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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.

Thermo-sensor Lab

Purpose: to amplify a thermo-sensor to a specific output range.

Preperation

     Given:

• A LM35 that produces 10 mV/°C.
• work between 15 °C to 35 °C.

Using a difference amplifier, we shifted the range produced from 150 mV - 350 mV to

0V - 5V.

 V_1 = 150 mV, V_2 is the range given by the LM35
 Our gain is a factor of 25 so, R_f = 150 kΩ and R_i = 6 kΩ.

Experiment

We built the following circuit:

V_1 was measured at the left potentiometer while V_2 was measured at the one on the right

We made

V_2 = 350 mV to verify it was working.

 V_out was measured to be 5.05 V

Conclusion

We amplified 350 mV into 5V by using a power supply and voltage dividers to represent the LM35 at 35 degree C. The lab was a success.

MatLab and Complex Numbers

Purpose: To understand how to work with complex numbers in MatLab.

Tutorial:

1) Example with simple functions

1. 
   
2. 
   

2) Finding Magnitude and Phase angle

Assignment 1)

Assignment 2)

Assignment 3)

Assignment 4)

Conclusion:  Matlab provides a quick and easy way to work with imaginary numbers and solve linear systems of equations.

MOSFET Control of an Electric Motor

Purpose: To control the speed of the motor with a MOSFET circuit.

Experiment: We set up the following circuit:

Varying the resistance on the POT varied the speed of the motor. Going below 3.9V made the motor stop.

The POT was replaced with a function generator producing square waves at 10kHz with duality on and the oscilloscope to see the motor voltage.

When the frequency was reduced to only a few hertz, depending on the voltage the motor turned on and off.

Conclusion: Changing the speed on the motor was as simple as varying the voltage on the motor. This could be done with a varying voltage supply (function generator) or varying resistance (POT). The function generator worked much better than the POT.

Second Order Circuit Problem Example

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

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

Example:

These problems are not so bad when you take it one step at a time.

Introduction to Oscilloscopes

Purpose: To introduce the purpose and how to work an oscilloscope.

Introduction:
      We will use the following:

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

Experiment:

     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.

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

     Next we had the function generator 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:

     Finally, we were given a mystery signal to identify. Once the oscilloscope was properly adjusted.we saw the following:

                                               

                                             

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

Conclusion: 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.