Power Supply Construction Project

Electrical Engineering 310

Section 002

Shawn R Moser

2

Introduction:

In this lab, my partner and I have been tasked with constructing a power-supply circuit that takes the AC

voltage from the wall input (120 Vac, 60 Hz) and outputs a regulated DC voltage that meets with

specifications given to our group at the beginning of design. In this circuit, we plan on building a standard

unregulated power supply circuit and attach it to an IC voltage-regulator. At the output of the unregulated

supply we hope to achieve a nominal value of -12 volts to ensure that the voltage regulator continually

outputs a nominal value of -5 V. The circuit must maintain a variance below 15% in the ripple voltage

output of the unregulated power supply. This requirement will be met by using the minimally-valued

filter capacitor in the unregulated, supply circuit. This unregulated supply will then be attached to two

different kinds of voltage regulators: a Shunt regulator that requires the usage of a Zener diode, and an

integrated circuit (IC) voltage regulator. With each individual regulator connected to the unregulated

supply, we will have a complete AC-to-DC power supply which we will test by connecting to a rated load

resistance of 1 W. In order to meet specifications, we will ensure that this complete power supply will

output a steady DC voltage of -5V with a maximum variance of 0.5 V.

Circuit Design and Reasoning:

To meet the specifications set forth in our initial design, my partner and I determined to use a full-wave,

center-tapped rectifier circuit in order to rectify the sinusoidal input wave to a purely-negative voltage

signal. We choose this configuration, instead of the bridge rectifier, as its output voltage most nearly

meets the nominal -12 V that we require at the regulator input. In addition, this rectifier will not reduce

the signal by the same amount as a bridge rectifier; this is because in the full-wave rectifier that we use

the voltage only passes through single series of diodes and not two, as would be the case in the four-diode

bridge rectifier circuit. This reduces the voltage drop of the signal across the rectifier from 2 Vγ to Vγ. The

values that we have used for the filter capacitor and test load-resistance were determined theoretically,

and then substituted with nearest practical values.

Schematic 3.1: Unregulated Power Supply

With the unregulated power supply designed, we next designed a practical Shunt regulator, to output a

nominal voltage of -5 V. The circuit we use requires a single Zener diode, to cut-in when the load-voltage

drops below a relative value. In order to do this, we insert a resistance to help condition the input current

to the regulator. This resistance, along with the resistance of the load we test the circuit with, are

determined in the next section.

D1

1N4004G

D2

1N4004G Creg

470µF

Input

169.71 Vpk 60 Hz 0°

T2

12:1:1

Rl

172.3Ω

3

Schematic 3.2: Shunt Voltage Regulator

While the Shunt regulator will provide the power supply with decent output regulation, we ultimately use

a IC voltage regulator. The input of the above voltage regulator circuit is the output of the unregulated

power-supply design without the terminating 172.3 Ω load. This signal, which we hope to keep at about -

12 V, is sent into the first terminal of the packaged IC. The common terminal is connected to the ground.

The final terminal of the IC is the output, which should be regulated to maintain a value close to -5 V

across a range of loads.

Schematic 3.3: IC Voltage Regulator

Supporting Analysis:

First, we modeled the transformer in the power-supply as the circuit shown in Schematic 3.5. The

resistances Rw1 and Rw2 model the internal resistance of the outputs of the transformer. The center tap of

the transformer is connected directly to ground to represent its relative voltage level in the power supply.

Since this resistance in negligible, we ignored it in our calculations for the output voltage of the device.

We confirmed that this resistance will only have a minor impact in our calculations as connecting the

transformer to a load only caused a change in output voltage of 200 mV, which we found negligible in

further designs of the power supply.

In order to determine the internal lead resistance present we first find the resistor value that we can

connect across the A and C terminals of the transformer that would produce a power output of roughly 1

W. Using measurements of the transformers terminal voltage difference without a load, we find a test

resistor with the value of 428.49 Ω.

𝑅𝑇𝑒𝑠𝑡 = (20.7 𝑉)2

1 𝑊= 428.49 Ω

Dz

1N4732A

Ri

75.4Ω

RL

63.2Ω

Vi

+VL

-

+Vz

-

C2

0.33µF

C3

100nF

U2

LM7905CT

LINE VREG

COMMON

VOLTAGE

Vi Vo

4

After determining this resistance, we measured the voltage difference between an unloaded output VO and

a loaded output with RTest connected to the VO nodes. Using the value we measured, along with the loaded

output current, we were able to determine the internal resistance of the transformer leads and construct an

equivalent Thevenin-model of the circuit.

