Lab Experiments 11 and 12:

DC Power Supplies

Bo Bayles

Department of Electrical and Computer Engineering

University of Missouri-Rolla

Abstract

Alternating Current (AC) is typically used to distribute electricity from power companies to consumers. An AC signal alternates cyclically between maximum and minimum values, and is therefore sinusoidal. This contrasts with Direct Current (DC), which stays at a constant value over time.

In the U.S., AC is typically supplied at 120 volts at 60 Hz. Many consumer devices, however, require a DC supply at a different voltage. A power supply that converts an AC input to a DC output at a specified voltage is called an AC adapter.

Using components and tools from the lab, DC power supplies were designed, constructed, and comparatively tested. The tests showed that more sophisticated circuit designs with a voltage-regulating Zener diode and bridge rectifier outperformed simpler designs with voltage-limiting resistances.

Contents

Introduction

An AC adapter is a device used to convert an alternating (AC) input to a constant (DC) output. There are a number of possible realizations of this function. By using relationships between capacitance, current, power, and voltage, DC power supplies were designed, constructed, and tested in the lab. The goal for these power supplies was to convert a conventional 120 V 60 Hz AC supply from a wall outlet to a 9.1 V DC supply for a range of loads.

Background and Theory

Alternating and Direct Current

Power companies distribute electricity as an AC signal. Normal wall outlets in the U.S. deliver a 120 V signal at 60 Hz. This means that the voltage waveform is sinusoidal, alternating between +120 volts and -120 volts (RMS) 60 times per second.

AC is convenient for the distribution of electricity, but many consumer devices require a non-alternating (i.e. DC) power supply at lower voltages. A DC power supply that converts an AC input to a DC output is an AC adapter.

A simple AC adapter starts with an AC source such as a wall outlet. This is the first stage of the adapter. The next stage uses a "transformer" to raise or lower the input voltage to a desired value. The third and fourth stages use a "rectifier" and "filter" to remove the alternating part of the signal and output a nearly constant voltage.

Transformers

A transformer is a device that is used to change the voltage of an AC signal. Transformers generally consist of a ferrous "core" surrounded by coils of wire. Due to magnetic induction, a current flowing through a coil on one side of the transformer causes a current to flow on the other side of the transformer. The ratio between the number of coils on each side determines the voltage between each side. A "step down" transformer produces a smaller output; a "step up" transformer produces a larger one. The symbol for a transformer is shown in Figure 1.

Diodes and Bridge Rectifiers

A diode is a device that restricts a current waveform to one "direction." When a diode is connected one way, a "forward biased" signal sees the diode as a closed circuit. When the diode is connected the other way, the signal is "reverse biased," and treats the diode as an open circuit. Diodes are used to form the "rectifier" part of the DC power supply. The symbol for a diode is in Figure 2. The arrow indicates the direction in which conventional current flows.

In the first set of DC power supply designs, a single diode was used as a rectifier. When a single diode is connected to a sinusoidal source, only the "forward biased" part of the input waveform (the positive part) will flow through. For this reason, a single diode rectifier is called a "half-wave" rectifier.

In the second set of designs, a four-diode "bridge rectifier" was used. This "bridge rectifier" is also called a "full wave" rectifier - the signal it passes is positive for the full wave. In the arrangement used in the DC power supply designs, current flows through the top-right diode, and has a return path through the bottom-left diode. The symbol for a bridge rectifier is in Figure 3.

Capacitors

A capacitor is a device that stores charge. Capacitors are constructed by placing a non-conducting material (a "dielectric") between two conductors. When connected to a circuit, a capacitor will store a charge and develop a voltage across its terminals. When it reaches its charge capacity, it will act as an open circuit until there is a change in the current flowing through the circuit. At that point, the capacitor discharges at an exponential rate. Because the capacitor's discharge offsets a changing signal, capacitors are used to "smooth out" changes in waveform. A capacitor forms the "filter" part of a DC power supply.

When connected in parallel with a rectified sinusoidal signal, a capacitor smooths out the wave to form a "ripple" wave. After the peak of the sine wave, the capacitor discharges while the sine wave decreases and increases, and then recharges until the next cycle begins.

Zener Diodes

A Zener diode is a special type of diode that makes use of the "Zener effect" to hold the voltage across it constant for a specified range of currents. In the second set of DC power supply designs tested, a Zener diode was used to regulate the voltage across the connected load. As the graph of current vs. voltage in Figure 4 shows, voltage across a Zener diode is constant for current values in a certain range.

