SBOA551 June   2022 INA240

 

  1.   Abstract
  2.   Trademarks
  3. 1Introduction
  4. 2One, Versus Two Reference Pins
  5. 3Bidirectional Current Sense Amplifier Topologies
    1. 3.1 Single-Stage Difference Amplifier
    2. 3.2 Difference Amplifier Input Followed by Noninverting Output Buffer
    3. 3.3 Voltage Feedback Multi-Stage Difference Amplifier
    4. 3.4 Single-Stage Current Feedback
    5. 3.5 Current Feedback Multi-Stage Difference Amplifier
    6. 3.6 Isolated Bidirectional Current Sensors
  6. 4Options for Driving Reference Pins and Input Referred Reference Error
  7. 5Resistor Divider as Reference
    1. 5.1 Resistor Divider and Equivalent Circuit
    2. 5.2 Reference Source Impedance Error in Difference Amplifier
    3. 5.3 Reference Source Impedance Error in Voltage Feedback Multi-Stage CSA
    4. 5.4 Reference Source Impedance Error in Current Feedback Multi-Stage CSA
    5. 5.5 Reference Source Impedance Error in Difference Amplifier with Output Buffer
  8. 6Examples
    1. 6.1 Calculating Reference Source Impedance Error in Difference Amplifier
    2. 6.2 Calculating Reference Source Impedance Error in Voltage Feedback Multi-Stage CSA
    3. 6.3 Calculating Reference Source Impedance Error in Current Feedback Multi-Stage CSA
  9. 7Summary

5.2 Reference Source Impedance Error in Difference Amplifier

Figure 5-2 shows a non-ideal voltage source, Vref_x, driving the reference pin of a difference amplifier. The output impedance of Vref_x is represented by Rx. The difference amplifier input is connected to common-mode voltage source Vcm, as well as differential voltage source Vdiff.

Figure 5-2 Difference Amplifier Output Error Due to Reference Source Impedance

The following expression can be derived for the output:

Equation 10. V o u t = R i + R f R i + R f + R x V r e f _ x + R x R i + R f + R x V c m + R f R i V d i f f + R x R i + R f + R x V d i f f 2

For ideal Vref_x, its output impedance equals to zero. Therefore, setting Rx = 0 yields the familiar ideal output equation:

Equation 11. V o u t _ i d e a l = V r e f _ x + R f R i V d i f f

Note that Vref = Vref_x for ideal voltage source. Taking the difference of the two previous equations gives the equation for output error due to reference source impedance:

Equation 12. V o u t _ e r r o r = V o u t - V o u t _ i d e a l = R x R i + R f 1 + R x R i + R f - V r e f _ x + V c m + V d i f f 2

Upon inspection, the following observations are made:

  1. The first two terms are due to Vref_x and Vcm respectively and have opposite signs. Combined together, it represents an equivalent output offset. The third term represents a gain error that is proportional to the differential input voltage.
  2. The differential input is normally under a couple hundred millivolts considering the input range for common gain options and supply voltage range, while common-mode input could be many tens of volts. As a result, the offset term is normally much larger than the gain error term.
  3. Both the offset and gain error terms are proportional to the ratio Rx / (Ri+Rf), when Rx << (Ri+Rf). This coefficient can be used as an indicator of the output error magnitude.
  4. When referred to input, all terms in the output error are divided by the gain of the difference amplifier.

So far, it is assumed that the output is measured single-end relative to ground. The reference voltage Vref_x is then subtracted from the measured results. If differential measurement is made with respect to the reference pin, the output error cancels. In this situation, the finite source impedance, Rx, has no impact on accuracy. Figure 5-3 shows the preferred measurement setup when using a voltage divider to drive the reference, or when output impedance of the driving source is not negligible.

Figure 5-3 Differential Measurement

Comparing with single-ended measurement, differential measurement is a great improvement. However, it does not mean that the source impedance has no impact on performance at all. The price to pay is output dynamic range. Because the error voltage is still added to the output and reduces its effective swing range that is otherwise available to respond to differential input.