Schematic 3.4: Thevenin Equivalent of Center-Tapped Transformer

2𝑅𝑤 = 𝑅𝑇ℎ =𝑉𝑂𝐶 − 𝑉𝐿

𝐼𝐿=

20.7 𝑉 − 20.5 𝑉

52.3 𝑚𝐴= 3.82 Ω

𝑅𝑤 =3.82 Ω

2= 1.91 Ω

Schematic 3.5: Model Transformer w/Lead Resistance

After determining the model for our transformer, my partner and I determine the kind of diodes that we

would use in our full-wave rectifier. First, we determine the peak inverse voltage (PIV) of each of the

rectifier diodes, which will be equal to the peak input voltage of the transformer. With a PIV of roughly

14.28 V, we were able to use any of the following diodes provided to use: 1N4004, 1N4934, or 1N4935.

We decided upon using the 1N4004 diodes because they provided the largest possible PIV for the same

relative price.

Next, we remove the test resistor and connect the predetermined rectifier circuit that was selected for the

power-supply’s specifications. After connecting the rectification circuit, we then determined a filter-

capacitor and load resistor to finish the construction of the unregulated power-supply. To determine the

load, RL’, we assumed a load that would output 1 W of power when put across the average output voltage

of the filter capacitor. We find that a value of 177.42 Ω will fulfill these requirements, and we use a

resistor with a value of 172.3 Ω as our actual resistance.

V114.21 Vpk 60 Hz 0°

Rint

3.82Ω

+Vo

-

V114.28 Vpk 60 Hz 0°

V214.14 Vpk 60 Hz 0°

Rw1

1.91Ω

Rw2

1.91Ω

+Vo

-

Rtest

392.1Ω

5

𝑉𝑐 ≈ 𝑉𝑀 (𝑉𝑟

2) ≈ −14.4 𝑉 (

2.16 𝑉

2) ≈ −13.32 𝑉 𝑉𝑟 = .15𝑉𝑀 = .15|−14.4 𝑉| = 2.16 𝑉

𝑅𝐿′ =

𝑉𝑐2

1 𝑊=

(−13.32 𝑉)2

1 𝑊= 177.42 Ω

With the load for the unregulated supply determined, we then determined the capacitance necessary to

achieve a ripple voltage of a maximum variance of 15% of the nominal DC voltage rectifier’s output , as

specified in the our design requirements. With the help of an oscilloscope we determine that our

maximum output voltage from the rectifier is -14.4 V. Using this value as our nominal value, we

determine that we would hope to achieve a maximum ripple voltage of only 2.16 V.

𝐶 =|𝑉𝑀|

2𝑓𝑅𝐿𝑎𝑐𝑡𝑢𝑎𝑙𝑉𝑟=

14.4 𝑉

2(60 𝐻𝑧)(172.3 Ω)(2.16 𝑉)= 322 𝜇𝐹

We decide to use a capacitor of 470µF, as this is the closest capacitance value offered to us in the form of

electrolytic capacitors that is equal to or above our derived necessary capacitance.

Next, we determine the maximum current that will flow through each of the diodes used in the rectifier

circuit. We do this by applying the provided equation using the values of the output waveform of the

unregulated supply.

𝑖𝐷,𝑚𝑎𝑥 =𝑉𝑀

𝑅𝐿(1 + 2𝜋√

𝑉𝑀

2 𝑉𝑟) =

13.7 𝑉

172.3 Ω(1 + 2𝜋√

13.7 𝑉

2(2.0 𝑉)) = 1.04 𝐴

In order to further investigate the maximum diode current, we develop a Multisim simulation for the

diode current circuit. Attached at the end of the lab is a print out of the simulation circuit, along with the

oscilloscope capture from the Multisim lab. We will use these values, along with values measured via the

lab’s oscilloscope to determine the actual peak current through the rectifier diodes. From the plots from

this simulation, we observe that the maximum current through the diode is roughly the following:

𝑖𝑑𝑖𝑜𝑑𝑒 = 𝑣𝑑𝑖𝑜𝑑𝑒

𝑅=

817 𝑚𝑉

3.1 Ω= 263.5 𝑚𝐴

Next we determine the parameters for the Zener-diode voltage regulator. To determine this, we must

consider the manner in which the circuit works. First we analyze the range of voltage regulation we wish

to achieve. To meet the specifications of the design, we will use a 1N4732 Zener diode, which has a

Zener-voltage of 4.7 V. We assume that IZmax occurs when power dissipated by the diode is ½ W. This

information allows us to determine maximum and minimum current that will flow through the Zener

diode along with the resistances used in the regulator circuit (input resistance Ri and load RL).

