Clemson ECE Laboratories ECE 211 Electrical Engineering Lab

Clemson ECE Laboratories ECE 211 - Electrical Engineering Lab VI Pre-labs for ECE 211 Guneet Bedi Created: 10/09/2012 Updated: 10/09/2012 1

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Clemson ECE Laboratories Introduction • This lab focuses on the The venin equivalent and maximum power transfer theorems. • Complex circuits are often replaced with their The venin equivalent to simplify analysis. • Maximum power transfer is also an important concept which allows the designer to determine an optimal design when power is a constraint. 3

Clemson ECE Laboratories The venin Equivalent Circuit • Thevenin equivalent circuit is an independent voltage source VTh in series with a resistor RTh, which replaces an interconnection of sources and resistors. • This series combination of VTh and RTh is equivalent to the original circuit in the sense that, if we connect the same load across the terminals a, b of each circuit, we get the same voltage and current at the terminals of the load. • This equivalence holds for all possible values of load resistance. 4

Clemson ECE Laboratories The venin Equivalent Circuit contd… • To calculate the Thevenin voltage VTh, we simply calculate the opencircuit voltage in the original circuit. • If we place a short circuit across the terminals a, b of the Thevenin equivalent circuit, the short-circuit current directed from a to b is • This short-circuit current must be identical to the short-circuit current that exists in a short circuit placed across the terminals a, b of the original network. • Thus the Thevenin resistance is the ratio of the open-circuit voltage to the short-circuit current. 5

Clemson ECE Laboratories 6 Maximum Power Transfer • Maximum power transfer occurs when the load resistance equals the Thevenin resistance i. e. RL=RTh • The maximum power delivered to RL is

Clemson ECE Laboratories Lab Objective • By the end of this lab, the student should be able to verify The venin's equivalence theorem and the concept of maximum power transfer. 7

Clemson ECE Laboratories Equipment Needed • NI-ELVIS workstation • Resistance substitution box • Individual resistors (220Ω, 330Ω, 680Ω, 1 kΩ) 8

Clemson ECE Laboratories Procedure-The venin’s Theorem • • Set up the circuit as shown in figure. Adjust the output of the DC power supply to 10 V. Measure the open circuit voltage between nodes A and B. Now connect the ammeter between nodes A and B and measure the short circuit current between nodes A and B. • Using these measurements, determine the The venin equivalent circuit. • Set up the newly determined The venin equivalent circuit and verify that this circuit has the same open circuit voltage and short circuit current as the previous circuit. 9

Clemson ECE Laboratories Procedure-Maximum Power Transfer Theorem 10 • Use the The venin equivalent circuit developed in Part 1. • For a resistance substitution box RL between nodes A and B, measure the current through and voltage across RL for RL=0Ω. • Repeat for RL=100Ω, 120Ω …… 500Ω (in 20Ω increments). • Determine the power dissipated by the resistor for each value of RL. • Plot Power vs. Resistance. • At which value is the power a maximum?

Clemson ECE Laboratories Lab 6 -Student Tasks • Students are required to solve the ‘Probing Further’ section, given in the lab manual, in their laboratory notebooks. • Lab notebooks are due on the same day as your report for lab 5. 11

Clemson ECE Laboratories Preparations for Next Week • Review 'XYZs of Oscilloscopes', available at: www. tek. com (60+ pages). • o o o Be familiar with the following: Voltage scaling (Volts/division) Time base (seconds/division) Input coupling Triggering Measurement probes 12

Clemson ECE Laboratories References • ECE 211 – Electrical Engineering Lab I. Latest Revised July 2010. • Electric Circuits 8 th Edition by James W. Nilsson & Susan A. Riedel. 13

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Clemson ECE Laboratories ECE 211 - Electrical Engineering Lab VII Pre-labs for ECE 211 Guneet Bedi Created: 10/19/2012 Updated: 10/19/2012 15

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Clemson ECE Laboratories Introduction • Oscilloscopes are indispensable tools for anyone designing, manufacturing or repairing electronic equipment. • The digital oscilloscope allows the engineer to examine time varying waveforms to determine the magnitude, frequency, phase angle, and other waveform characteristics which depend upon the interaction of circuit elements with the sources driving them. • The usefulness of an oscilloscope is not limited to the world of electronics. With the proper sensor, an oscilloscope can measure all kinds of phenomena. 17

