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					        LABORATORY EXERCISE 2

    Diodes and Half-wave Rectifiers

                    EE3401


                From: Jordan Hall


             To: Dr. Wesley Hartburg


                For: 10/17/2011


    SOUTHERN POLYTECHNIC STATE UNIVERSITY


DIVISION OF ENGINEERING – ELECTRICAL ENGINEERING
                                                                                                                                              Jordan Hall




Table of Contents



DESCRIPTION................................................................................................................................................. 2

PRE-LAB ASSIGNMENT .................................................................................................................................. 3

CALCULATIONS .............................................................................................................................................. 7

MEASUREMENTS......................................................................................................................................... 10

SIMULATIONS .............................................................................................................................................. 14

CONCLUSION............................................................................................................................................... 19

APPENDIX A ................................................................................................................................................. 20

APPENDIX B ................................................................................................................................................. 22




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DESCRIPTION

The primary purpose of this laboratory exercise was to analyze the function of the rectifying diode in a

simple DC circuit and two different rectifier circuits. The basic analysis involved calculating and

measuring the current through a 1N4007 rectifying diode in a DC circuit as the voltage across the diode

was increased. The second portion of the lab required the waveform analysis of a rectification circuit as

an alternating current was provided from the secondary windings of a step-down transformer to a

rectifying circuit using a 1N4007 diode, a configuration of resistors, and ultimately a filtering capacitor.

In the pre-lab exercise, the aforementioned analysis was conducted theoretically; the values were

calculated, and the waveforms were sketched based upon fundamental circuit and electronics theory.

These same values and waveforms were then attempted to be duplicated in practicality in the

electronics lab.


The tools/components utilized in this lab consisted of the following:


       Digital multimeter

       Oscilloscope

       Jameco ACU120100 AC/DC adaptor/transformer

       DC power supply

       Cables with banana plugs/probes/alligator clips

       Variety of resistors

       1N4007 rectifier diode

       TI 89

       pSpice




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PRE-LAB ASSIGNMENT

The Pre-Lab assignment initially involved the calculation of the diode current based on the provided

values for the voltage across the standard pn diode and the given diode equation. The diode voltage

ranged from 0V – 0.7V. The diode current was then plotted versus this diode voltage (using Excel) with

100 data points to obtain the desired resolution of the data plot. The voltage was plotted on the x-axis

and the current was plotted on the y-axis; the result resembled the forward-biased characteristic curve

of the diodes turn-on voltage range between 0.5V and 0.7V.


Next, two rectifier circuit schematics were given, and the output voltages were calculated and

represented in a variety of ways. The waveforms were sketched to show the negative half-cycles were

lost, and the peak value, rms value, dc average, and ripple of the output voltages were also calculated.

The difference between the two rectifier circuits was that the second one had a filter capacitor and the

first one did not. The resulting waveform due to the filter capacitor provided a higher DC average with a

smaller ripple factor. The fundamental concept of an AC to DC adapter was thus theoretically derived.


The following results were obtained:




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    1.




    2.


                                             Diode Characteristic Curve
                       0.016

                       0.014

                       0.012
Diode Current Id (A)




                       0.010

                       0.008

                       0.006

                       0.004

                       0.002

                       0.000
                               0.00   0.10     0.20   0.30       0.40     0.50   0.60   0.70     0.80
                                                        Diode Voltage Vd (V)




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3.




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4.




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CALCULATIONS

As mentioned before, the pre-lab consisted of the theoretical analysis where the diode current was

calculated with respect to the varying voltage across the diode, and the output voltages of the rectifier

circuits were calculated and sketched. The practical lab was conducted to obtain the related measured

data to compare the experimental results to the theoretical results. The main purpose is to determine

the accuracy of the actual lab results versus the theoretical results, or rather, to calculate the error

involved due to various reasons. Error can results from human inconsistencies, equipment

limitations/incompetence, and misrepresented independent variables.


