Most designers make level shifters with op amps and 1%-tolerance discrete resistors. Discrete-resistor mismatching limits the op amp's CMMR (common-mode rejection ratio) to 40 dB, so you cannot use op amps in circuits that require high CMRR. Differential amplifiers contain precision matched internal resistors, so ICs such as the INA133 can readily achieve CMRRs of approximately 90 dB. They can offer such high CMRR by trimming internal matched resistors. Assume that each input in the circuit of Figure 1 has an associated noise voltage (V_N1, V_N2, and V_NREF). The transfer function of the amplifier circuit is V_OUT=(V_REF+V_NREF)+(V_IN2+V_N2)–(V_IN1+V_N1). Note that the reference voltage shifts the output signal, either single or differential. Once this level shifting occurs, you can turn your attention to the noise cancellation. Careful cabling and differentially coupling the signal into the differential amplifier's inputs force the noise on the signal inputs to be equal (V_N1=V_N2). The input noise is a common-mode signal, so the differential amplifier rejects it to the best of its ability (nominally, 90 dB). Now, V_OUT=V_IN2–V_IN1+V_REF+V_NREF.

Now, you need to eliminate the reference noise to obtain a clean level-shifted signal. You could connect the X end of C₁ to ground to shunt the reference noise to ground, but this solution may be ineffective because the source impedance of the reference is low. When, however, you connect the X end of C₁ to the V_IN1 signal source, the differential amplifier acts as a lowpass filter and rejects the reference noise. This circuit keeps the input impedance of the differential amplifier low (approximately 25 kΩ for the INA133) to facilitate matching. Thus, you must keep the signal source impedance low to prevent gain errors. The source impedance should be less than 1/1000 the input impedance to minimize gain error. If this situation doesn't occur naturally, then it is best to buffer the inputs.

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