Operational Amplifiers I

Purpose: To use an inverting amplifier to design a Signal Conditioning circuit that has corresponding output ranges between 0 and -10V when the sensor's output is 0 to +1.

Introduction:
a. using the constraints of the problem we find the value of an acceptable input resistance.

b. In order to acheive the required gain we find the feedback resistance.

c. Determine Rx of the voltage divider

d. Determine the maximum setting of Ry

e. With Ry set to the value from d, determine the thevinin equivalent of the divider circuit.

Experiment:

set up the circuit as so:

Measure voltage across Rf and Ri.

V in (V)	V out (V)	Gain	V Ri (V)	I Ri (mA)	V Rf(V)
0.00	0	N/a	0.00	0	0
0.25	-2.51	-10.04	0.25	0.000256	-2.51
0.50	-5.04	-10.08	0.50	0.000512	-5.04
0.75	-7.56	-10.08	0.75	0.000768	-7.56
1.00	-10.07	-10.07	0.999	0.001024	-10.09

current I_v1= 2.27mA

current I_v2= -1.613mA

Calculations:

Conclusion:

      This shows a gain of -10 from input to output. This is an inverting amplifier.This agrees with the 30mW power constraint for each supply. To reduce the power drawn without changing the amplifier we could reduce the power supply.

Thevinin Equivalent

Purpose: To find the Thevinin equivalent circuit and verify it experimentally.

Experiment:

The initial circuit as well as the calculations and transformations used to find the thevenin equivalent circuit as well as practical values used in the experiment.

We also calculate the smallest acceptable R_L2 that will give a minimum load of 8V.

We build the simple circuit using the equivalents and take the voltage and resistances.

We then build the original circuit and get the data.

Data:

As it is seen the values did match up showing that the thevinin equivalents worked.

PSpice Tutorial.

Purpose: To become familiar with the PSpice program and how its uses.

Tutorial Results:

Here is an examples of a circuit that can have voltage and current calculated with PSpice.

We can also get graphs of voltage, current and power.

Problems:
1.

Maximum Power Transfer

Purpose: To analyze power transferred by a circuit and see the relation to maximum power.

Introduction:

We will set up the following simplified circuit.

Experiment:

We use DMMs to measure the voltage and resistance to find power.

We now set up the original circuit and measure the current and voltage with Logger Pro.

Data:

Measured V0 (Volt) Measured Rx (ohm) Calc. P0 (Watt)
0 13.                         5                            0.0000E+00
0.16                          330                        7.7576E-05
0.34                          691                        1.6729E-04
0.51                          1126                      2.3099E-04
0.68                          1707                      2.7088E-04
0.85                          2390                      3.0230E-04
1.02                          3020                      3.4450E-04
1.19                          5680                      2.4931E-04
1.36                          2280                      8.1123E-04
1.53                          2780                      8.4205E-04
1.7                            3270                      8.8379E-04
1.87                          3800                      9.2024E-04
2.04                          4440                      9.3730E-04
2.21                          5120                      9.5393E-04
2.38                          5940                      9.5360E-04
2.54                          6850                      9.4184E-04

The graphs of current, voltage and power are shown below.

 The maximum power output happens around 5.2 k Ohms. This is a 7.1% error from the theoretical value of 5600 ohms.
  Logger Pro had a lot of noise in the data but there was a visible trend and we were able to get a decent power graph. In this case it was better to do the data recording manually.

Transistor Switching

Purpose: To understand the applications of a transistor and analysis of a transistor circuit.

Introduction:
   We will use

• Voltage source
• Breadboard and wire
• DMM
• 2N3904 Transistor
• Pot
• Resistors

Resistors (Ohms):
R1 = 180
R2 = 10k
R3 = 680

Demonstration: We set up the following circuit and when a finger was used to connect the circuit,  the LED would light. This displayed how the transistor can amplify current.

Experiment: To understand how a transistor works we set up the following circuit. 

 R1 and R3 changed to 39 Ohm resistors.

The resistance above and below the transistor is the same until the potentiometer is added to change the voltage  of the base.

We will measure the Amps through the base at A1 and the amps moving through the emitter at A2

Data:

Beginning with the potentiometer halfway we measured the following values.

Conclusion:

     The beta gain of the transistor is 136.02 (if you only use the first 4 points before saturation). It saturates around 0.2 to 0.4 amps.

Free Mat Lab

Purpose: To explore freemat and see how it can be used in an engineering environment,

Experiment: 
              Display of sine graph:

             Display of sine and cosine graphs.

Examples:
1)
It is possible to solve the following circuit with the gven information :V1 = 15V, V2 = 7V, R1 = 20Ω, R2 = 5Ω, and R3 = 10Ω

Setting the information into matrix form we get-->

The current found through R3 is -0.1857A




2)
Circuit 1 has a time constant of 100 ms and circuit 2 has a time constant of 200ms. The output is 2e^(-t/ τ) where τ is the time constant. Using graphs, identify which circuit will have the lower output sooner.

Circuit A will have a lower output.

comparing the curves of 2e^(-t/tau) and 2(1-e^(-t/tau)):

3)

Determining the output of adding the sinusoids: 3sin(2t+10) and 5cos(2t-30)

The function and their sum.

When we change the frequency to 10Hz we have:

This shows that changing the frequency changes the period.

Voltage Dividers

Purpose:   To see the changes that occur in branch currents and voltages when using voltage dividers and see the effects on unregulated power sources.

Introduction:  

• Using three 1k Ohm resistors in parallel with a voltage source
• Using breadboard
• Using Labvolt power source

Preperations

Max resistance = 1 Ohm
Upper V bound = 6.25 V

Min resistance = 1/3 Ohm
Lower V bound = 5.75 V

Vs  = 6.53 V
Rs = 45.45 Ohm

IMax  = 6.25mA
IMin  = 17.23mA

We will use the circuit in the picture to the right.

Measure of 3 Resistors (left to right):
R1: 978 Ohms
R2: 976 Ohms
R3: 979 Ohms

Rs was created with a variable resistance box.

Data:

	R(Bus)            Ohms	V    (±0.05)	mA      (±0.02)	P load    (mW±0.1)
1 Load	978	6.08	6.04	83.8
2 Loads	488.5	5.65	11.28	63.7
3Loads	325.3	5.33	15.73	83.8

Calculations:

The load volatage variation exceeding our theiretical value is due to non ideal values of resistance such as with Rs. If we added another 1k Ohm resistor in parallel then the voltage variation would be around 16.7%