The formula used for calculating percent error is:                               x 100%


                                          Table 1 – Percent Error


                               Id (calculated)     Id (Measured)     % error
                                       0.00E+00           0.00E+00     0.00%
                                       7.50E-07           1.25E-07    83.33%
                                       3.90E-05           2.65E-05    32.10%
                                       2.79E-04           2.85E-04     2.19%
                                       7.46E-04           6.84E-04     8.35%
                                       1.99E-03           2.76E-03    38.55%
                                       5.02E+01           7.14E-03    99.99%
                                       1.42E-02           2.03E-02    42.66%



Sample calculation:




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The diode DC resistance was calculated to be:




The rectifier circuits required the calculation of the inductances (or inductance ratio) to allow simulation

in pSpice. In pSpice, inductance coupling simulates the behavior of a transformer. First, the peak

voltages had to be calculated:




Next, the turns ratio was computed based on the primary and secondary voltages:




An arbitrary inductance was chosen, L1 = 10mH, for the primary winding inductance because no value

was given or could be determined from the Jameco AC/DC adaptor.


The secondary winding inductance L2 could then be calculated like the following:




Now, all values are provided to successfully simulate both rectification circuits using pSpice.


The last calculation made for the lab was the RMS ripple voltage of the ‘saw-tooth’ waveform produced

by the capacitor-filtered rectifier circuit:




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The results of the half-wave rectifier circuits are compared to what was calculated in the pre-lab to find

the percent error:


Unfiltered:


Vi peak = 19.8V theoretical and 21V actual 


Vo peak = 19.1V theoretical and 20.3V actual 


VDC average = 6.30V theoretical and 6.27V actual 


VRMS = 9.55V theoretical and 10.09V actual 


The percent error is relatively low and means that the pre-lab and lab were conducted successfully.


Filtered:


Vi peak = 19.8V theoretical and 21V actual 


Vo peak = 19.1V theoretical and 20.3V actual 


VDC average = 19.05V theoretical and 19.3V actual 


VR = 1.49V theoretical and 1.26V actual 


The percent error is relatively low and means that the pre-lab and lab were conducted successfully. The

22.2% is still low considering the small magnitude of the values being compared.




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MEASUREMENTS
The 1N4007 rectifying diode was measured to have a 0.551V turn-on voltage with the diode-check-

mode setting on the DMM. The forward-biased resistance of the diode measured 36kΩ, and the reverse-

biased resistance measured to be 1.41 MΩ.


Table 2 lists the measured values obtained when the schematic in Figure 0 (in the lab instructions) was

constructed, powered and measured. The voltage across the diode was varied to match the given

values, and the input voltage from the DC power supply was measured using the oscilloscope. The DMM

was set to measure current, the circuit was broken to incorporate the DMM into the circuit in series,

and the diode current was measured.


                              Table 2 – Measured diode current vs. voltage

                                  Vi          Vd          Id (Measured)
                                          0           0         0.00E+00
                                        0.2         0.2         1.25E-07
                                       0.41         0.4         2.65E-05
                                       0.66         0.5         2.85E-04
                                       0.88        0.55         6.84E-04
                                       1.47         0.6         2.76E-03
                                       2.82        0.65         7.14E-03
                                       7.34         0.7         2.03E-02



Like in the pre-lab, the current of the diode was plotted versus the voltage of the diode, but the data

used was the actual data obtained in the lab. This plot is available in Fig. 1. The plot resembles that of

the characteristic curve of the forward-biased operation of the diode, and it closely resembles the plot

in the pre-lab assignment. The turn-on voltage appears to be between the 0.5V and 0.7V range.