𝐼𝑖 = 𝐼𝑍 + 𝐼𝐿 = 𝐼𝐿 = 0; 𝐼𝑍 = 𝐼𝑖 𝑁𝑜 𝑙𝑜𝑎𝑑

𝐼𝑍𝑚𝑖𝑛 = 𝐼𝑖 − 𝐼𝐿 𝐹𝑢𝑙𝑙 𝑙𝑜𝑎𝑑

𝐼𝑍𝑚𝑎𝑥 = 𝑃𝑍

𝑉𝑍=

0.5 𝑊

4.7 𝑉= 10.6 𝑚𝐴

𝐼𝑍𝑚𝑖𝑛 = .3𝐼𝑍𝑚𝑖𝑛 = .3(10.6 𝑚𝐴) = 3.18 𝑚𝐴

6

|𝑉𝐶| = 𝑅𝑖𝐼𝑖 + |𝑉𝑍| → 𝑅𝑖 =|𝑉𝑐| − |𝑉𝑍|

𝐼𝑖=

12.9 𝑉 − 4.7 𝑉

10.6 𝑚𝐴= 77.36 Ω

𝑅𝐿 =𝑉𝑍

𝐼𝑍𝑚𝑎𝑥 −. 3𝐼𝑍𝑚𝑎𝑥=

𝑉𝑍

. 7𝐼𝑍𝑚𝑎𝑥=

4.7 𝑉

. 7(10.5 𝑚𝐴)= 63.3 Ω

Due to time constraints and an inability to get an exact match in value, we use resistances of 75.4 Ω and

63.2 Ω for Ri and RL, respectively.

DATA:

The following is the values that we measured between the taps of the lab provided transformer. This

transformer is a 12:1 step-down, center-tapped, transformer. In addition we used a resistor that would

output roughly 1 watt when connected to the transformer to study the impact that a load would have on its

output voltage.

𝑣𝑎𝑏 = 10.1 𝑉𝑅𝑀𝑆 𝑣𝑏𝑐 = 10.1 𝑉𝑅𝑀𝑆 𝑣𝑎𝑐(𝑛𝑜 𝑙𝑜𝑎𝑑) = 20.7 𝑉𝑅𝑀𝑆

𝑅𝑇𝑒𝑠𝑡 = (20.7 𝑉)2

1 𝑊= 428.49 Ω 𝑣𝑎𝑐(𝑙𝑜𝑎𝑑) = 20.5 𝑉𝑅𝑀𝑆

To confirm these values, below is an oscilloscope capture displaying the waveform that was captured

from the transformer’s A-to-C taps. Please note that the Pk-Pk value is higher than the value of 20.7 VRMS

value that we measured.

Figure 3.1: Transformer Output

The signal displayed in Figure 3.1 represents the input signal that is received as the output of the 12:1:1

transformer, and is the input to the full-wave rectifier circuit that we implemented. In Figure 1.2, we see

the output of the full-wave rectifier. This is a rectified wave where the positive half of the input wave is

flipped to be a negative value.

7

Figure 3.2: Full-Wave Rectifier Output

𝑉𝑀 = −14.4 𝑉

The waveform in Figure 3.2 is the input into the filter-capacitor component of the power-supply where its

voltage is made to look more like a DC-value with a small ripple voltage. The output from the filter

capacitor circuit is displayed in Figure 3.3. We see that there is less variance in the signal than that of the

transformer’s secondary output seen in Figure 3.1.

