SBOA551 Application note

SBOA551 June 2022 INA240

5.4 Reference Source Impedance Error in Current Feedback Multi-Stage CSA

Figure 3-5 is redrawn and shown in Figure 5-5. The two current sources are shown for illustration only and are not independent stimuli. They represent the differential small signal current due to input shunt voltage, V_diff. The relationship can be rewritten as:

Equation 16.

\frac{∆ I}{2} = \frac{V_{d i f f}}{2} \times \frac{1}{R i}

Comparing with Figure 5-2, the only difference in Figure 5-5 is that current now acts as differential input instead of voltage. Similar to voltage feedback, the input to the difference amplifier is an internal node of the CSA. Vbias is the common-mode voltage of the difference amplifier. Since knowledge of its value is not essential for an end user, it may not be listed in product data sheets.

It can be derived that the differential term of the output error equation is:

Equation 17.

V_{o_e r r_d i f f} = \frac{\frac{R_{x}}{R_{L} + R_{f}}}{1 + \frac{R_{x}}{R_{L} + R_{f}}} \frac{V_{d i f f}}{2} \frac{R_{L}}{R_{i}}

Rewriting the output error equation for two stage CSA, with V_bias being the common-mode voltage:

Equation 18.

V_{o u t_e r r o r} = \frac{\frac{R_{x}}{R_{L} + R_{f}}}{1 + \frac{R_{x}}{R_{L} + R_{f}}} ({- V}_{r e f_x} + V_{b i a s} + \frac{V_{d i f f}}{2} \frac{R_{L}}{R_{i}})

Figure 5-5 Current Feedback Multi-Stage CSA Output Error