ESalasSanchezENGR44

Sunday, May 1, 2016

26-Apr-2016: Day 17

Integrating Operational Amplifier

In an RC circuit by setting the current through the resistor and through the capacitor equal we may solve for the voltage output and find our gain.

What do they do... they integrate. Below we can sketch the output signal based off the input signal graph.

Lab time!
We are to build a simple op amp circuit with a capacitor on the input terminal and a resistor connecting the feedback. We constructed it using a 1.5 kilo Ohm resistor, and a 100 nano Farad capacitor.

We then applied 3 sinusoidal wave inputs to the circuit.

1) Frequency = 1kHz
Amplitude = 1V
Offset = 0V

2) Frequency = 2kHz
Amplitude = 1V
Offset = 0V

3) Frequency = 500Hz
Amplitude = 1V
Offset = 0V

Below is our calculated, theoretical data.

Stepping and Ranpping

14-Apr-2016: Day 16

Current through an inductor changes over time as it resists a sudden change. Below is the representation of current as the inverse of the inductance multiplied by the integral of the voltage with respect to time. After a long time the inductor will act as a short circuit.

Inductors are added just as resistors in series and parallel.

Below is an updated list of equations for RL, R, and RC circuits.

Below, being that we are told the circuit is opened at time zero to the right we see a sketch of ideal versus real world voltage over time.

Below we find an expression for the voltage as a function of time for an RC circuit.

The product of the resistance and capacitance is called the time constant. Below 1% of the initial voltage we may consider the capacitor "fully" discharged. Below, we find that at about 5 time constants we can consider the any capacitor discharged.

Using that current is the product of capacitance and derivative of voltage with respect to time we may find an expression for power. We used the expression of voltage we found above.