Figure 3.3: Unregulated-Power-Supply Output

𝑉𝑀(𝐴𝑐𝑡𝑢𝑎𝑙) = −13.7 𝑉 𝑉𝐿(𝐴𝑐𝑡𝑢𝑎𝑙) = −11.7 𝑉

𝑉𝐶(𝐴𝑐𝑡𝑢𝑎𝑙) = −12.7 𝑉 𝑉𝑟(𝐴𝑐𝑡𝑢𝑎𝑙) = 2.00 𝑉

8

In Figure 3.4 we see the output voltage waveform for the diodes of the rectifier circuit. This plot is used

to estimate the maximum current that flows through each of the diodes during the circuit’s operation.

Using a resistance of a resistance 3.1Ω, the value determined in lab, we are able to deduce that the

maximum observed diode current is roughly 203.2 mV. This value is much smaller than the estimated

max diode current, and also less than the max diode current determined through the Multisim simulation.

𝑖𝐷,𝑚𝑎𝑥 =| − 630 𝑚𝑉|

3.1 Ω= 203.2 𝑚𝑉

Figure 3.4: Maximum Diode Current

Figure 3.5 displays the output from the Shunt regulator when there is no load attached to the regulator,

corresponding to when IZ is at its maximum value. The additional signal plotted, is the input voltage from

the filter capacitor. The voltage regulator noticeably reduces the ripple by a factor of 7. Note that the

capacitor ripple voltage appears to be much higher than previously measured. This is a result of the

change in load resistance when we remove the test load in previous design steps. In addition, this capture

does not display the average output voltage of the waveform, which is 4.52 V.

𝑅𝑖𝑝𝑝𝑙𝑒 𝑟𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛 =𝑉𝑟(𝑖𝑛𝑝𝑢𝑡)

𝑉𝑟(𝑜𝑢𝑡𝑝𝑢𝑡)=

2.24 𝑉

320 𝑚𝑉= 7

9

Figure 3.5: Shunt Regulator Output w/o Load

𝑉𝑟(𝑜𝑢𝑡𝑝𝑢𝑡) = 320 𝑚𝑉 𝑉𝑟(𝑖𝑛𝑝𝑢𝑡) = 2.24 𝑉

Figure 3.6 displays the output from the regulator when there is a load RL of 63.2 Ω attached to the

regulator. There is an increase in the voltage ripple when the load is applied.

Figure 3.6: Shunt Regulator Output w/ Load

𝑉𝑟(𝑜𝑢𝑡𝑝𝑢𝑡) = 340 𝑚𝑉

The next two plots are the output waveforms of the IC 7905 Regulator. Figure 3.7 is the output using this

regulator circuit without a load connected.

10

Figure 3.7: IC Regulator Output w/o Load

Figure 3.8 is the output of the IC regulator circuit, with a load of 46.1 Ω. This is the actual value of the

resistor we use to model a resistance with a load current equivalent to IZmax from the Shunt regulator.

𝑅𝐿 =𝑉𝐿

𝐼𝑍𝑚𝑎𝑥=

5 𝑉

10.6 𝑚𝐴= 47.2 Ω ≈ 46.1 Ω

Figure 3.8: IC Regulator Output w/ Load

Figure 3.9 is a comparison between the ripple voltage seen at the output of the IC regulator and the ripple

seen at the input of the regulator from the filter capacitor. The output of the regulator is displayed on

channel 2 and its input is displayed on channel 1. Again, we determine that the regulator causes a

reduction in the ripple voltage. We determine the IC regulator to reduce the ripple seen at the input by a

factor of 10.33, which is greater than the reduction seen when using the Zener diode circuit regulator.

11

𝑅𝑖𝑝𝑝𝑙𝑒 𝑟𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛 =𝑉𝑟(𝑖𝑛𝑝𝑢𝑡)

𝑉𝑟(𝑜𝑢𝑡𝑝𝑢𝑡)=

2.24 𝑉

240 𝑚𝑉= 9.33

Figure 3.9: Filter Capacitor Output & IC Ripple Output

In Figure 3.10, we determined the resistance at which we start to notice irregularities in the output

voltage. We determine this value roughly by reducing the resistance of the load resistor until the output no

longer appears as a steady DC voltage. Distortion begins to appear around a value of 9.9 Ω. We believe

that this distortion takes places, because the IC regulator begins to overheat and shut off momentarily.

During this degradation period, the voltage begins to return to normal but is corrected by the IC restoring

function. If the load current were to be further increased, a more pronounced failure of the IC regulator

may occur, along with it being possibly damaged.

