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Output Voltage Of A Differential Operational Amplifier

The differential op-amp can be presented in more than one way. Figure 12.1 illustrates one of the ways.

Find the output voltage V_{o} of figure 12,1 and indicate the mathematical operation performed by the op-amp circuit. Assume the op-amp is an ideal op-amp.

**The strings**:
S_{7}P_{5}A_{51} (change - physical).
**The math**:

Pj Problem of Interest is of type *change* (physical - change).

Consider figure 12.1. If the op-amp is an ideal op-amp then V - V_{2} = V_{d} = 0 approximately, V = V_{2}, A_{OL} is infinitely large, and current into op-amp, i_{in} = 0.

Figure 12.1 can be viewed as a combination of a noniverting op-amp and an inverting op-amp.

Consider the ideal noninverting op-amp (first op-amp in figure 12.1):

output voltage = V_{o1} = ( 1 + R_{1}/R_{2})V_{1}

So, V = (1 + R_{1}/R_{2})V_{1} - i_{1}R_{1}

But V = V_{2}

So, (1 + R_{1}/R_{2})V_{1} - i_{1}R_{1} = V_{2}--------(1)

Consider the inverting op-amp (second op-amp i figure 12.1):

Current i_{1}, through R_{1} of the inverting op-amp = current through R_{2} of the inverting op-amp

So, i_{1} = (V - V_{o})/R_{2}

So, i_{1} = [(1 + R_{1}/R_{2})V_{1} - i_{1}R_{1} - V_{o}]/R_{2}

So, i_{1} = V_{1}/R_{2} - V_{o}/(R_{1} + R_{2})------- (2)

So, substituting the value of i_{1} of eq(2) into eq (1), we have:

(R_{2} + R_{1})/R_{2})V_{1} - [V_{1}/R_{2} - V_{o}/(R_{1} + R_{2})]R_{1} = V_{2}

So, V_{1}[((R_{2} + R_{1})/R_{2}) - (R_{1}/R_{2})] - (R_{1}V_{o})/(R_{1} + R_{2}) = V_{2}

So, V_{1} + (R_{1}V_{o})/(R_{1} + R_{2}) = V_{2}

So, V_{o} = (1 + R_{2}/R_{1})(V_{2} - V_{1}).

So, op-amp is a subtractor.

Math

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

Derivation Of The Area Of A Circle, A Sector Of A Circle And A Circular Ring

Derivation Of The Area Of A Trapezoid, A Rectangle And A Triangle

Derivation Of The Area Of An Ellipse

Derivation Of Volume Of A Cylinder

Derivation Of Volume Of A Sphere

Derivation Of Volume Of A Cone

Derivation Of Volume Of A Torus

Derivation Of Volume Of A Paraboloid

Volume Obtained By Revolving The Curve y = x^{2} About The X Axis

Single Variable Functions

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Equation Of The Ascent Path Of An Airplane

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Introduction To Group Theory

Advanced Calculus - Partial Derivatives

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Production Schedule That Maximizes Profit Given Constraint Equation

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Fourier Series

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Homogenizing-Non-Homogeneous-Time-Varying-IBVP-Boundary-Condition

The Universe is composed of *matter* and *radiant energy*. *Matter* is any kind of *mass-energy* that moves with velocities less than the velocity of light. *Radiant energy* is any kind of *mass-energy* that moves with the velocity of light.

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