Çhad Ostrowski
Partner: Mike Sobotka
E E 310.5
Lab 3 Formal Report
12 February 2008
Introduction
Power supplies are sometimes viewed as an afterthought in a complex electronic product or system. Circuit designers often take them for granted, or don’t want to bother with such ―low-tech‖ circuitry when there are more glamorous and exciting design tasks to occupy their time. But according to studies performed by the Navy, a very significant fraction of all electronic equipment failures are power supply related. The root cause of most of these failures, surprisingly, is not due to manufacturing defects or bad components, but rather to poor design. In 1982 they undertook to change this, publishing NAVMAT P4855-1, essentially a how-to book on designing reliable, state-of-the-art power supplies. The results were dramatic. Engineers designing power supplies and following the design recommendations of this document, which includes derating, were able to achieve an 8- fold increase in the reliability of their power supplies, from 50,000 hours to over 400,000 hours.1
In this lab we construct a power supply that converts 120Vrms at 60Hz to a DC signal of 15V for use in powering a load. All of the specifications of the various components are chosen so that they can withstand the loading conditions.
Circuit Design and Reasoning, as well as Some Results
Figure 1: basic layout of the power supply
As seen in figure 1 above, the power supply will simply plug into any wall in the U.S. and then a power transformer will get the voltage down to a more agreeable level. Then a rectifier will make the voltage all positive and a capacitor will make it more level. Then the voltage will drop over a voltage-limiting resistor inside the voltage regulator box and Zener diodes will be used to regulate the voltage. We then compare the results with the Zener diode to that obtained with a commercially available voltage regulator.
Figure 2: close-up of the transformer
In figure 2, a schematic of the transformer is seen. The voltage measured across terminals A-C was 20.79Vrms, that across terminals A-B and B-C were each 10.38Vrms. We need to use terminals A-C, then, so a bridge rectifier will be best. This is gone into below. Before hooking that up, though, we need to determine the inherent resistance of the transformer. Using the open readings and then hooking up a resistor designed to dissipate 1W (P=1W=V2/R=>R=432ohm, and the closest we could get was 424ohm, rated at 2W, which is quite safe) we found that Rw=20.79*424/2/20.45*(1-20.45/20.79) = 3.52ohm.
Figure 3: bridge rectifier
a bridge rectifier is seen above, where the output current is said to be “DC”. This is obviously not true: after passing through our rectifier circuit, our voltage looked like Figure 4:
Figure 4: output voltage of bridge rectifier circuit
The diodes we used were each rated at 60V PIV, when the maximum we expect is 20.8*sqrt(2)=29.4V, we are well within the allowed range. Now that the current has been rectified, the next step towards making it DC is to pass it through a capacitor.
The required capacitance is given by C=VM /(f*RL *Vr ) = 1/(f * VM *Vr ) = 1/(120 * 27 * 4.05) = 76.2microF. The closest cap available to this is 100microF.
Here we pause and take some measurements before constructing the Zener diode rectifier. We find:
Vo via DMM = 25.0Vrms.
Vo via Oscope = 25.0Vrms, VM = 26.4V, VL = 23.8V, Vr = 2.60V Figure 5 below shows this
Figure 5: output of power-supply-minus-Zener-diode-voltage-regulator with some measurements
Comparing this to the output of the transformer with the same settings, we can see what a drastic change these two circuit elements created. The output of the transformer can be seen in figure 6.
Figure 6: transformer secondary voltage before being rectified.
Next we measured and plotted the current through one of the diodes by inserting a 1-ohm resistor (rated at 5W, which is more than safe) in series with it and using the oscilloscope to measure the voltage drop across it. The result can be seen in figure 7. The current was determined to be 226mA with this measurement. However, when calculating it, we found that ID,Max = VM/RL*(1+2*pi*(VM/2/VR)^0.5) = 944mA.
Figure 7: current through one of the rectifier diodes.
With all of these measurements looking good, it’s time to press on to the Zener diode voltage regulator!
We use a 1N4742 in series with a 1N4728 to get close to the desired voltage drop of 15, ending up instead at a close and acceptable 15.3V. With no load, PZ = 0.5 => IZ=PZ /VZ = 0.5/15.3=32.67mA.
According to the data sheet, RZ for the two diodes in series is 19ohm. So, using all of this to find the limiting resistor, we find that V=IR=> VC – VZ = 32.67(Rlimiting + 19ohm) =>
Rlimiting = (24.95-15.3)/32.67 – 19 = 276ohm.
IZ,Min = .3*IZ,Max = 9.8mA
So IZ,Min = Itot *(RL / (RL+RZ) ) solving, we find that RL = 7.61ohm. Not finding these available, we instead use two 16ohm resistors, each rated at five watts, in parallel to achieve an equivalent resistance of 8ohm.
Hooking all of this up and taking some measurements, we find the %Regulation to be:
%Regulation = (VL(no load) – VL(full load) )/VL(no load) * 100% = (12.7 – 12.5)/12.7 *100% = 1.57%
Next, we graphed the voltage across the capacitor and the voltage across the voltage regulator on the same graph with the same resolution, obtaining figure 8.
Figure 8: ripple voltage across capacitor compared to ripple voltage across regulator Zener diode with relevant measurements.
As can be seen in the figure, the voltage regulator Zener diode reduces the ripple significantly, from 2.4V to 1.4V, which is a factor of 0.58. (This can also be calculated using Multisim, though doing the computations on paper lead to a belief that there will be no ripple at all over the voltage regulator.)
So our approximate total circuit looks like Figure 9.
Figure 9: total circuit schematic
After running these tests with our Zener diode regulator, we decided to set up the same circuit with a commercially available voltage regulator out of curiosity. We used a 7815A IC between the limiting resistor and the load resistor. With this, we found that the %Regulation was
%Regulation = (VL(no load) – VL(full load) )/VL(no load)*100% = (15.31-15.30)/15.31 *100% = .065%
Which is, of course, better than we could do with our Zener diode.
The voltage across our load, “ripple” and all, can be seen in figure 10. Both this output and the voltage across the capacitor can be compared in figure 11, which can also be compared to Figure 8, which was as good as we could get with a Zener diode regulator.
Figure 10: DC and AC components of the output across our load when using the IC voltage regulator.
Figure 11: ripple voltage across capacitor compared to ripple voltage across IC voltage regulator. Compare to figure 8.
Discussion:
As noted in the introduction, power supplies are an essential part of electronic systems design, though often engineers overlook it in pursuit of more glamorous design projects. A crucial aspect of this design is to calculate the power specifications of each of the components in the supply to make sure they can withstand minor voltage fluctuations, power surges, accidental short circuits, etc. As we worked through this lab, we were careful to ensure that all of these specifications were met.
Many of our outputs did not quite match up with our desired outputs exactly. This is due to nonideal wires & components, as well as the general nature of breadboards: a whole lot of capacitance and inductance arises in all of the extra wire we have everywhere.
Conclusion:
Power supplies are muy importante. Obviously, the fully-trained people that make IC voltage regulators do a much better job than we can do with a low-tech Zener diode. However, we were able to obtain pretty good results just with our original voltage regulator. I wouldn’t actually want to power a computer or a cell phone with our supply, but these are the first steps towards the power supplies that are attached to the chords of chargers for such devices. As noted in the introduction, a well-designed power supply can increase the live of a device from 5.7 years to 45.6, which is nothing for an engineer to turn up their nose at. Power supplies need to be well-planned.