Clemson ECE Laboratories The Oscilloscope • The oscilloscope is basically a graph-displaying device. • The graph shows how signals change over time. • The vertical (Y) axis represents voltage and the horizontal (X) axis represents time. The intensity or brightness of the display is sometimes called the Z axis, as shown in figure. 18

Clemson ECE Laboratories Waveforms • A waveform is a graphic representation of a wave. • Waveform shapes reveal a great deal about a signal. • Any time you see a change in the height of the waveform, you know the voltage has changed. • Any time there is a flat horizontal line, you know that there is no change for that length of time. • Straight, diagonal lines mean a linear change – rise or fall of voltage at a steady rate. • Sharp angles on a waveform indicate sudden change. 19

Clemson ECE Laboratories Waveform Measurements-Frequency & Period • If a signal repeats, it has a frequency. • The frequency is measured in Hertz (Hz) and equals the number of times the signal repeats itself in one second, referred to as cycles per second. • A repetitive signal also has a period, which is the amount of time it takes the signal to complete one cycle. • Period and frequency are reciprocals of each other, 20

Clemson ECE Laboratories Waveform Measurements-Voltage • Voltage is the amount of electric potential, or signal strength, between two points in a circuit. • Usually, one of these points is ground, or zero volts, but not always. • One may measure the voltage from the maximum peak to the minimum peak of a waveform, referred to as the peak-to-peak voltage. 21

Clemson ECE Laboratories Waveform Measurements-Amplitude • Amplitude refers to the amount of voltage between two points in a circuit. • Amplitude commonly refers to the maximum voltage of a signal measured from ground, or zero volts. • The waveform shown in figure has an amplitude of 1 V. 22

Clemson ECE Laboratories Waveform Measurements-Phase • The voltage level of sine wave is based on circular motion. • Given that a circle has 360°, one cycle of a sine wave has 360°. • Phase shift describes the difference in timing between two otherwise similar signals. • The waveform in figure labeled “current” is said to be 90° out of phase with the waveform labeled “voltage, ” since the waves reach similar points in their cycles exactly 1/4 of a cycle apart (360°/4 = 90°). 23

Clemson ECE Laboratories Controls of an Oscilloscope • The front panel of an oscilloscope is divided into three main sections: o Vertical: The attenuation or amplification of the signal. Use the volts/div control to adjust the amplitude of the signal to the desired measurement range. o Horizontal: The time base. Use the sec/div control to set the amount of time per division represented horizontally across the screen. o Trigger: The triggering of the oscilloscope. Use the trigger level to stabilize a repeating signal. 24

Clemson ECE Laboratories Probes • Even the most advanced instrument can only be as precise as the data that goes into it. • A probe functions in conjunction with an oscilloscope as part of the measurement system. • Precision measurements start at the probe tip. • The right probes matched to the oscilloscope and the device-under test (DUT) not only allow the signal to be brought to the oscilloscope cleanly, they also amplify and preserve the signal for the greatest signal integrity and measurement accuracy. 25

Clemson ECE Laboratories Probe Types Passive Probes Active & Differential Probes Logic Probes Specialty Probes 26

Clemson ECE Laboratories NI-ELVIS Series II Workstation. Additional Features Oscilloscope (Scope) Connectors (Input): o CH 0 BNC Connector: The input for channel 0 of the oscilloscope. o CH 1 BNC Connector: The input for channel 1 of the oscilloscope. SYNC (Output): o 5 V TTL signal synchronized to the FGEN signal. o This signal is most used as a trigger signal for the oscilloscope. 27

Clemson ECE Laboratories NI ELVIS Instrument Launcher- Scope (Oscilloscope) 1. 2. 3. 4. 5. 6. 7. 8. 9. Scope Graph Channel Settings Probe & Coupling Volts/Div (Vertical sensitivity) & Vertical Position Trigger Log Timebase (Horizontal Sensitivity) Display Measurement Cursor Settings 28

