Series RLC Circuit Step Response (Week 10 - Day 19)

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Inverting Differentiator (Week 9 - Day 17)

Pre-lab:

v_OUT(t)=-RC^dv_IN(t)⁄_dt          v_IN(t) = Acos(ωt)
         

v_OUT(t) = RCAωsin(2π f t)

R = 470 Ω , C = 470 nF , τ = 0.221 ms

R_measured = 465 Ω , C = 424 nF , τ = 0.197 ms

Part a

Part b

Part c

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Passive RC Circuit Natural Response (Week 8 - Day 16)

Pre-lab:

(a)                                                                                (b)

τ = R_eq x C                                                                 τ = R_eq x C

τ = ^R₁R₂C⁄_R1+R2                                                                τ = ^R₁R₂C⁄_R1+R2 

vc(t) = V0e^-t⁄_τ                                                                                                        vc(t) = V0e^-t⁄_τ

^{_{R1 = 1 kΩ, R2 = 2.2 kΩ, C = 22 μF}}

^{_{τtheo = 15.13 ms}}

vc(t) = 3.44e^-t⁄0.01513

Capacitor voltage response for figure a

Capacitor voltage response for figure b

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Capacitor Voltage-Current (Week 8-Day 15)

     In this assignment, we were asked to measure the relationship between the potential difference across a 1 μF capacitor and the current passing through it. In order to achieve this, we constructed a series RC circuit and applied our knowledge in order to make predictions on the voltage-current relations. 

Predictions of current and voltage behavior in RC circuit

We felt pretty confident about our assumptions.

Schematic of our circuit along with the actual construction

 Scope collected data from our simple circuit. We set our v_C, v_R, and i_C as channel 1(yellow), channel 2(blue), and a custom math channel(red).

Oscillations with f = 1kHz. 

Oscillations with f = 2kHz

Oscillations with a triangle wave at f = 100Hz

Overall, we were able to accurately predict the behavior of the current and voltage across the capacitor with the voltage-current relations of this circuit element. Yay!
One way our measured values can depict our predictions more accurately is by adjusting the frequency. We couldn't really tell the difference when we were using the sinusoidal function on the scope, but when we changed the output function to a triangle wave, we did not obtain a perfect square wave.

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Temperature Measurement System Design (Week 7- day 14)

Complete setup of circuit. Difference amplifier (Left), Wheatstone bridge (middle), thermistor (right)

The resistance of the thermistor varied by temperature differences:

Resistance at 22° C = 11.23kΩ 

Resistance at 37° C = 9.98kΩ

 

Our Wheatstone bridge simulated on EveryCircuit

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Inverting Voltage Amplifier (Week 7 - Day 13)

      This experiment is the first of many that uses operational amplifiers. These neat little package allows us to manipulate our output voltage by performing mathematical operations for us. Our goal in this lab was to achieve a gain of 2V with our inverting amplifier circuit (shown below).

The circuit below samples three resistors. This was in an attempt to achieve a ratio of 2 between the feeder and input resistance.
R₁ = 3.3kΩ + 0.1kΩ = 3.4kΩ
R₂ = 6.8kΩ
And there measured values were:
R₁ = 3.26kΩ + 0.0996kΩ = 3.36kΩ
R₂ = 6.75kΩ

A schematic of this circuit was constructed on EveryCircuit before attempting.

This circuit shows an inverting voltage amplifier with a gain of 2V

After doing calculations, we constructed the actual circuit

Plugging in some numbers into the appropriate equation:

v_out = -(^R₂⁄_R1)v_in

...

From the data and graph, it is clear that we were successful. We achieved an inverted voltage gain of about 2V. Where the blue and yellow lines diverge, we can see where saturation begins to occur (typically below -3.5V and above 3.5V). I believe these precise measurements were due in great part to how close the ratio of the feeder an input resistances were. The ratio between R₁ and R₂ was 2.009 which was only off by a thousandth of an ohm. Hardly anything at all!

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Difference Amplifier (Week 6 - Day 12)

     In the previous experiment, we were to use an operational amplifier in order to sum voltages. In this segment, we tested the versatility of an op-amp by finding the difference between input voltages.

A schematic of the circuit was created on EveryCircuit.

We chose all our resistors to have same values

The equation that describes the output voltage is given by v_b - v_a.

Below is an image of the circuit we constructed from our schematic.

R₁ =R₂ = R₃ = R₄ = 10kΩ 

Their measured values were 9.91kΩ, 9.90kΩ, 9.92kΩ, and 9.89kΩ, respectively.

In the first part of this experiment, we kept v _{at a constant 1V, and the returned values were:}

Graph of V_b = 1V (Vout v. Vin)

Graph of V_b = -1V (Vout v. Vin)

     This experiment was a success as the one before. We were not surprised by the values we measured, except for some, but they were due to the same error as our previous lab. We reached saturation at voltages above ~3.5V and below ~-3.5V. It was an overall success with minimal percent error. 

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