Solving Complex Number with FreeMat

In this activity, we will be practicing to solve complex number math problems by using the FreeMat solfware.

Some practice exercises:

let A = 3 + 4j
     B = 3 - 2j
     C = 2 <50˚

and compute D = (A+C)/B

D = 0.14+1.94j

 

 

let A = 2 + 2j

      B = -1 + 3j

      C = 2 + j

 

and compute D = (A*B)/C

        compute E = (A+B)*C

        find the magnitude and the phase angle for E.

        find the read component and the imaginary component for E.

 

D= -2.4 + 3.2j         E = -3 + 11j

phase angel = 105.26˚ , magnitude = 11.41

imaginary component = 11

real component = -3

 

Assignments:

 

let A1 = 3+ 2j

      A2 = -1+4j

      B = 2-2j

 

solve for C = (A1*B)/A2



 



hand calculation, C = -1.06 -2.24j

 

using FreeMat, C = -1.06 -2.24j

 

the magnitude and the phase angle for C

 

Solve for D = (A1+B)*A2

hand calculation

calculation with FreeMat, D = -5 +20j

 

Solving Matrix with complex numbers:

 

Matrix calculation with complex number has the same inputting method as real numbers



 

 

Conclusion:

     Why waste time on inefficient hand calculation when you can solve for complex numbers easily on freeMat? The result will be the same but FreeMat is so much faster.





Controlling Electric Motor Using MOSFET

 The main purpose in the experimient was to achieve a stable speed control of an electric motor using a MOSFET.

Procedure:

 Part 1:
 Building the MOSFET voltage control circuit shown below.

note: the "FET N" is the MOSFET, and there is a diode between the positive ad the ground wire connecting to the electric motor. The external resistor is used to limit the current in the circuit.

A completed MOSFET voltage control circuit on breadboard.

By adjusting the resistance in the potentiometer, we can adjust the voltage through the motor, and therefore, control its speed.

Part 2:

This time, the potentiometer is replaced with a Function Generator.
The Function Generator would produce Square Waves, and its duality was set to be on, as well as its duty cycle.

The completed view of the modifited circuit.

Eventhough the potentiometer was left on the breadboard, it was no longer connected to the circuit.

The voltage on the motor is correspondance with the Oscilloscope.

Displaying the speed control by increasing and decreasing duality.

 Answer to questions for discussion:
The motor rotates faster with a larger duty cycle.
The graph is the on/off times of the square function.
The time required to decelerate is 0.7s.
The voltage is 0.16 V at 30%

The voltage of motor at 30% of its maximum.

 The converter allows a smooth speed control.
T = 1/110 = 9.1ms

Conclusion:
 We had successfully controlled the voltage across the motor with both the potentiometer and FG, but the FG allowed for better speed control than the potentiometer.

2nd Order Circuit Tutorial

In this lab, an online tutoring program will be used to learn how to solve 2nd order circuits step by step. Each screen shot will be a step.

 

Conclusion:  2nd order circuits are hard to solve because they have so many steps ( so easy to make a

                     small error that will ruin the whole problem). However, they may not necessary be

                     difficult to solve.

 

Remarks: Hope i can keep myself calm whiling frustrating with all the math in these questions when

                 they are presented in exams and hw.

Oscilloscope 101

The objective of the lab is to learn, use, and anaylze an oscilloscope.

Procedure:
We connect the oscilloscope with a frequency generation.

Exercise 1: Sinusoid

f = 5 kHz, V = 5V

Once the trigger was set, we took measurements.
Period = 0.2 ms
Peak to Peak = 11.4 V
Zero to Peak = 5.8 V
Anticipated RMS = 3.53 V

Using DMM to read the Voltage values
VDC = 0.026 mV
VAC = 3.35 V
The VAC is close to our anticipated RMS value.

Exercise 2: Include DC Offset
We add an offset of 2.5 V, and another one at 5V

DC Coupling at 5V

AC Coupling at 5V

The difference is that we can see the offset in DC coupling while nothing changes in AC.
2.5V offset measurements:
VDC = 2.51 V
VAC = 3.37 V
The VDC shows the offset in the output like the graph while the offset does not affect VAC.

Exercise 3: Square Wave with offset

VDC = 10 mV
VAC = 5.34 V
The measured value was close to the theoretical VAC = 5 V.

Exercise 4: Mystery Signal

Mystery Signal

DC Voltage = 448 mV
f = 70.42 Hz
Pk-Pk = 940 mV

Conclusion:
 A digital oscilloscope was more easy to opertate than a traditional one since a digital one displays all reading of the properties of the wave on the screen. Meanwhile, the digital oscilloscpe also the screen to be printed and saved into a computer connected with a USB cable.