Clemson ECE Laboratories Lab Objective • By the end of the lab the student should be familiar with the controls of a digital oscilloscope and be able to use the instrument to observe periodic waveforms. 29

Clemson ECE Laboratories Equipment Needed • NI-ELVIS workstation • 100Ω resistor • 1 kΩ resistor 30

Clemson ECE Laboratories 31 Procedure-Basic Setup • Connect a cable with BNC fitting to the BNC jack for CH 0 of the oscilloscope on the left side of the NI-ELVIS II. • Connect the cable’s red lead to the FGEN output; connect the cable’s black lead to GROUND. • Set the function generator to output a 100 Hz sine wave with amplitude = 3. 0 VPP and DC offset = 0 V. • Open the oscilloscope window in the NI-ELVIS software. • “ENABLE” the display for Channel 0. • “RUN” the function generator and the oscilloscope. • Turn on the prototype board. • Record the measured values for RMS voltage, peak-to-peak voltage, and waveform frequency. • Sketch the displayed waveform in your laboratory notebook. • Compare your measurements with the expected values based on the function generator output.

Clemson ECE Laboratories Procedure-Source Control • Connect CH 0 to “SYNC” (adjacent to FGEN). • Sketch this waveform in your laboratory notebook. • Reconnect CH 0 to FGEN. • Change the function generator output to a square wave. • Record the displayed waveform in your laboratory notebook. • Measure the peak-to peak output voltage. • Repeat this measurement for a triangular wave. 32

Clemson ECE Laboratories Procedure-Voltage Scaling • Reset the function generator to output a sine wave. • Vary the vertical scale control for Channel 0 using either the control knob or pull-down menu. • Record the effect that this control has on the displayed waveform. • Set the control to 500 m. V/div. • Measure the peak-to-peak magnitude of the displayed waveform by counting (estimate) the number of peak-to-peak divisions and multiplying by the vertical scale. • Compare this result with the measurement given by the oscilloscope. 33

Clemson ECE Laboratories 34 Procedure-Voltage Offset Manipulation • Vary the vertical position control in the oscilloscope and record the effects in your laboratory notebook, noting any changes in the measured RMS voltage. • Return the offset to zero and add a DC offset of 0. 5 V to the function generator output. • Record the effects in your laboratory notebook, noting any changes in the measured RMS voltage.

Clemson ECE Laboratories 35 Procedure-Time Scaling • Return the DC offset in the function generator to 0 V. • Using either the timebase dial or pulldown menu, adjust the timebase of the oscilloscope display to the fastest setting (5μs/div). • Record the effect that this setting has on displayed measurements for the waveform. • Gradually increase the timebase through each available setting until the slowest setting has been reached (200 ms/div). • Record the effect that this control has on the measurement of voltage and frequency. • Return the timebase to a setting where 1 -3 full cycles of the output sine wave is viewable. • Set the Acquisition Mode to ‘RUN ONCE’ and press ‘RUN’ to capture a single sweep of the output waveform. • Measure the period of the waveform by counting (estimate) the number of time divisions for a single cycle and multiplying by the time scale. • Compare this measurement to the inverse of the frequency measured by the oscilloscope.

Clemson ECE Laboratories Procedure-Triggering/Synch Function • Return the screen update to 'RUN'. • Adjust the triggering pull-down menu to edge and record the oscilloscope response. • Vary the function generator peak amplitude to verify that the oscilloscope is continuing to update the display in this mode of operation. 36

Clemson ECE Laboratories 37 Procedure-Cursor Function • Set the function generator to output a 100 Hz sine wave with peak amplitude = 3. 0 VPP and DC offset = 0 V. • Return the triggering function to 'Immediate'. • Display a single screen update of between 1 -3 cycles of the output function. • Switch the cursors function on and drag the cursors to appropriate points on the waveform to measure the period of the sine wave. • Then adjust the cursors to measure the peak-to-peak voltage of the sine wave. • Compare these measurements to those expected based on the function generator's output settings.

