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Impedance and AC Analysis

Impedance and AC Analysis

Introduction

The purpose of this lab is to analyze inductors and the affect that changing frequencies can have on the impedance in a circuit.


Procedure

We set up the following circuit

The function generator was set to generate 5V at 1000 Hz

We measured each component and garnered the following values:

R_L = 8.3 Ω

R_ext = 67.2 Ω

V_in,rms = 4.93 V

I_in,rms = 65.0 mA  

Note: The voltage reading differs from the function generator because of its internal resistance

We then used the measured values to complete the following calculations:

V_in/I_in = Z_L = 75.8 Ω

Z_L = sqrt((R_ext + R_L)^2 + (ωL)^2)

ω = 2πf = 6280 rad/s

L = 1.16 mH

We then found the value of a capacitor needed to cancel the impedance provided by the inductor

1/ωC = ωL

C = 1/(ω^2*L) = 2.19 *10^-5 F

We then built the following circuit:

V_pp, CH1 = 1.5V

V_pp, CH2 = 20mV

deltaT = 0.4 ms

Phase difference = (deltaT) *6240* 360 ° = 184.32 °

Analysis

Frequency (kHz)	V_in (V)	I_in (A)	|Z_in| (Ω)
5	4.6	0.073	63.0137
10	4.2	0.0719	58.41446
20	3.51	0.0691	50.79595
30	3.51	0.0653	53.75191
50	4.5	0.0558	80.64516

1. The largest current should be seen at 1 kHz, as this is when the imaginary part cancels out.

2. V_L = Z_L/Z*V_in

V_L = 2.8574 +  1.2737j

Phasor = 24.0243 ° 

3. The circuit is more capacitive at frequencies below 1kHz because of the fact that the impedance provided by the capacitor increases when frequency is decreased.

4. The circuit is more inductive at frequencies above 1kHz because of the fact that the impedance provided by the inductor increases when frequency is increased.

Complex Numbers Matlab

MatLab and Complex Numbers

To understand how to work with complex numbers in MatLab.


1) Example with simple functions








2) Finding Magnitude and Phase angle



Assignment 1)




Assignment 2)









Assignment 3)







Assignment 4)

MOSFET

Controlling Electric Motors with a MOSFET

The objective of this activity is to  control the speed of an electric motor by using a MOSFET.

This is circuit is first assembled

The resistance being output by the potentiometer causes the voltage that is supplied to the motor to vary thereby controlling its speed. the motor turned on when at least 3.9 V were being delivered to it.

We then replaced the potentiometer with a function generator.

We set the function generator to produce square waves at 10 KHz while its duality was set to be on. We then used an oscilloscope to displace the waveform of the motor voltage. 

Lastly,the frequency was reduced to a few Hertz, at which point the motor turns on and off depending on the amplitude of the square-wave.

 

Finally, both the potentiometer and the function generator were able to achieve motor speed control. The function generator was much more effective due to its increased precision, thereby making specific motor speeds more achievable..

Second Order Circuits

Second Order Circuits

Objective: To go through various steps to understand how to do a second order circuit problem.

We went through the "Second Order Systems" example at http://www.mhhe.com/engcs/alexander2e/netan_tutorials/tutorials/tutmenu.htm

Oscilloscopes

Introduction to Oscilloscopes

Purpose: To explore the properties and applications of O-Scopes
Introduction:
      the following is used

an Oscilloscope
a Function Generator set to 5kHz sine wave and 5 Volts
a DMM



     The oscilloscope was adjusted to show about 2 periods and above the x-axis. The period is 200 microseconds. The voltage was adjusted to have a peak-to-peak voltage of 5 volts. The was a measured DC voltage of 0V and an AC voltage of 1.05V.


    The DC offset  was set on the Function Generator measured a DC voltage of 2.517V and an AC voltage of 1.051V. It showed the following: 


    The  function generator was then used display square waves. The square waves gave a DC voltage of 2.516V and and AC voltage of 1.375V. The Oscilloscope displayed the following:

    Lastly, A mystery signal was given in for us to "find".Once the oscilloscope was properly adjusted.we saw the following:
                     

                                              

 From this we identified the signal as a time varying ramp function!


Oscilloscopes can show voltage in a circuit as well as how it varies with time. It can also calculate frequency and allows one to focus on certain parts of a signal.

Capacitors

Capacitor Charging/ Discharging

Purpose

To examine the charging and discharging of a capacitor circuit using thevenin equivalences.

We have to circuits, one for charging and one for discharging.

The goal is to design build and test a circuit that does the following:

1.utilizes a 9V power

2. Employs a charging interval of 20s with a stored energy of 2.5mJ

3. discharges the 2.5mJ in 2s

   To fulfill these requirements we have the following for charging resistance and capacitance

The peak current, discharge and resistance were then determined.

the actual values used were.

 

the circuit was the built.

logger pro was then used to record the results 

Data:

Charging Curve.

The capacitor saturates at around 8.5V due to its internal resistance.

Discharge curve.

Its not  done completely in 2 secs but it is close.

he charging and discharging of capacitors is exponential and the time to make them discharge and charge can be easily controlled by changing the value of the resistance and/or capacitors.