8 Design Procedure for Input Resistance at CSA Reference Pins

When CSAs have external input resistance at the REF pin, the designer must confirm that the reduced dynamic range of CSA output can still meet system requirements. This requires considering all possibilities of resistor tolerance, CSA process variation, bus voltage variation, and supply voltage (Vs), if using a resistor divider of Vs pin.

1. Before the analysis, understand what are the maximum and minimum bounds of the linear operating range of V_OUT, as well as, how are these bounds are further constrained by device output voltage noise.
   1. V_{OUT, MAX} = V_{OUT, MAX linear} – V_{OUT, noise pk-pk}/2
   2. V_{OUT, MIN} = V_{OUT, MIN linear} + V_{OUT, noise pk-pk}/2
      1. Usually V_{OUT, MAX linear} can be 100mV below output's swing to supply voltage.
      2. Usually V_{OUT, MIN linear} can be 100mV above output's swing to ground.
2. For each PV corner, examine all 4 possible worst-case Ra and Rb combination at maximum temperature swing (assume the PV corner can have both PTC and NTC).
   1. Calculate the designed for reference voltage value $V_{REF\_x} = V_S \times R_a\left|\right|R_b$
   2. Calculate the effective input resistance (Rx = Ra||Rb).
3. For each combination, calculate the effective reference voltage (V_{REF_EFFECTIVE}) using Equation 21 as shown outlined in the following Driving Voltage Reference Pins of Current-Sensing Amplifiers, application note.
   1. Equation 21. $$\begin{gathered} V_{OUT\_error} = m(-V_{REF\_x} + V_{CM} + \raisebox{1ex}{$V_{DIFF}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.) \\ {V}_{REF, EFFECTIVE Predicted} = V_{REF\_x} + V_{OUT\_error} \end{gathered}$$
   2. Note that if the CSA has external input resistors at input pins, then R_EXT needs to be added to in-series with R_INT.
   3. Assume maximum possible V_CM.
4. Determine the worst-case maximum and minimum V_{REF_EFFECTIVE}
   1. Maximum V_{REF_EFFECTIVE} usually occurs at -PV, -PV_TC, minimum Ra, and maximum Rb.
   2. Minimum V_{REF_EFFECTIVE} usually occurs at +PV, +PV_TC, maximum Ra, and minimum Rb.
5. Confirm the circuit's measurable dynamic range at maximum temperature swing. For each PV corner:
   1. Determine the worst-case total RTI offset ±(V_{OS, EXT RTI}+ V_{OS, RTI})
   2. Calculate the device's worst-case gain error.
   3. Calculate the worst-case V_OUT at no load (V_{OUT_0A}) with V_{OUT_0A} = ±V_{OS, total}*Gain + V_{REF_EFFECTIVE, MAX/MIN}
      1. Usually the maximum V_{OUT_0A, MAX} occurs at minimum PV/PV_TC, maximum V_{OS, Total}, and maximum V_{REF_EFFECTIVE}.
      2. Usually the minimum V_{OUT_0A, MAX} occurs at maximum PV/PV_TC, minimum V_{OS, Total}, and minimum V_{REF_EFFECTIVE}.
   4. Determine measurable current assuming a differential measurement of output
      1. I_{Measurable, low} = (V_{OUT, MIN} - V_{OUT_0A, MIN})/(Gain_Typical*R_SHUNT)
      2. I_{Measurable, high} = (V_{OUT, MAX} - V_{OUT_0A, MAX})/(Gain_Typical*R_SHUNT)