Clemson ECE Laboratories 38 Procedure-Test Circuit • Connect the voltage divider circuit shown in figure. • Set the function generator to output a 1 k. Hz sine wave with amplitude 2 Vp-p and DC offset = 0. • Display the function generator output on channel 0 of the oscilloscope and the voltage across the 100Ω resistor on channel 1. • Display and measure these voltages simultaneously. • Measure the period of both waveforms using the cursor function. + -

Clemson ECE Laboratories 39 Procedure-Test Circuit contd… • Sketch the waveforms in your laboratory notebook and record your settings for Volts/div and seconds/div. • Compare your voltage measurements with theoretical calculations based on the voltage divider equation. • Compare your waveform period measurement with theoretical value obtained from the input frequency. + -

Clemson ECE Laboratories 40 Procedure-Test Circuit contd… • Reverse the polarity for the output voltage measurement on Channel 1. • Repeat your voltage and period measurements. • Sketch the resulting waveforms in your laboratory notebook. • Record your settings for Volts/div and seconds/div. +

Clemson ECE Laboratories Lab 7 -Student Tasks • Students are required to solve the ‘Probing Further’ section, given in the lab manual, in their laboratory notebooks. 41

Clemson ECE Laboratories Preparations for Next Week • Read Appendix C, Fundamentals of Statistical Analysis. • o o Become familiar with the following concepts: Mean Standard deviation Variance and The formulas used for calculating these quantities. 42

Clemson ECE Laboratories References • ECE 211 – Electrical Engineering Lab I. Latest Revised July 2010. • XYZs of Oscilloscopes-Primer by Tektronix • Otago University Electronics Group-NI ELVIS II Orientation Manual. 43

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Clemson ECE Laboratories ECE 211 - Electrical Engineering Lab VIII Pre-labs for ECE 211 Guneet Bedi Created: 11/09/2012 Updated: 11/09/2012 45

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Clemson ECE Laboratories Introduction • A resistor–capacitor circuit (RC circuit) or RC network, is an electric circuit composed of resistors and capacitors driven by a voltage or current source. • A resistor–inductor circuit (RL circuit) or RL network, is an electric circuit composed of resistors and inductors driven by a voltage or current source. 47

Clemson ECE Laboratories Time Constant-RC Circuit • The time taken for the capacitor to charge or discharge to within a certain percentage of its maximum supply value is known as its Time Constant ( τ ). • Mathematically, τ=RC 48

Clemson ECE Laboratories Time Constant-RL Circuit • The time taken for the current in an inductor to grow or decay to within a certain percentage of its maximum value is known as its Time Constant ( τ ). • Mathematically, τ=L/R 49

Clemson ECE Laboratories Lab Objective • By the end of this lab, the student should know how to measure the time constants of RC and RL circuits. 50

Clemson ECE Laboratories Equipment Needed • • NI-ELVIS workstation Resistance substitution box Capacitance substitution box Inductance substitution box 51

Clemson ECE Laboratories Procedure-RC Time Constant Measurement (1) • Set up the RC circuit shown in figure. • Set the function generator to give a square wave output with magnitude equal to 500 m. V. • Measure both the source voltage and the voltage across the capacitor with the digital oscilloscope. • Adjust the frequency of the function generator so that the waveform shown has definite flat sections at the top and bottom. • Using the oscilloscope cursors function, determine when the voltage reaches 0. 632 times its final value. 52

Clemson ECE Laboratories Procedure-RC Time Constant Measurement (1) contd… • Sketch the waveform for a complete cycle in your notebook, recording the voltage scale and time scale values. • Clearly label the sketched waveforms, including the initial and final values. • Repeat these steps using C=0. 047μF and C=0. 1μF. • For each circuit the frequency of the waveform generator may have to be changed to achieve the flat sections at top and bottom of the waveforms. 53

Clemson ECE Laboratories Procedure-RC Time Constant Measurement (2) • Now modify the circuit as shown in figure. • Repeat the measurements in part 1 using C=0. 01μF, 0. 047μF, 0. 1μF while observing the voltage across the resistor. • Find the time when the voltage reaches 0. 368 times its initial value. • Compare your measured values of the RC circuit time constant in Parts 1 and 2 with theoretical values. 54