Figure 3.10: IC Regulator Failure

12

Both of regulators used in the design of this power supply, regulate the output voltage to within a certain

range with changes in load resistance. To determine how well each regulated, we determine the %

regulation using the following equation:

% 𝑅𝑒𝑔𝑢𝑙𝑎𝑡𝑖𝑜𝑛 = 𝑉𝐿(𝑛𝑜 𝑙𝑜𝑎𝑑) − 𝑉𝐿(𝑓𝑢𝑙𝑙 𝑙𝑜𝑎𝑑)

𝑉𝐿(𝑛𝑜 𝑙𝑜𝑎𝑑)∗ 100%

From this equation we determine the regulation of output voltage for both the Shunt regulator and the IC

regulator chip 7905. We determine, and assumed initially, that the IC regulator much better regulated the

voltage between no load and full load. This is borne out by the face that % Reg(IC) < % Reg(Shunt).

% 𝑅𝑒𝑔(𝑆ℎ𝑢𝑛𝑡) = 4.56 𝑉 − 4.32 𝑉

4.56 𝑉∗ 100% = 5.26%

% 𝑅𝑒𝑔(𝐼𝐶) = 4.88 𝑉 − 4.86 𝑉

4.88 𝑉∗ 100% = 0.41%

To meet the requirements of having a reliable, resilient power supply, we have measured the maximum

operating parameters for each of the components used in the design of the power supply. First, we

determine the max power rating of each device, and then we compare this value to the rating for each

component to determine a safety margin for each component. We note that each component used should

be rated to operate up to roughly twice the max power dissipation that is demanded of it in the power

supply.

The diodes used in power supply more than meet the requirements of the max PIV, as we discussed

earlier. To ensure that the power output is below the power rating, we must first determine the power

rating of the diodes. We use the PIV of the 1N4004 diode and the maximum instantaneous forward

voltage drop to determine that the diodes have a rating roughly equal to 400 W.

𝑃𝐷1 = 𝑃𝐷2 = 𝑖𝐷,𝑚𝑎𝑥𝑣𝑀 = (203.2 𝑚𝐴)|13.7 𝑉| = 2.78 𝑊

𝐷𝑖𝑜𝑑𝑒 𝑆𝑎𝑓𝑒𝑡𝑦 𝑀𝑎𝑟𝑔𝑖𝑛 = 𝑃𝐷(𝑟𝑎𝑡𝑖𝑛𝑔) − 𝑃𝐷 = 400 𝑊 − 2.78 𝑊 = 397.22 𝑊

The power rating of the load resistors we use in the design of the lab is 2 W. This is meant to meet with

the design procedures we used where we used resistance to dissipate nominally 1 W. Therefore our device

provides us a safety margin of roughly 1 W.

𝑃𝑅𝐿 =𝑣𝐿

2

𝑅𝐿=

(−12.7 𝑉)2

172.3 Ω= 0.94 𝑊

𝑈𝑛𝑟𝑒𝑔𝑢𝑙𝑎𝑡𝑒𝑑 𝐿𝑜𝑎𝑑 𝑅𝑒𝑠𝑖𝑠𝑡𝑜𝑟 𝑆𝑎𝑓𝑒𝑡𝑦 𝑀𝑎𝑟𝑔𝑖𝑛 = 𝑃𝑅𝐿(𝑟𝑎𝑡𝑖𝑛𝑔) − 𝑃𝑅𝐿 = 2 𝑊 − 0.94 𝑊 = 1.06 𝑊

𝑃𝑅𝑖 = 𝑖𝑖2𝑅𝑖 = (108.75 𝑚𝐴)2(75.4 Ω) = 0.89 𝑊

𝑈𝑛𝑟𝑒𝑔𝑢𝑙𝑎𝑡𝑒𝑑 𝐼𝑛𝑝𝑢𝑡 𝑅𝑒𝑠𝑖𝑠𝑡𝑜𝑟 𝑆𝑎𝑓𝑒𝑡𝑦 𝑀𝑎𝑟𝑔𝑖𝑛 = 𝑃𝑅𝑖(𝑟𝑎𝑡𝑖𝑛𝑔) − 𝑃𝑅𝑖 = 2 𝑊 − 0.89 𝑊 = 1.11 𝑊

