En_ina=√((e(nr ) )^2+(e(ni ) )^2+(e_nv ) )^2 )≈153.48uV(Resistor Noise/Current Noise/Voltage Noise)

ADS8689:  V(FSR_rms)=0.5∙FSR∙0.707≈7239.68mV

                  E(n_adc)=V(FSR_rms)/(10^(SNR/20)) =7239.68mV/(10^(91.5dB/20)) ≈192.63uV

                 

                   E(n_total)=√((E(n_ina))^2+(E_(n_adc))^2 )≈246.30uV

I want to know if there is something wrong in the above formula?

And I want to calculate total error(Etotal) ,including offset error, gain error and noise error.

Can I calculate like this?

E_total=√((V_OST/Vin )^2+E_G^2+(E(n_total)/Vin )^2 )=???

Is this formula right? And Vin is -10V~+10V, so I choose 2.5Vref as shown in figure.

E_total=√((V_OST/Vin )^2+E_G^2+(E(n_total)/Vin )^2 )=√((256.16uV/10V)^2+0.101%^2+(246.30uV/10)^2)=???%

I think there is something wrong and it's too small. Could you tell me which formula is wrong? Or provide me some document about this calculation(error about amp+adc).

Thank you so much!

  • Hale,

    You do not specified what is the full-scale ADS range. Your calculations above were done for typical bipolar case at 25 deg C but for the worst case error analysis, you must used maximum offsets and gain limits specified in the datasheets and not typical you used.  

    Thus, 

    offset voltage error:

    INA823:  G=1, V(OS_RTI)=V_OSI+V_OSO∕G=(+/-100+/-450∕1)uV=+/-550uV  

    ADS8689:     V(OS_ADC)=Eo=±1.0mV;     

    Also, for worse-case you must assume they add linearly and not as vector quantities. 

    V_OST=V(OS_INA)+V(OS_ADC)≈+/-1.55mV

    You must also include differential and integral nonlinearity - see below.

    Gain Error:

    worst-case E_G=E(INA_G)+(E(ADC_G)+(E_R1) = 0.04%+.025%+0.1% = 0.165% (is R1 a shunt resistor? Please show schematic)

    Noise:

    INA823:     En_ina=[√((e(ni)^2+(e_no)^2 )]*√(BWn)=√(21^2+120^2)*√(1.9e6*1.57) = 122nV/√(Hz)*√(2.98MHz) = 211uVrms

    You also need to include the differential and integral nonlinearity - see below.

  • Hi Tan,

    You may also find the following TI Precision Labs Sessions useful.  They discuss error calculation of amplifiers +ADCs:

    5.1 Statistics behind error analysis of ADC system

    5.2 Understanding and calibrating the offset and gain for ADC systems

    Thank you and Regards,

    Luis

  • Hi, Marek!

    Thanks for your reply. I want to ask if I need to calculate ADC noise in this case and the formula is shown. 

    When calculating INL/DNL/Eg/Eo, is ADC noise included?

  • Hi Tan,

    ADC noise is not included and need to be added using above formula - INL, DNL, Eg and Eo are all DC parameters and do not include the ADC noise.

    Having said that, as discussed in https://training.ti.com/ti-precision-labs-adcs-statistics-behind-error-analysis?context=1139747-1140267-1128375-1139104-1128656 the worst case analysis must be done by linearly adding maximum values of all error components (a very conservative approach) or you may use a vector addition of all typical values (1-sigma) and then multiplying the result by acceptable failure rate (number of sigmas) - see example below.