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.

Capacitor Charging/Discharging

Purpose: To observe the properties of a capacitors in their charging and discharging states.

Introduction: 
We have 2 different circuit models for the charging and discharging with Thevenin equivalent as shown:

We want to design build and test a circuit that does the following:

• utilizes a 9V power
• Employs a charging interval of 20s with a stored energy of 2.5mJ
• discharges the 2.5mJ in 2s

   To fulfill these requirements we have the following for charging resistance and capacitance:

       The peak discharge current and discharge and resistance were then calculated.

 Experiment:
     The actual charge and discharge resistances used are as follows along with the voltage source.

      The circuit was then built. For capacitance we used 3 capacitors is parallel and hooked up logger pro voltage sensors.

     The   Charging and discharging was recorded on logger pro.

     Data:

The charging curve:

     The capacitor charges up to about 8.5V. The reasons for it not charging all the way are a leak resistance which is inherent to every capacitor. The main reason for the biggest loss is that logger pro capped it off around this voltage.

The discharging curve:

     The capacitor doesn't completely discharge in 2 seconds but it is extreemely close.

Conclusion:

     The charging and discharging of capacitors is exponential and the time to make them discharge and charge can be easily controlled by changing the value of the resistance and/or capacitors.

Practical Question:

OP-AMPS II

Purpose: See the effect of changing the feedback resistor and input resistances.

Introduction:

We need to calculate the resistances necessary to get a gain of -10 and what the current coming out of the op amp would be if Vs were 1V:

 

Experiment:
We then build the circuit setting the Vs to 0.25 and vary it while recording the voltages across the input and output resistors. A voltage divider was used to get Vs .

The circuit was then built with a 1K Ohm load according to the following schematic:

The same data was recorded with this set up.

\Data:

    Inverting Op-Amp

     

Vin Desire(V)	V_IN Actual(V)	V_Out Measured(V)	V_Rf Measured(V)	I_op Calculated(mA)
0.25	0.26	-2.59	2.58	0.026
0.5	0.52	-5.18	5.18	0.052
1	1.01	-10.11	9.94	0.101

       For V_IN = 1V

       Measured I_cc = 0.867 mA
                Calculated P_cc = 12*0.867 mP = 10.404 mP
       Measured I_ee = -0.979 mA 

                 Calculated P_ee = 12*0.979 mP = 11.748 mP

       I_cc + I_ee = 0.112 mA
       The percent error is 12% therefore, it is consistent with KCL.

 

      Circuit with 1k Ohms load

    

Vin Desire(V)	V_Out Measured(V)	V_Rf Measured(V)	I_op Calculated(mA)	I_cc Measured(mA)	I_ee Measured(mA)
1	-10.02	9.77	0.1	0.877	-0.984

    For V_IN = 1V

    Measured I_cc = 0.877 mA
            Calculated P_cc = 12*0.877 mP = 10.524 mP
    Measured I_ee = -0.984 mA
             Calculated P_ee = 12*0.984 mP = 11.808 mP
     I_cc + I_ee = 0.107 mA
     The percent error is 07% therefore, it is consistent with KCL.

Conclusion:

    With percent errors of 12% and 7% this experiment is considered a success and obeys Kirchhoff's Current Law. We saw that the gain depends directly on Rf/Ri.

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.