Clemson ECE Laboratories Procedure-RL Time Constant Measurement (1) • Set up the RL circuit shown in figure. • Set the function generator to give a square wave output with magnitude equal to 500 m. V. • Measure both the source voltage and the voltage across the resistor with the digital oscilloscope. • Adjust the frequency of the function generator so that the waveform has definite flat sections at the top and bottom. • Using the oscilloscope cursors function, determine when the voltage reaches 0. 632 times its final value. 55

Clemson ECE Laboratories Procedure-RL Time Constant Measurement (1) contd… • Sketch the waveform for a complete cycle in your notebook, recording the voltage scale and time scale values. • Clearly label the sketched waveforms, including the initial and final values. • Repeat these steps using L=400 m. H, 600 m. H and 800 m. H. • For each circuit the frequency of the waveform generator may have to be changed to achieve the flat sections at top and bottom of the waveforms. 56

Clemson ECE Laboratories Procedure-RL Time Constant Measurement (2) • Now modify the circuit as shown in figure. • Repeat the measurements in part 1 using C=200 m. H, 400 m. H, 600 m. H and 800 m. H while observing the voltage across the inductor. • Find the time when the voltage reaches 0. 368 times its initial value. • Compare your measured values of the RC circuit time constant in Parts 1 and 2 with theoretical values. 57

Clemson ECE Laboratories Lab 8 -Student Tasks • Students are required to solve the ‘Probing Further’ section, given in the lab manual, in their laboratory notebooks. 58

Clemson ECE Laboratories Preparations for Next Week • Review the material in the textbook on the RLC circuit response. • Review the concepts of overdamped, underdamped, and critically damped response. • Calculate theoretical parameter values of s 1, s 2, α, ωd, and T for the circuit used in the lab (i. e. , do Part 0 of the Procedure). 59

Clemson ECE Laboratories References • ECE 211 – Electrical Engineering Lab I. Latest Revised July 2010. • Wikipedia 60

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Clemson ECE Laboratories ECE 211 - Electrical Engineering Lab IX Pre-labs for ECE 211 Guneet Bedi Created: 11/16/2012 Updated: 11/16/2012 62

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Clemson ECE Laboratories Introduction • A series RLC circuit (or LCR circuit) is an electrical circuit consisting of a resistor, an inductor, and a capacitor, connected in series with the voltage source. • The RLC part of the name is due to those letters being the usual electrical symbols for resistance, inductance and capacitance respectively. 64

Clemson ECE Laboratories Series RLC Circuit Properties-Circuit Response • The differential equation for the circuit has the following characteristic equation • The circuit response or the roots of the characteristic equation is given by or 65

Clemson ECE Laboratories Series RLC Circuit Properties-α, ω0 & ζ • α is called the neper frequency, or attenuation, and is a measure of how fast the transient response of the circuit will die away after the stimulus has been removed. • ω0 is the angular resonance frequency. • Damping factor, ζ is defined as the ratio of α and ω0 66

Clemson ECE Laboratories Series RLC Circuit Properties-Time Period (T) • Let us define ωd as Where T=Time Period 67

Clemson ECE Laboratories Transient Response-Overdamped Response • If α is large compared with the resonant frequency ωo, the voltage or current approaches its final value without oscillation, and the non-oscillatory response is called overdamped. • ζ>1 68

Clemson ECE Laboratories Transient Response-Underdamped Response • If α is small compared to ωo, the response oscillates about its final value, and this response is called underdamped. • The smaller the value of α is, the longer the oscillation persists. • ζ<1 69

Clemson ECE Laboratories Transient Response-Critically Damped Response • If the dissipative element is removed from the circuit, α=0 and the voltage or current response becomes a sustained oscillation. • The critical value of α occurs when α = ωo; in this case, the response is on the verge of oscillation and is called the critically damped response. • ζ=1 70

Clemson ECE Laboratories Transient Response-Graphical Summary 71

Clemson ECE Laboratories Total Resistance Calculation • Let Rtot is the total resistance of the circuit. • In practice, part of that resistance is due to the internal resistance of the function generator (RFGEN) and part is supplied by the resistance substitution box (RS). where RFGEN is the internal resistance of the function generator, and RS is the resistance set on the resistance substitution box. 72

Clemson ECE Laboratories Lab Objective • By the end of this lab, the student should be able to relate the nature of the physical response of a series RLC circuit to the parameter values α and ωd determined by the component values. 73

Clemson ECE Laboratories Equipment Needed • • NI-ELVIS workstation Resistance substitution box Capacitance substitution box Inductance substitution box 74

Clemson ECE Laboratories 75 Procedure-Theoretical Calculations • Calculate the values of s 1, s 2, α, ωd, and T for the circuit shown in figure.

