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The zero and span circuit is frequently used in instrumentation and measurement processes. This circuit adjust the slope and zero point of the signal which correlation between input and output.

A linear op amp transfer function is limited to the equation of a straight line (Eq1)


         y  = +-mx +- b                        (1)


The equation of a straight line has four possible solutions depending upon the sign of m (slope) and b (intercept), thus the equations yield solutions in four forms.


CASE1:                Vout = +mVin + b                (2)

CASE2:                Vout = +mVin - b                (3)

CASE3:                Vout = -mVin + b                (4)

CASE4:                Vout = -mVin - b                (5)




Four circuits must be developed follow-up to the equation CASE1 to CASE4:

CASE1: Vout = +mVin + b



CASE2: Vout = +mVin - b



CASE3: Vout = -mVin + b



CASE4: Vout = -mVin - b



Example: Given a set of two data points for Vout and Vin, and equations are solved to determine m and b for the equation that satisfies the given data; i. e., a sensor output signal ranging from 0.1 V to 0.2 V must be interfaced into an analog-to-digital converter that has an input voltage range of 1 V to 4 V.

These data points (Vout = 1 V @ Vin = 0.1 V, Vout = 4 V @ Vin = 0.2 V) are inserted into Equation 2 (CASE 1), to obtain m and b for the specifications.


 1 = m(0.1) + b                                (6)

 4 = m(0.2) + b                                (7)


After algebraic manipulation of Equation 6, 7, yield the solution, m = 30 and b = -2.

Now m and b are rewrite to new equation.


 Vout = 30Vin - 2                        (8)


The equation (8) similar to  the CASE2: Vout = +mVin - b circuit. The next step required to complete the problem solution is to develop a circuit that has an m = 30 and b = –2 (CASE 2).

As mentioned all above are the preliminary to understand more complex of op-amp design technique, zero-span circuits are use to the examples to solve the complexities of analog signal conditioning problems. For more details, you can study from the references [4].