Lab 10 - AC Signals #1

In this lab, we investigated AC signals and the corresponding phase effects on circuit elements.  This was achieved by hooking up an AC signal from a function generator into a simple RC circuit and then analyzing the results using an oscilloscope and multimeter.  The time difference between the signals was determined on the oscilloscope which was then used to determine the phase difference. 

Unfortunately no picture is available.

Data:
AC Signal	3 V peak to peak @ 2 kHz
Anticipated V RMS	2.12 V
Measured V RMS	2.0 V
Z C	-j717 ohm
V C peak to peak	2 V
Measured VC RMS	.61 V
∆t between sign	90 ms
phase θ	199.8 deg

This phase angle indicates that capacitor signal leads the resistor.

Lab 9 - Oscilloscope 101



This lab was an introduction to the oscilloscope which is a tool used to analyze time-varying signals.  The scope operates by deflecting an electron beam onto a special phosphor-coated screen which lights up when the beam hits it.  Controls allow you to vary the voltage and time scale so that the input signal can be displayed as desired.  In our case we used a function generator to generate the 4 different signals below which could then be analyzed.  The first 3 were known sinusoid and squarewave signals with/without DC offsetting and the final was an unknown mystery signal.  This mystery signal appeared as a modified squarewave with a slight decay at the peaks.

Ex 1:	5 kHz 5V Sinusoid
	Period	200 microsec
	Pk-Pk ampl	10 V
	Zero-Pk ampl	5 V
	RMS	3.53 V
	DMM readings:
	VDC	0 V
	VAC	3.3 V
Ex 2:	5 kHz Sinusoid w 2.5 V DC Offset
	DMM readings:
	VDC	2.51 V
	VAC	3.32 V
Ex 3:	5 kHz Squarewave w 2.5 V DC Offset
	DMM readings:
	VDC	2.51 V
	VAC	5.25 V
	Calculated RMS	3.34 V
Ex 4:	Mystery signal
	DC voltage	2.5 V
	Frequency	100 Hz
	Pk-Pk Amp	.4 V

Lab 8 - Operational Amplifiers I

In this lab, we took a look at op amps by applying them to a real world scenario.  The idea was that in the real world, different sections of your circuit may require different signal voltages/currents.  In order to provide the correct signal to these sections, you have to pass them through an intermediate conditioning circuit, and op amps are an excellent way to produce the conditioning needed.  Our problem involved a conditioning circuit where the input needed to be 0 to 1V while the output need to be 0 to -10V.  So we created a voltage divider to provide the 0 to 1V input and then set up an op amp(LM741) as an inverting amplifier to get the 0 to -10V output.  The calculated values for the input and feedback resistors needed to produce a gain of -10 were Ri=1kohm and Rf=10kohm.  We used a variable resistor in our voltage divider to vary the input voltage at .25V increments from 0 to 1V and measured the output voltage at each reading.  The gains at each of these readings was then calculated and most came out to be right around -10. 

Component	Nominal	Measured	Power Rating
Ri	1000 ohm	990 ohm	1/8 W
Rf	10000 ohm	9870 ohm	1/8 W
Rx	360 ohm	354 ohm	1/8 W
Ry	68 ohm	67.7 ohm	1/8 W
V1	6 V	6.01 V	36 W
V2	6 V	6.05 V	24 W

  

V in	V out	Gain	V ri	I ri	V rf
0.00 V	0.00 V	0.00	0.00 V	0.00 mA	0.00 V
0.25 V	-2.31 V	-9.91	0.233 V	0.235 mA	2.31 V
0.50 V	-4.99 V	-10.00	0.499 V	0.504 mA	4.99 V
0.75 V	-6.99 V	-9.98	0.700 V	0.707 mA	6.99 V
1.00 V	-9.96 V	-9.98	0.997 V	1.00 mA	9.95 V

Ideally the circuit would have been set up best with 3 power supplies, but we used only 2 which caused some undesired consequences.  Since our + op amp supply was also being used to power the voltage divider, the current drawn from our 2 op amp power supplies came out to be 75.5mA and -1.8mA which is not what we desired.  

PSpice Thevenin & Max Power (Homework)

Homework#1 Circuit

Homework#1 Thevenin (Vth=64.3V, Rth=3.4 kOhm)

Homework#1 Power (Pmax=301 mW)

Homework#2 Circuit

Homework#2 Thevenin (Vth=61.4 V, Rth=68.6 ohm)

Homework#2 Power (Pmax = 13.8 W)

Lab 7 - PSpice Tutorial #2: Thevenin & Norton Equivalents

In this lab we dove into some of the other useful tools in PSpice.  To start, we went further into DC Nodal Analysis and added the use of the voltage ViewPoint and current IProbe tools which allow you to find readings at particular circuit locations(pic 1 below).  Then, we got a feel for the DC Sweep tool which helps enable circuit design flexibility by calculating voltages and currents when a source source is swept over various ranges (pics 2-5 below). 

Pic 1: DC Nodal analysis with Viewpoints and IProbe

Pic 2: DC Sweep of V1 in above circuit

Pic 3: DC Sweep Plot - Thevenin (Vth = 20V, Rth = 6 Ohm)



Pic 4: DC Sweep Plot - Norton (In = 3.335A, Gn = .17S)



Pic 5: DC Sweep Plot - Max Power Transfer (Pmax = 250mW)

Lab 6 - Thevenin Equivalents

Step A: Thevenin Eq Circuit
Config	Theoretical	Measured	Error
R L2 = R L2 min	V load2 = 8.0 V	7.74 V	-3.25%
R L2 = infinite R	V load2 = 8.643 V	8.63 V	-0.15%
Step B: Original Circuit
Config	Theoretical	Measured	Error
R L2 = R L2 min	V load2 = 8.0 V	5.91 V	-26.10%
R L2 = infinite R	V load2 = 8.643 V	6.32 V	-26.90%

Pmax

275mW

In this lab we attempted to verify Thevenin's theorem.  The idea is that in a system of multiple power sources and loads we want to be able to easily calculate the affect of replacing one element so we reduce it into it's Thevenin equivalent (a source in series with a resistor).   We took a complex circuit and solved for it's Thevenin equivalent values(Vth =8.643V, Rth = 66ohms) and also for the value of the resistor necessary to produce an 8V drop across the load(R load min = 820 ohm).  Then we set up two circuits to verify - the first was the actual Thevenin Eq circuit and the second was the original circuit.  Our results were very accurate for the Thevenin Eq circuit but not for the original circuit.  This may have been due to a faulty breadboard and the additional wire resistance required for the full circuit.   

Lab 5 - PSpice Tutorial

In this lab we ran through a tutorial of the PSpice program.  PSpice is a powerful circuit analysis tool that was developed in the 1970's and which has gone through a number of versions since then.  It allows you to create a circuit using many common components and then run a simulator which will give a user all sorts of useful information about the circuit.  Above are two circuits in PSpice which have the voltage and current measurements displayed.