Clemson ECE Laboratories Procedure-Part 1 (Measurements across L) Circuit Setup 76 • Set up the circuit as shown in figure. • Since the function generator has internal resistance RFGEN in the range of 50Ω to 150Ω, set the resistance substitution box to RS=100Ω. • Set the function generator to output a square wave with amplitude = 2 VPP, DC offset = 0 V, and frequency in the range of 10 Hz to 100 Hz.

Clemson ECE Laboratories Procedure-Part 1 (Measurements across L) Underdamped Response 77 • Connect CH 0 of the oscilloscope to display the voltage across the inductor. To avoid a grounding error, the inductor must have one lead connected to ground. • To get a stable image of the circuit oscillations, connect a lead from the FGEN output to CH 1 of the oscilloscope. Then set the scope’s trigger to EDGE, CH 1, rising slope. • Adjust the period of the square wave, if necessary, so that the damped sinusoidal waveform decreases to a negligible value (i. e. , dampens out) before the next square-wave pulse occurs. Something in the range of 10 Hz to 100 Hz probably will be adequate. • Draw an accurate representation of the transient sinusoidal waveform (the damped oscillations) in your laboratory notebook.

Clemson ECE Laboratories Procedure-Part 1 (Measurements across L) Measuring T • Expand the time scale of the oscilloscope to show 3 to 6 peaks of the damped sinusoidal oscillation. • Using the CURSORS function of the oscilloscope, measure the period of the damped sinusoidal waveform. • Compare this value to T obtained in Part 0. 78

Clemson ECE Laboratories Procedure-Part 1 (Measurements across L) Measuring α • Measure the peak height of the first full peak of the damped sinusoidal waveform and the peak height at the next peak (+1 cycle). Measure the time difference Δt between these two peaks. • Determine the Neper frequency (damping coefficient), α, using your measurements and the equation • Compare your measured α to the value you calculated before. 79

Clemson ECE Laboratories Procedure-Part 1 (Measurements across L) Measuring Rtot & RFGEN • For your experimental α, calculate the total resistance Rtot in the circuit using • Calculate the function generator’s internal resistance using 80

Clemson ECE Laboratories Procedure – Part 1 (Measurements across L) Re-measuring RS & α • Now knowing RFGEN, adjust RS so that Rtot=250Ω. • Again measure the damping coefficient, α, and compare the new measured value to your calculated value. 81

Clemson ECE Laboratories Procedure-Part 2 (Measurements across C) Circuit Setup • Swap the positions of inductor and capacitor as shown in the figure. 82

Clemson ECE Laboratories Procedure-Part 2 (Measurements across C) Underdamped Response • Connect CH 0 of the oscilloscope to measure the voltage across the capacitor, being careful to avoid grounding errors. • Continue to trigger the scope using the FGEN signal on CH 1, as before. • In your laboratory notebook, sketch the waveform of the voltage across the capacitor. • If you were to perform the calculation for α using these data, you would need to subtract from the peak heights the 1 -volt offset provided by the pulse from the function generator. 83

Clemson ECE Laboratories Procedure-Part 2 (Measurements across C) Critically Damped Response • For the values of L and C used in this circuit, calculate the value of total series resistance Rtot that gives critical damping. • Change the resistance RS so that Rtot equals this value. • Again observe the voltage drop across the capacitor and sketch the resulting waveform in your laboratory notebook. 84

Clemson ECE Laboratories Procedure-Part 2 (Measurements across C) Overdamped Response • Change RS so that Rtot is 10 times the value you calculated for critical damping. • Observe and record the capacitor voltage response. 85

Clemson ECE Laboratories Lab 9 -Student Tasks • Students are required to solve the ‘Probing Further’ section, given in the lab manual, in their laboratory notebooks. 86

