B&B Electronics RS-485 Simplified Analog Input Analysis, 1 2 LSB = R s + 1k Ω × 60pF × ln2048

Simplified Analog Input Analysis

Using the equivalent circuit in Figure B-1, the time required to charge the analog input capacitance from 0 to Vs within ½ LSB can be derived as follows:

The capacitance charging voltage is given by

Vc = Vs (1 − e−tc RtCi )

where

Rt = Rs + ri

The final voltage to ½ LSB is given by

Vc (12 LSB) = Vs − (Vs 2048)

Equating equation 1 to equation 2 and solving for time tc gives

Vs − (Vs 2048) = Vs (1 − e−tc RtCi )

and

tc (12 LSB) = Rt × Ci × ln(2048)

(1)

(2)

(3)

(4)

Therefore, with the values given the time for the analog input signal to settle is

tc (1 2 LSB) = ( Rs + 1kΩ) × 60pF × ln(2048) (5)

This time must be less than the converter sample time shown in the timing diagrams.

VI = Input Voltage at A0 - A10

VS = External Driving Source Voltage RS = Source Resistance

ri = Input Resistance

Ci = Equivalent Input Capacitance *Driving source requirements:

∙Noise and distortion for the source must be equivalent to the resolution of the converter.

∙RS must be real at the input frequency.

B-2 Appendix B 485SDA103798 Manual

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