Procedure, Results, and Calculations

The exploration of DC power supplies was conducted in two parts. The first set of designs used a basic design and components in construction. The second set of designs used more advanced components to improve the performance. The goal for these power supplies was to supply a 9.1 V DC signal to a variety of loads.

Equipment

The equipment used during this experiment included:

• Variable resistance decade box

• Agilent oscilloscope with 10:1 probe

• Various capacitors, diodes, resistors, and wires

• Solderless breadboard

Part 1 - Basic DC Power Supply

1) The transformer was plugged into the wall. The transformer's leads were connected to the oscilloscope with the 10:1 probe. The output of the oscilloscope appears in Figure 5.

This output shows the action of the transformer. It is delivering a the sinusoidal signal it receives from the wall outlet, but is stepping down the voltage to 41.3 V peak-to-peak. The average value of this wave is very nearly zero (0.410 V) because the sign function alternates evenly between negative and positive values.

Next, the circuit in Figure 6 was constructed on the breadboard by connecting a 2 kW load resistance (R_L) and a diode to serve as a rectifier. This load resistance was constructed by wiring two 1 kW resistors in series. The voltage signal across R_L, shown in Figure 7, was observed with the oscilloscope.

This output shows how the diode acts as a half-wave rectifier. The "reverse-biased" (negative) portion of the signal is stopped by the diode, so only the positive part of the signal remains.

2) The circuit in Figure 8 was constructed by adding a 10 mF capacitor (C) to the previous circuit. The voltage across the capacitor was viewed with the oscilloscope. Its output appears in Figure 9 below.

This output shows the "ripple" effect the capacitor creates. The capacitor smooths out the changes in voltage quite dramatically compared to the previous circuit. This helps deliver a constant voltage to a load.

The average and peak-to-peak voltage measurements for the load resistance by itself, the load resistance with the diode, and the load resistance with the diode and capacitor appear in Table 1.

Table 1: Average and Peak-to-Peak Voltages

To limit the amount of voltage across the load resistor to 9.1 V, a series resistance (R_S) was necessary. Using the voltage-division relationship, the equation (R_S+R_L)/R_L = V_c/9.1 was solved for R_S, where R_L was 2 kW and V_c was the average voltage measured across the capacitor in the last step. The calculated value was 1.160 kW.

To construct R_S, a 1 kW resistor and two 100 W resistors were connected in series for a total of 1.2 kW. R_S was added to the previous circuit as in Figure 10.

The new voltage across R_L was observed with the oscilloscope. The output appears in Figure 11.

This output shows that the series resistor limits the voltage across the load's terminals. The average voltage observed was higher than expected - 9.933 V compared to 9.1 V. This difference can be attributed to the difference between the calculated series resistance (1.16 kW ) and the one used (1.2 kW ), and the difference between the nominal and actual values of the resistors used.

3) To test the range of loads for which the constructed power supply delivers a desired voltage, R_L was replaced with a decade box. Load values from 100 W to 100 kW were tested and the voltage across the load measured. The measurements appear below in Table 2. A plot of load voltage vs. load resistance appears in Figure 12.

Table 2: Load voltage vs. load resistance

The plot of the voltage due to different load resistances shows that as the load resistance increased, the voltage supplied increase. This increase seems to asymptotically approach the peak-to-peak voltage of the half-rectified wave observed in the first step. This plot also shows that the power supply is not reliable for loads other than its "native" load of 2 kW. This is to be expected - the 2 kW resistance was used to calculate the voltage-limiting series resistance.

4) Finally, the values of the resistors used for the series and load resistances were measured. These measurements appear in Table 3 below.

RL1	990.6 W
RL2	997.7 W
Total	1.985 kW
RS1	991.3 W
RS2	100.49 W
RS3	99.92 W
Total	1.191 kW

Table 3: Measured resistance values

Part 2 - Improved DC Power Supply

1) To improve the performance of the DC power supply, the circuit design was modified to use a diode bridge to make a full-wave rectifier. The circuit in Figure 13 was constructed. The voltage across the load resistor was observed with the oscilloscope. This output appears in Figure 14.

This output shows that the action of the full-wave rectifier. It should be noted that the average voltage for this wave, 12.080 V, is very nearly twice that of the half-rectified wave from Part 1. This is consistent with theory - the wave that is positive for twice as long should have twice the average value. The peak-to-peak voltage, 19.7 V, is close to the peak-to-peak voltage from before - this is also expected; both waves have a minimum at 0 and a maximum at around 20 V.