Clemson ECE Laboratories Preparations for Next Week Final Exam 87

Clemson ECE Laboratories References • ECE 211 – Electrical Engineering Lab I. Latest Revised July 2010. • Wikipedia 88

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Clemson ECE Laboratories ECE 211 - Electrical Engineering Lab X Pre-labs for ECE 211 Guneet Bedi Created: 10/26/2012 Updated: 10/26/2012 90

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Clemson ECE Laboratories Introduction • Uncertainty or some error in measurement is introduced by assuming ideal meters in the measurement process and by the use of the circuit components themselves. • While a component is designed to have a particular value (its "nominal" value), which is marked on the outside covering (the "case" or "encapsulation"), random fluctuations in materials and production processes will result in some range of values for the manufactured devices. • Thus, components are usually specified by a nominal value and a range, called the tolerance, in which the actual value is expected to lie. 92

Clemson ECE Laboratories Fundamentals of Statistical Analysis. Random Errors • When the human errors and systematic errors associated with a measurement procedure have been eliminated or brought under control, there will still be some variability in the measurements when they are repeated. These are called random errors. • Random errors are characterized by irregularity, which may appear to be a source of potential disagreement or confusion. • The use of statistical analysis methods makes possible the extraction of essential information. • Two characteristics of the measurements are of special interest: o The average/mean value of a series of measurements o Measure of the degree of variability about the mean. 93

Clemson ECE Laboratories Fundamentals of Statistical Analysis. Average or Arithmetic Mean • Consider a series of measurements: x 1, x 2, x 3, . . . , xn of some quantity. • For each sample of n measurements one can calculate an average or arithmetic mean value from 94

Clemson ECE Laboratories Fundamentals of Statistical Analysis. Variance & Standard Deviation 95 • Variance can be calculated from • Variance is the mean-square deviation of each measurement from the average value. • Standard deviation, s is the square root of Variance. • Standard Deviation is the root mean-square deviation of each measurement from the average value.

Clemson ECE Laboratories Fundamentals of Statistical Analysis. Example 96 • Consider 6 measurements of a voltage source over a period of an hour, repeated for 5 consecutive hours.

Clemson ECE Laboratories Fundamentals of Statistical Analysis. Example (Observations) • The most probable value that can be assigned to a measured magnitude, on the basis of equally trustworthy direct measurements, is the arithmetic mean. • In any large number of measurements positive and negative errors of the same magnitude are equally likely to occur. • Small errors are much more likely to occur than large ones. • All of the errors of measurement in a given series lie between equal positive and negative limits. 97

Clemson ECE Laboratories Lab Objective • By the end of this lab, the student should: o Know how to identify the tolerance of the resistors used in a particular circuit. o Understand what the specified nominal value and tolerance for a component means statistically. o Know how to apply statistical methods to obtain the best estimate of the true value of a circuit component. 98

Clemson ECE Laboratories Equipment Needed • NI-ELVIS workstation • Resistors 99

Clemson ECE Laboratories Procedure • Groups of resistors labeled GROUP A, GROUP B, GROUP C, etc. will be passed in turn from lab team to lab team. • For each group of resistors, measure the resistance of each component using the NI-ELVIS digital multimeter. • Make a table for each group, recording the resistances. 100

Clemson ECE Laboratories Observation Table I-Individual Resistance Record Resistor # 1 2 3 4 5 Total Resistor Gp A (330Ω) Resistor Gp B (1. 5 KΩ) Resistor Gp C (3. 9 KΩ) Resistor Gp D (5. 1 KΩ) 101

Clemson ECE Laboratories Procedure contd… • For the resistors in each group, calculate the mean, the standard deviation, and the variance. • Make a table showing these values for each of the groups and the values determined by other lab teams. • Find the average of the mean, variance and standard deviation values obtained by all the lab teams. 102

Clemson ECE Laboratories Observation Table II-Mean Record Resistor Gp # Mean (Team 1) Mean (Team 2) Mean (Team 3) Mean (Team 4) Total Average A B C D (330Ω) (1. 5 KΩ) (3. 9 KΩ) (5. 1 KΩ) 103

