Signals with Multiple Frequencies (Week 14 - Day 28)

     In this lab, we compared different frequencies in our circuit. We used a custom mathematical function as our input voltage and then measured the output voltage across the second resistor (as seen below) which was in parallel with our capacitor.

Simple circuit with a channel across the resistor and capacitor in parallel

     Below are screenshots of the data our Analog Discovery retrieved from our circuit setup.  

     These waves represent the voltage gain of the input function from our first resistor and the output as seen by the orange cables in the figure above.

V_IN at 10 kHz

V_IN at 1 kHz

 V_IN at 500 Hz

Sinusoidal Sweep across the capacitor

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Apparent Power and Power Factor (Week 14 - Day 27)

Measured value of R_T

Measured value of first R_L

Measured value second R_L

Measured value third R_L

Measured value of Inductance

We found the internal resistance of the inductor

Found to resistance values to calculate internal resistance

Measured value of capacitance

 Part 1:

R_L = 10.3 Ω

R_L = 46.9 Ω

R_L = 100.1 Ω

Part 2:

Adding the capacitor in parallel with the load

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Op Amp Relaxation Oscillator (Week 12 - Day 24)

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Inverting Voltage Amplifier (Week 12 - Day 24)

Setup of Inverting op-amp with 2V sinusoidal V_in

Scope - 100 Hz

Scope 1KHz

Scope - 5kHz

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Phasors: Passive RL Circuit Response (week 12 - Day 23)

Image of Nodal analysis with phasors

Checking for measured resistance

Calculation of frequency and gain

Setup of circuit. V_L represented by Channel 1

Our wicked graph depicting our calculations, phase shifts, etc.

Notes: 

     The Analog Discovery was not working properly with our magnitude of frequency. A safe range to use with the device was 10kHz to about 20kHz. In our experiment, we input a frequency of 21.5 kHz into the waveform(off by a x10 from our calculation) and we received a reasonable graph from scope. 

     We did not have access to inductors other than the 1μH ones in class; therefore, we could not manipulate the circuits angular frequency.

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Impedence Lab (Week 11 - Day 22)

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How Oscilloscopes Work, Explained by Professor Mason (Week 11 - Day 21)

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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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