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Op-Amps

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Submitted By hoshi4ever
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Part 4.5
An integrator amplifier is a circuit which output voltage proportional to the time integrator of the input voltage. As the name implies, the function of integrator amplifier is configure to perform the mathematical calculus, integration. Integration is the process to find the area under the graph. Hence integrator amplifier, the output voltage it designed to work responds to the input voltage respect to the time.
By applying KCL
VinRin=-C(dVoutdt)
Vout=-1RC×0tVin(t)dt
The integrator also always has a phase shift of +90⁰ to the output voltage. In which, the input voltage of a sine wave will be outputted with a cosine wave and vice versa. The interchanging of capacitor, Cf and resistance, R1 will become a differentiator circuit.
∅= +90°-tan-1(2πRC)
As an ideal cases, there are no current can flow into the op-amp. This is due to the grounding at the non-inverting terminal and result in the 0V in the inverting terminal. During the experiment, one of the procedures is to use the dc offset to make sure no dc voltage is in Vin. This is because the input offset voltage is not zero or another word, the supplied voltage work together with AC and DC. Hence, the dc input voltage will be integrated and the output voltage starts to drift.

Part 4.6
An op-amp without a feedback resistance is original a difference amplifier. The difference op-amp produces the algebraic difference between the two input signals. Few cases can be done in the difference op-amp. Example like the two input voltage have the same magnitude and the output voltage will be zero which will be the most common. There are no amplification take places when all the external resistors value is the same. Hence, the amplification of the difference op-amp is depends on the ratio of the resistor value.
V+
V-
B
A

The output voltage equation can be derived using super position theorem and voltage

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