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                                    2.50E-02

                                    2.00E-02



                Diode Current (A)
                                    1.50E-02

                                    1.00E-02

                                    5.00E-03

                                    0.00E+00
                                                0     0.1    0.2     0.3    0.4    0.5    0.6    0.7   0.8
                                    -5.00E-03
                                                                     Diode Voltage (V)



                                                Fig. 1 – Diode i-v curve from measured results



The rectification circuit in Figure 1 (from the lab instructions) was constructed using the Jameco

ACU120100 AC/DC adaptor/transformer and the same 1N4007 rectifying diode, and the input voltage

waveform of the stepped-down voltage was displayed on the oscilloscope as seen in Fig. 2.




                                       Fig. 2 – Unfiltered rectifier circuit input voltage waveform

                                        Note: the waveform sketches are available in APPENDIX B

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The peak-to-peak voltage was measured at 42V which gave an amplitude (or peak voltage) of 21V and

occurred at a 60Hz frequency. One full cycle took 16.67ms.


The output voltage in Fig. 3 was displayed on the oscilloscope when the voltage was measured after the

diode rectification at the load resistor (4.7kΩ). The peak voltage was measured to be similar to the input

waveform (and only the positive half-cycles remained). The peak voltage measured to be 20.3V for the

unfiltered, rectified waveform. The oscilloscope also provided the DC average voltage of 6.27V and an

RMS voltage of 10.09V.




                       Fig. 3 – Unfiltered rectifier circuit output voltage waveform



When the 47μF capacitor was added in parallel to the load resistor, the output voltage waveform was

filtered and is seen in Fig. 4. The waveform of the output voltage still had a 20.3V peak relative to the

reference voltage (0V line), but the peak-to-peak (or ripple voltage) was measured to be 1.26V. This



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provided a 19.3V DC average and is congruous with the fundamental principles of diode AC/DC

adaptors. The small ripple voltage of the ‘saw-tooth’ waveform only had an RMS value of 1.09V.




                  Fig. 4 – capacitor-filtered rectifier circuit output voltage waveform

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                                                                    Jordan Hall


SIMULATIONS

From: http://www.cadence.com

Schematic 1 – (Figure 0 in lab instructions)




Simulation 1.1 – (Figure 0 in lab instructions)

DC sweep from the input voltages measured in the lab (0V – 7.34V)




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Schematic 2 – (Figure 1 in lab instructions)




Simulation 2.1 – (Figure 1 in lab instructions)

Primary voltage in the Jameco AC/DC adaptor(169V peak)




Simulation 2.2 – (Figure 1 in lab instructions)

Secondary voltage in the Jameco AC/DC adaptor(19.8V peak)




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Simulation 2.3 – (Figure 1 in lab instructions)

Output voltage measured across the load resistor (RL) (17.9V)




Schematic 3 – (Figure 2 in lab instructions)




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Simulation 2.1 – (Figure 2 in lab instructions)

Primary voltage in the Jameco AC/DC adaptor (169V)




Simulation 2.2 – (Figure 2 in lab instructions)

Secondary voltage in the Jameco AC/DC adaptor (19.8V)




Simulation 2.3 – (Figure 2 in lab instructions)

Output voltage measured across the load resistor (RL) (17.9V)




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CONCLUSION
This laboratory assignment was relatively straightforward, but the fundamental principles of the

rectification circuit were reinforced. The concept of converting an AC voltage signal to a DC voltage

signal incorporates the behavior of a standard pn diode and a filter capacitor to reduce the voltage

ripple as much as possible. Perhaps, if a larger capacitance was used, the voltage ripple would be even

smaller since the discharging time would be increased and the ‘saw-tooth’ signal would have a smaller

peak-to-peak value. DC rectifiers are a $10 billion industry, and understanding the underlying theory is

critical in the application of many every-day electronic devices and appliances.




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APPENDIX A

Resistor color code chart used:




http://www.elexp.com




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http://www.fairchildsemi.com/ds/1N%2F1N4001.pdf




APPENDIX B




http://info-afric.net/27/tips-for-online-movies-for-free-and-strategies-on-
how-to-improve-your-house/




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http://levier-dev.com/31/simple-download-instantly-tips-for-being-your-own-
handyman-or-handywoman/




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