𝑃𝐿 = (108.75 𝑚𝐴)(4.7 𝑉) = 0.51 𝑊

𝑈𝑛𝑟𝑒𝑔𝑢𝑙𝑎𝑡𝑒𝑑 𝐼𝑛𝑝𝑢𝑡 𝑅𝑒𝑠𝑖𝑠𝑡𝑜𝑟 𝑆𝑎𝑓𝑒𝑡𝑦 𝑀𝑎𝑟𝑔𝑖𝑛 = 𝑃𝐿(𝑟𝑎𝑡𝑖𝑛𝑔) − 𝑃𝐿 = 2 𝑊 − 0.51 𝑊 = 1.49 𝑊

13

The capacitor used in this lab is rated to work with a voltage of 50 V. This is well over the value output

by the rectification circuit in the power supply. The power dissipated is about 0 W if we assume an ideal

capacitor. Since this is a small capacitor, we ignore the real effects of the capacitors internal resistance

and assume that the power dissipation in the capacitor in negligible.

𝑃𝐶 = 𝐶𝑉(𝑡)𝑑𝑉

𝑑𝑡= (470𝜇𝐹)(13.7 𝑉)(0 𝑉) = 0 𝑊

𝑃𝑍 = 0.5 𝑊

Discussion

One of the primary concerns that was discussed in the design of the power supply, was the power

dissipation for each of the individual components used in its construction. In the previous section we

determined that we were able to meet these concerns by using devices which were rated to work at power

levels roughly twice that of what we designed the power supply to work at. By using 2-W resistors,

diodes with considerably high PIV, and certain capacitors and Zener diodes we were able to provide a

safety margin of a minimum 1 W for all components. Along with using these certain components, we also

made sure to incorporate the power output we wished to have for each component as parameters to

designing the circuits. This can be seen when we determine the current and voltage we expect to

maximally see across a load resistor and pick a resistance so that only 1 W is dissipated. Without using

this process, there is a much greater chance that we would not have the safety margins that we do, which

could result in a faulty or unreliable power supply.

Throughout this design project, my partner and I observed many values that did not meet up with the

expected value we determined through our theoretical calculations. In an attempt to quantify these errors

we determine the relative error between the measured and derived values. When a relatively large error

occurs, we hope to explain it through issues in design, procedure, or estimation.

% 𝑒𝑟𝑟𝑜𝑟 =|𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 − 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑣𝑎𝑙𝑢𝑒|

𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒∗ 100%

The largest error that we determined was definitely between the maximum diode current and what was

observed. Fortunately, the observed values were much smaller than those we derived which means that

we do not expect for this to cause issues during the circuit’s operation. This error, which is derived below,

we believe is the result of both using an imperfect equation to theoretically derive the maximum current,

and the imperfect means through which we measured the current across the diodes. The insertion of the

resistor in order to determine the current changed the loading properties of our circuit, along with

minoring altering the ripple voltage and max voltage of the signal; this leads to differences in the values

used to derive the theoretical value of max current.

% 𝑒𝑟𝑟𝑜𝑟 =|1.04 𝐴 − 263.5 𝑚𝐴|

1.04 𝐴∗ 100% = 74.7% 𝑒𝑟𝑟𝑜𝑟

14

% 𝑒𝑟𝑟𝑜𝑟 =|1.04 𝐴 − 203.2 𝑚𝐴|

1.04 𝐴∗ 100% = 80.5% 𝑒𝑟𝑟𝑜𝑟

As mentioned previously, much of the error that resulted in the design was a result of using resistor and

capacitor values that did not directly match those values which we derived. This is a realistic limitation to

any design and is the result of not having resistor’s with values across the whole real number range.

Below is the relative error between the resistor values that we used in lab and the resistance that we

theoretically derived.

𝑅𝑇𝑒𝑠𝑡 % 𝑒𝑟𝑟𝑜𝑟 =|428.49 Ω − 391.7 Ω|

428.49 Ω∗ 100% = 8.58% 𝑒𝑟𝑟𝑜𝑟

𝑅𝑖 % 𝑒𝑟𝑟𝑜𝑟 =|77.36 Ω − 75.4 Ω|

77.36 Ω∗ 100% = 2.53% 𝑒𝑟𝑟𝑜𝑟

𝑅𝐿 % 𝑒𝑟𝑟𝑜𝑟 =|63.3 Ω − 63.2 Ω|

63.3 Ω∗ 100% = 0.16% 𝑒𝑟𝑟𝑜𝑟

𝑅𝐿′ % 𝑒𝑟𝑟𝑜𝑟 =

|177.42 Ω − 172.3 Ω|

177.42 Ω∗ 100% = 2.88% 𝑒𝑟𝑟𝑜𝑟

𝐶 % 𝑒𝑟𝑟𝑜𝑟 =|322 𝜇𝐹 − 470 𝜇𝐹|

322 𝜇𝐹∗ 100% = 46.0% 𝑒𝑟𝑟𝑜𝑟

Finally, we look at the error and difference that we find between the output of the power supply design

