Differential Amplifier Output Common-Mode Voltage Calculator by Adrian S. Nastase A differential amplifier frequent use is the amplification of the voltage difference between its inputs, while rejecting the common-mode level.
Input ResistanceOne problem with selecting the difference amplifier resistors as R 2 = R 1 and R 3 = R 4 is that the input resistances for both inverting amplifier and non-inverting amplifier are unequal.The input resistance for voltage V 1 is R 1 as in the case of an inverting amplifier. For the non-inverting input, i.e. For input voltage V 2, the input resistance is (R 2 + R 4).This difference in the input resistances causes one of the input signals to be more amplified than the other.The output equation of the difference amplifier V O, can be obtained by making the ratio R 4 / R 2 the same as R 3 / R 1, instead of making R 2 = R 1 and R 4 = R 3.The input resistance difference will not cause a problem if the signal source resistances are much smaller than the input resistances. Also, it is usually desirable to have R 2 = R 1 and R 4 = R 3, in order to minimize the input offset voltages.Differential GainThe differential gain of a difference amplifier is defined as the gain obtained at the output signal with respect to the difference in the input signals applied.The output voltage of a difference amplifier is given as,V O = A D (V 1 – V 2)where, A D = – (R 3 / R 1) is the differential gain of the amplifier.Common Mode InputA difference amplifier amplifies the difference between the two input voltages. Ideally, a common mode input V cm would make the inputs (V 1 + V cm) and (V 2 + V cm), which will result in V cm being cancelled out when the difference of the two input voltages is amplified.Since the output of a practical difference amplifier depends upon the ratio of the input resistances, if these resistor ratios are not exactly equal, then one input voltage is amplified by a greater amount than the other input.Consequently, the common mode voltage V cm will not be completely cancelled. Because it is practically impossible to match resistor ratios perfectly, there is likely to be some common mode output voltage.With the common mode input voltage present, the output voltage of the differential amplifier is given as,V O = A dV d + A c V cWhere Vd = the difference voltage V 1-V 2Vc = the common mode voltage (V 1+V 2)/2Common Mode Rejection Ratio (CMRR)The ability of a differential amplifier to reject common mode input signals is expressed in terms of common mode rejection ratio (CMRR).
The common mode rejection ratio of a differential amplifier is mathematically given as the ratio of differential voltage gain of the differential amplifier to its common mode gain.CMRR = A d / A c Ideally, the common mode voltage gain of a differential amplifier is zero. Hence the CMRR is ideally infinite.Characteristics of a Differential Amplifier. High Differential Voltage Gain.
Low Common Mode Gain. High Input Impedance. Low Output Impedance.
High CMRR. Large Bandwidth. Low offset voltages and currentsDifferential Amplifier as ComparatorA differential amplifier circuit is a very useful op-amp circuit, since it can be configured to either “add” or “subtract” the input voltages, by suitably adding more resistors in parallel with the input resistors.A Wheatstone bridge differential amplifier circuit design is as shown in the figure above.