SLPS755 Data sheet

SLPS755A October 2023 – December 2023 RES11A-Q1

ADVMIX

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DDF|8

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slps755a_oa

8.1.1.1 Difference-Amplifier Common-Mode Rejection Analysis

In this simple difference amplifier configuration, the nominal CMRR is calculated as:

Equation 24.

CMRR = 20 \times \log_{10} (|\frac{A_{D}}{A_{CM}}|)

The term A_D is the differential gain of the circuit, and the term A_CM is the common-mode gain of the circuit. These are defined as the following:

Equation 15.

A_{D} \times = \frac{V_{OUT}}{V_{D}} = 0.5 \times \frac{(\frac{R_{G1}}{R_{G1} + R_{IN1}}) + (\frac{R_{G2}}{R_{G2} + R_{IN2}})}{(\frac{R_{IN2}}{R_{G2} + R_{IN2}})}

Equation 16.

A_{C M} = \frac{V_{OUT}}{V_{CM}} = \frac{(\frac{R_{G1}}{R_{G1} + R_{IN1}}) - (\frac{R_{G2}}{R_{G2} + R_{IN2}})}{(\frac{R_{IN2}}{R_{G2} + R_{IN2}})}

Therefore,

Equation 17.

CMRR = 20 \times \log_{10} (|2\times \frac{R_{G1} \times (R_{IN2} + R_{G2}) - R_{G2} \times (R_{IN1} + R_{G1})}{R_{G1} \times (R_{IN2} + R_{G2}) + R_{G2} \times (R_{IN1} + R_{G1})}|)

When this expression is evaluated with the definitions given in Section 7.3.1, assuming the worst-case scenario of the most unbalanced divider matching possible,

Equation 18.

CMRR = 20 \times \log_{10} (|\frac{G_{nom} +1+ {t_{Rx}}^{2} (1- G_{nom})}{4\times t_{Rx}}|)

Because t_Rx² << 1, the worst-case CMRR is approximated as

Equation 19.

CMRR = 20 \times \log_{10} (|\frac{G_{nom} +1}{4\times t_{Rx}}|)

By definition, the parameter t_M describes the effective error that is otherwise equivalent to 4 × t_x for an unmatched divider network, and so the maximum value of t_M can be used to calculate the same worst-case result. Likewise, the typical value of t_M can be used to approximate the typical CMRR.

Equation 20.

CMRR = 20 \times \log_{10} (|\frac{G_{nom} +1}{t_{M}}|)

For example, the worst-case CMRR for a RES11A40-Q1 device with G = 4 is approximately 74.0 dB, with a typical CMRR of approximately 95.4 dB. In comparison, implementation of a comparable G = 4 difference amplifier with unmatched 0.1%-tolerance resistors results in a worst-case CMRR of approximately 62 dB.

In a difference amplifier configuration, the CMRR of the op amp contributes error as well. The op-amp CMRR is considered in parallel with the CMRR of the resistor network, as per the following equation:

Equation 21.

\frac{1}{{CMRR}_{TOTAL}} = \frac{1}{{CMRR}_{AMP}} + \frac{1}{{CMRR}_{RESISTORS}}

Additional mismatches in the divider end-to-end resistances reduce the effective CMRR of a difference amplifier. While the low absolute tolerance span of the RES11A-Q1 (235 ppm typical) helps reduce these concerns, parasitic trace resistances can lead to additional mismatches that impact the CMRR specs. Bench results from a difference amplifier implementation of the RES11A40-Q1 and the OPA210 are presented for various deliberate input-impedance mismatches.

Figure 8-2 Effect of Input Impedance Mismatch on Common-mode Rejection Ratio