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Step of 2.007P Refer to Figure 2.4 and for signal representation in the text book. The output voltage of non-ideal operational amplifiers response to both the differential and common-mode components of their input signals, which can be written as, (1) Here, is the differential gain and is the common-mode gain. Refer to Figure E2.3 in the text book. The operational amplifier's effectiveness in rejecting common mode signals is measured by its CMRR. Mathematically, it can be written as follows. 20log Ad Write the expressions of the transconductance of the two Step of 8 Write the expression for input to the two channels. Here, is the mode input signal is the differential input signal. Consider the following expressions for input currents. Step of 8 The current in the resistor R is, The voltage across the resistor R Step of 8 From the circuit, the output voltage is, Substitute the values of 2 for for and for V2 in the equation. = From the circuit diagram, the voltage is nothing but output voltage. So, replace with Therefore, (2) Step of Compare equation (2) with equation (1). Therefore, the expression for differential gain, A, is and the expression for common mode gain, Acm Step of Derive the common-mode rejection ratio (CMRR). 20log 20log 20log Gm Therefore, the expression for CMRR of the operational amplifier is 20log Step of 8 The value of differential gain, in dB is, = 60dB Calculate the value of A, V/V Step of 8 Determine maximum permitted percentage mismatched between the two channels of Tran's 100 = x100 1000 =10% Thus, the required mismatch permitted percentage is, AG. =10%