Clemson ECE Laboratories 104 Observation Table III-Variance Record Resistor Gp # Variance (Team 1) Variance (Team 2) Variance (Team 3) Variance (Team 4) Total Average A (330Ω) B C (1. 5 KΩ) (3. 9 KΩ) D (5. 1 KΩ)

Clemson ECE Laboratories 105 Observation Table IV-Standard Deviation Record Resistor Gp # Standard Deviation (Team 1) Standard Deviation (Team 2) Standard Deviation (Team 3) Standard Deviation (Team 4) Total Average A (330Ω) B (1. 5 KΩ) C (3. 9 KΩ) D (5. 1 KΩ)

Clemson ECE Laboratories Questions • Why do the values of mean, variance and standard deviation obtained by other teams differ from what you obtained? • Using the information from the tables, what would be the best estimate of the resistance of each group? Why? • How does the mean value of resistance obtained by your lab team, compare to the nominal value of resistance marked on the resistor’s body? • How does the standard deviation obtained by your team compare to the tolerance marked on the resistor case? 106

Clemson ECE Laboratories Preparations for Next Week • Review the material in your circuits textbook on voltage dividers. • Read and implement the procedure of Lab 11 (Design Lab). • Before you come to lab, you should have completed your circuit design i. e. the design procedure and resulting circuit. • This is NOT a team exercise. Each individual will be required to have a design completed in the notebook prior to coming to lab class. 107

Clemson ECE Laboratories References • ECE 211 – Electrical Engineering Lab I. Latest Revised July 2010. 108

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Clemson ECE Laboratories ECE 211 - Electrical Engineering Lab XI Pre-labs for ECE 211 Guneet Bedi Created: 11/02/2012 Updated: 11/02/2012 110

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Clemson ECE Laboratories Introduction • In this lab you will design and build a circuit to meet certain criteria. • In calling for a circuit design, two fundamental questions must be answered: o "What function is the circuit to perform? ", and o "How well is the circuit expected to perform this function? ". • The detailed answers to these questions are usually called the functional requirement and the specifications, respectively. 112

Clemson ECE Laboratories Lab Objective • The objective of this laboratory exercise is to introduce you to the nature of the engineering design process, i. e. , the process of selecting combinations of components to perform a given function with a given degree of precision. • You will be designing a Voltage Regulator to maintain a voltage of 7 V across the load resistance RL for 1000Ω ≤ RL ≤ 1500Ω. 113

Clemson ECE Laboratories Specifications • Voltage across RL(load resistor), VL=7 V • 1000Ω ≤ RL ≤ 1500Ω • Supply Voltage, VS=10 V 114

Clemson ECE Laboratories Functional Requirements • Use two resistors R 1 and R 2 between VS and RL in a Voltage divider network. • Select R 1 and R 2 to obtain no more than +5% variation about 7 V as RL ranges from 1000Ω to 1500Ω. • How would your design vary if the required VL specification of 7 V+5% was modified to 7 V± 5%? 115

Clemson ECE Laboratories Equipment Needed • • • NI-ELVIS workstation R 1=? (You specify) R 2=? (You specify) 1000Ω ≤ RL ≤ 1500Ω (I’ll specify) Make sure that the values of R 1 and R 2 are standard resistors (and not arbitrary resistors) as given in the table on the next slide. 116

Clemson ECE Laboratories Standard Resistor Values 117

Clemson ECE Laboratories Procedure • You Specify 118

Clemson ECE Laboratories Lab 11 -Student Tasks • Students are required to submit a lab report on this experiment. • Students MUST strictly adhere to the format as described in the lab manual. • For the ‘Questions’ section of the lab report, the students are required to solve the problems given as a part of ‘Probing Further’ section of this lab in the manual. • Your report is due in TWO WEEKS from today. 119

Clemson ECE Laboratories Preparations for Next Week • Review the material in the textbook on RC and RL circuits. • Before coming to the lab, determine theoretical time constants of the circuits used in the lab. • Be sure to account for the 150Ω output impedance of the function generator in your calculations. 120

Clemson ECE Laboratories References • ECE 211 – Electrical Engineering Lab I. Latest Revised July 2010. • http: //ecee. colorado. edu/~mcclurel/resistorsandcaps. pdf 121