Final Project "Color Organ"

Team Members:
Manuel Castaneda
Michael McGowen

Impedance and AC Analysis I Lab

In this lab we studied how a real inductor model needs a resistor in series to react to the resistance shown within the inductor.

Radial inductor used for this experiment

The impedance expresion of such combination looks like:

ZL, real = RL + jwL

The magnitude of the impedance relates also to the Voltage and Current phasors, |Vin| and |Iin|.

Step 1.
We measured the resistance of the unknown inductor to be
RL = 8.4 ohms

Step 2. Before proceeding to using the oscilloscope and the function generator, we first constructed the following circuit. Overwhelming current could potentially harm the equipment.

Because the function generator has a considerably high resistance, we also needed a DMM to measure voltage. In the picture above, Rext is to be valued at 68ohms.

Rext, actual = 71.3 ohm.

Once having done this, we set up the circuit and ran the frequency to be at 1Khz instead of 20khz.

We compared the voltages from the function generator and the Vrms voltage of the DMM to be at around 5 Volts each.

VIn, rms = 4.97V                         IIn, rms = 4.4 mA

As expected, there was a minor difference between the voltage readings from both devices because there are more operating components in the function generator.

Calculating the magnitude of the impedance  using the values above gives us

Z = V/I = 435.97ohms

Rewriting the expresion as a complex number gives us
Z  = Sqrt(R^2 + jwL) or,
435.97 = sqrt(5083.69 + jwL)

The angular frequency at which the circuit was being tested was
w = 125.669 rads/s

Having w, we can now solve for the value of L
L = 12.118mH

Step 3.
For this case we look at the following circuit which now contains a capacitor;

With this in mind and running at the same frequency of 1Khz, we want to set both the inductor and capacitor equal to each other

jwL = 1/jwC;           Using the value of L, we get the value of the capacitor to be:

C = 0.00218 mcFarads

We got the following reading in the oscilloscope:

The following readings were reported:
Vpp Ch1 = 10V
Vpp Ch2 = 5V
Delta t = 3mcseconds

We then used the DMM to obtain the following data:

Freq (Khz)	Vin (V)	Iin (mA)	|Zin| Ohms
5.00	5.66	0.67	8.45
10.00	5.29	1.60	3.31
20.00	4.90	2.14	2.29
30.00	5.49	1.10	3.66
50.00	7.43	1.72	4.32

FREEMAT - Complex Numbers

Assignment

Matrix Problem;

MOSFET Control of an Electric Motor Lab

For this lab we studied the behavior of a motor which basically is an inductor with magnets inside that reacts to voltage input.

We used a function generator as well as an oscilloscope to obtain graphs.

Flyback Voltage

In the first part we tested flyback voltage which consisted on just the motor and a 2.2 Kohm resistor.

We set up the oscilloscope for single sweep with vertical scale of 10v/div and time scale of 0.1 ms/div.

We obtained the following graph:

A 1N4007 diode was adapted to the circuit so that it could correct the noise in the graph.

We noticed that even with the diode, we could still see the flaws on the graph (eg. the sharp, uneven peaks).
We also noticed that the diode would get warm after the motor was left running for a long period of time.

Open Loop MOSFET Voltage Control Unit

On the following part, we studied the effects of adding a MOSFET transistor which it's an analog of the variable transistor; source voltage controlled resistance. The function of a MOSFET is to control the flow of current in the Source and Drain leads which is governed by the Gate voltage. We also added a potentiometer that allowed us to change the resistance, and hence vary the voltage (gate voltage of MOSFET) on the motor.

By turning the potentiometer VERY SLIGHTLY, we measured the start-up voltage of the motor to be 3.9V.

Looking at the formula;
Rds =  VdRl / (Vs-Vd)
we can see that Rl (in this case the motor), is driven by the resistance of the MOSFET. And since the MOSFET behaves as a variable resistor, we can control it via the potentiometer. We also see that when the voltage drain is smaller than the voltage source Vs, the ratio Vd/(Vs-Vd) decreases as Vd decreases.

When we attempted to slowly increase the voltage gate from zero, it was quite difficult to have steady control of the motor. The voltage was fluctuating rapidly in short periods of time.

We measured the motor DC internal resistance to be 2.5 ohms.

Part 2: PWM Chopper MOSFET Motor Control

In the last part of this experiment we analyzed how motors act when a pulse is applied to them. In a broad picture, pulses continously turn on and off the motor in a periodic matter.The motor was fed by a function generator instead of a potentiometer, and it was set to generate a square wave.

When we reduced the frequency from 10 to 6.73 Khz we noticed that the motor emitted pulses

The duty cycle of the square wave was varied from 0 to 100% resulting in the motor's rotation decrease in speed.

Looking at the waves and the motor rotation, there was clearly an addition of waves going on. 

We found the time it took for the motor to go to 100 to 0% duty cycle and reach minimum speed: ~ 1 second.

2ODE Activity Lab