and the specifications that we tried to meet during the design. First, we look at the nominal DC voltage

that we expected to see at the regulator input. From the design, we see that we wish to have a voltage

signal that differs between -11.7 V and -13.7 V. This 2 V ripple is below our specifications of 2.16 V,

which is derived from the max voltage when attached to a load. The average output voltage VC is roughly

-12.6 V which is a little higher than the -12 V specification we were trying to meet. The resultant error is

5%. This error may have arisen from the usage of resistors that did not meet our exact requirements,

which caused the voltage to be a little higher than we expected to find at the test load.

% 𝑒𝑟𝑟𝑜𝑟 =| − 12 𝑉 − (−12.6 𝑉)|

−12 𝑉∗ 100% = 5% 𝑒𝑟𝑟𝑜𝑟

Next we examine the output voltages at the output of both regulators. As expected, the regulation in our

Shunt resistor did not fare as well as that of the IC regulator. We measured a -4.32 V output when the

regulator was connected to a 1 W load. This was far from out expect value of -5 ± 0.5 V, with an error of

13.6%. This error can be attributed to two primary sources: during the construction of the regulator, we

were unable to find resistors that exactly matched those values which we derived from our equations,

leading to some error in the circuit; we used a Zener diode with a reverse breakdown voltage smaller than

we deemed appropriate to meet the overall demand of the regulator, opting to use the 1N4732 with VZ of

4.7 V compared to the 1N4733 with a VZ of 5.1 V. These two compromises made the regulator not work

as ideally as it should have, and lead to a lower voltage output than was wanted.

% 𝑒𝑟𝑟𝑜𝑟 =| − 5 𝑉 − (−4.32 𝑉)|

−5 𝑉∗ 100% = 13.6% 𝑒𝑟𝑟𝑜𝑟

15

The IC regulator, in comparison to the Shunt regulator, functioned better in use but was still prone to

small errors. The output voltage with a load was -4.88 V, much closer to the desired output of -5 V than

the previous regulator. The relative output error was 2.4% and much of the error I believe can be

attributed not to the design of the regulator, but the variance to the input of the regulator circuit from the

filter capacitor. From observation, it can be seen that the value of our filter capacitor’s output voltage dips

below the recommended -12 V input during its life cycle, which leads us to deduce that this may cause a

dip in the IC’s output. To correct this difference in output voltage, would mean to reevaluate the

construction of the unregulated supply to better meet the input requirements of both regulator circuits

used in the design.

% 𝑒𝑟𝑟𝑜𝑟 =| − 5 𝑉 − (−4.88 𝑉)|

−5 𝑉∗ 100% = 2.4% 𝑒𝑟𝑟𝑜𝑟

Overall, our power supply met all of the specifications laid out at the beginning of design, with the

exception of the Shunt regulator’s output voltage. To better meet the parameters, we feel it would be

prudent to consider redesign and reconstruction of the unregulated supply as this is one of the main

sources of much of the error between our expected outputs and our measured outputs.

Summary & Conclusions

In this design project, my partner and I learned a great deal about what goes into the process of designing

a functional circuit to meet specifications. While the lab did reinforce concepts learned over the past few

weeks in lecture, I believe the real lesson we learned was related to the robustness that is required in

designing, implementing, and testing a circuit under many different conditions. Moving forward, we will

understand the intensive considerations that must go into making a circuit that meets the specifications set

out for its design.

Along with the overarching lesson in design some other concepts that were brought up during the

completion of this project included: understanding of how a simple power supply works, where errors can

occur in design of power-supply circuits, the importance of power specifications in designs with variable

loads, and the practicality of IC regulators in comparison to Shunt regulators. All of these concepts will

have highly practical usage in circuits other than power supplies, and help to reinforce concepts of

practical electronic design.