2) As in the previous designs, a 10 mF capacitor was added as a filter to smooth out the output signal. The circuit in Figure 15 was constructed. The voltage across the capacitor was observed with the oscilloscope. Its output is shown in Figure 16.

As with the previous design, this wave shows the "ripple" effect the capacitor has when filtering the rectified sine wave. Superimposing this wave on the fully-rectified wave shows how the capacitor discharges after the sine wave peaks, as in Figure 17.

Again, a series resistance (R_S) was needed to limit the supplied voltage to the desired value of 9.1 V. This series resistance was calculated to be 1.745 kW using the same formula as Part 1. The resistance was constructed by wiring a 1 kW resistor, three 220 W resistors, and one 100 W resistor in series for a total of 1.760 kW.

The voltage across the 2 kW load was observed with the oscilloscope. Its output is shown in Figure 18.

This plot shows that the filter and full-wave rectifier combination produce a signal that does not vary as much compared to the filter and half-wave rectifier combination (See Figure 11).

The supplied voltage (9.46 V) is somewhat above the desired one of 9.1 V. This result is likely due to the differences between the nominal and actual resistances of the resistors used, and the difference between the calculated series resistance and the one made from the available components.

3) To measure the change in supplied voltage as a result of varying the load resistance, the load resistor was replaced with a decade box. Voltage across the load for resistance values from 100 W to 100 kW were taken. The results appear in Table 4 below.

Table 4: Load voltage vs. Load Resistance

As with the first set of designs, the supplied voltage increased toward the peak-to-peak value of the rectified wave as the load resistance increased. This design only performs well for its "native" load of 2 kW, like its predecessor.

4) Before adding a Zener diode to the circuit, a suitable series resistance was calculated. This resistance was added to protect the Zener diode - the component was rated for 0.5 watts, but to be safe, the calculation was made to limit the amount of power dissipated by it to 0.25 watts. The formula V_z * I_z-max = 0.25 watts was solved for I_z-max, where V_z was 9.1 V. Then, the voltage divider relationship was used to calculate R_s using the formula (V_c - V_z) / I_z-max. The result was 289 W.

5) A Zener diode and the series resistance were added to the circuit in parallel with the load resistance and capacitor, as in Figure 19. The series resistance was constructed by wiring three 100 W resistors in series.

6) The voltage across the load terminals was measured for a number of decade box resistance values. The following observations were made:

• With the decade box disconnected (i.e. R_L at infinite resistance), the voltage supplied was 9.19 V.

• With the decade box set from 100 kW to 2 kW, the voltage supplied was also 9.19 V.

• Under 2 kW, noticeably at 1.5 kW, the voltage supplied dropped to 9.09 V.

These results show that the Zener diode improved the performance of the DC power supply. When enough resistance is present to divide the current between the parallel branches at values within the Zener diode's voltage regulation range (i.e. between its I_z-min and I_z-max values), voltage across the diode and load are pegged to 9.1 V. At low load resistances, more current flows through the series resistance, and moves the Zener diode out of its useful range.

When viewed with the oscilloscope, the voltage waveform across the load resistance (for values about 1.5kW,) appeared to be a straight line, or almost a constant value. This is a desirable result - a DC signal maintains a constant value, so this shows that the DC power supply is performing its function.

Conclusions

The first set of AC adapter/ DC power supply designs tested "stepped down" an AC source voltage, "rectified" half of the AC waveform, "filtered" the resultant wave, and then supplied a smaller voltage to a load. Because of the way these designs were constructed, the voltage supplied across the load terminals varied greatly with the resistance of the load. This shows that these designs are not very practical - a practical adapter would supply a desired voltage to a wide range of loads; an incorrect voltage can damage a load.

The second set of designs showed that the addition of a Zener diode could greatly improve the useful range power supply circuit. These designs also showed how a full-wave rectifier could supply a less-variable (i.e. more nearly DC) signal to a load. This type of design, with its effective voltage-regulation properties, could be used as the basis for a practical real-world DC power supply.

Acknowledgments

The preceding experiments were conducted by Bo Bayles and Bryan Brenner.

References

1. "Experiment 11 - Basic DC Power Supply." University of Missouri-Rolla Electrical and

Computer Engineering Department. 25 Sept 2005. <http://ece.umr.edu/files/circuitslab11.pdf>

2. "Experiment 12 - Improved DC Power Supply." University of Missouri-Rolla Electrical and

Computer Engineering Department. 25 Sept 2005. <http://ece.umr.edu/files/circuitslab12.pdf>