Maximum power transfer lab report

P2-1

Pre-Lab Exercises for

Experiment 2: Basic Circuit Principles

Read the handout for Experiment 2.

Questions:

1. Solve for 2R

V in the circuit of Figure E2.5 using the principle of superposition.

2. Determine the Thévenin Equivalent resistance and voltage for the circuit in Figure E2.8. (Show your work).

3. Use PSpice to show, for Figure E2.10, that the value of R that will absorb maximum power from the remainder of the circuit is equal to your Thévenin resistance.

EE 3342

E2 – 1

EQUIPMENT

1 – Breadboard

1 – DMM

1 – Power Supply

PARTS

1 – 100Ω Resistor

1 – 220 Resistor

1 – 330 Resistor

1 – 470 Resistor

1 – 1.2k Resistor

1 – 2.2k Resistor

1 – 3.3k Resistor

1 – 1k Potentiometer

Experiment 2

Basic Circuit Principles

OBJECTIVES

To experimentally verify for some simple DC circuits:

 Kirchhoff’s Current Law

 The Superposition Principle

 Thévenin’s Theorem

 The Maximum Power Transfer Theorem

THEORY

Kirchhoff’s Current Law states that the total current flowing into a node equals the total current

flowing out of the same node. For the circuit shown in Figure E2.1, this can be expressed as

 

 

1 234

1 2 34

1 2 3 4

1 2 3 4

T I I I

I I I

I I I I

I I I I

 

  

     

   

Figure E2.1. Illustration of Kirchhoff’s Current Law.

The Superposition Principle states that the current through, or the voltage across, any branch of

a multi-source network is the algebraic sum of the contributions due to each source acting

independently. When the effects of a single source are considered, all other sources are replaced

by their internal resistance. The superposition principle applies only to voltage and current

calculations in linear circuits. Power cannot be determined in this manner because of the

nonlinear square relationship associated with its calculation.

Analyzing complex circuits with the superposition principle is usually much easier than solving

the simultaneous equations required for mesh or nodal analysis. It is vitally important to take

voltage polarities and current directions into account when using the superposition principle.

EE 3342

E2 – 2

Ideally, any voltage source not being considered may be replaced with a short circuit and any

current source may be replaced with an open circuit. If, however, the internal resistance of the

source is not negligible, then an equivalent resistance must be substituted. Figure E2.2 illustrates

application of the superposition principle to the determination of the current 1 2

I I I  .

Figure E2.2. Illustration of the Superposition Principle.

Avoid damaging your equipment! Never short an active source such as a power supply or

function generator. Instead, do the following:

1. Disconnect the source. 2. Insert a short circuit in its place.

Thévenin’s Theorem is used to simplify analysis of a complex network by reducing a portion, or

all, of it to an equivalent circuit. Thévenin’s Theorem allows us to reduce any network of

independent sources, controlled sources and resistors to a circuit with a single independent

voltage source, T

V , in series with a single resistance, T

R . Figure E2.3 illustrates Thévenin’s

Theorem.

Figure E2.3. Illustration of Thévenin’s Theorem.

The value of the Thévenin equivalent voltage source is the open circuit voltage measured

between the two load terminals, with the load removed.

To determine the Thévenin equivalent resistance, remove the load, short all of the independent

voltage sources, open all of the independent current sources, and then calculate the equivalent

resistance of the remaining circuit. If the circuit contains controlled sources, the process is more

complicated, and this situation will not be discussed here.

The Maximum Power Transfer Theorem tells us that a DC voltage source will deliver

maximum power to a load resistor when that resistor has a value equal to the internal resistance

EE 3342

E2 – 3

of the source. Maximum power transfer in a complex network occurs when the load resistance is

equal to the Thévenin resistance “seen” by the load. With this resistance, the voltage across the

load will be one-half that of the Thévenin voltage source, and the power delivered to the load

will be one-half that delivered by the source. The power transferred to the load under this

condition is given by:

PROCEDURE

Exercise E2.1 – Kirchhoff's Current Law.

1. Measure the values of four resistors and record them in Table E2.1. 2. Connect the four resistors in parallel to a 10V power supply as shown in Figure E2.4.

Figure E2.4. Parallel Resistor Circuit.

3. Current is measured by connecting a DMM in series with the component through which the current is to be determined. Figure E2.4 shows how the current would be measured

through resistor 1

R . Measure the current flowing through each branch in the circuit and

record the data in Table E2.1.

4. Determine the error between the calculated and the measured current values for 1

I , 2

I ,

3 I ,

4 I ,

34 I ,

234 I and

T I using Table E2.2.

34 I ,

234 I and

T I are the currents at the top of

the circuit as shown in Figure E2.4.

    2 2

max

2

4

T T

T T

V V P

R R  

EE 3342

E2 – 4

Table E2.1 -- Kirchhoff's Current Law

Nominal

Values (k) 1

R 2

R 3

R 4

R

Measured Currents

(mA)

1 I

2 I

3 I

4 I

34 I

234 I

T I

Calculated

Currents by KCL

(mA)

1 I

2 I

3 I

4 I

34 I

234 I

T I

Table E2.2 -- Current Comparison

Calculated Measured % Error

1 I

2 I

3 I

4 I

34 I

234 I

T I

 If the calculated and measured values deviated by more than 10% discuss the reasons why.

 Does Kirchhoff’s Current Law successfully describe current flow in a circuit? Explain.

Exercise E2.2 – The Superposition Principle.

Figure E2.5. Two-Voltage Source Circuit.

1. Measure and record the resistor values 1

R , 2

R , and 3

R .

2. Construct the network in Figure E2.6 and use Table E2.3 to collect data.

3. Measure the currents 1R

I , 2R

I , and 3R

I .

EE 3342

E2 – 5

4. Use Ohm's Law to calculate the voltages 1R

V , 2R

V , and 3R

V for the source 1

V in

Figure E2.6.

Figure E2.6. Contribution from Voltage Source 1

V .

Figure E2.7. Contribution from Voltage Source 2

V .

5. Measure the voltages 1R

V , 2R

V , and 3R

V for the source 1

V in Figure E2.6 using a

DMM.

6. Construct the network in Figure E2.7.

7. Measure the currents 1R

I , 2R

I , and 3R

I .

8. Use Ohm's Law to calculate the voltages 1R

V , 2R

V , and 3R

V for the source 2

V in

Figure E2.7.

9. Measure the voltages 1R

V , 2R

V , and 3R

V for the source 2

V in Figure E2.7 using a

DMM.

10. Build the network in Figure E2.5.

11. Add the results from steps 3 and 7 to calculate 1R

V , 2R

V , and 3R

V for Figure E2.5.

12. Measure the voltages 1R

V , 2R

V , and 3R

V for the source 1 2

V V in Figure E2.5 using a

DMM.

 What is the percent error difference between the calculated and measured voltages

for 1

V , 2

V , and 1 2

V V ?

 Did the superposition principle hold true? Explain.

EE 3342

E2 – 6

Table E2.3 – Superposition Data

1RV

Measured 2R

V Measured

3R V

Measured 1R

V Calculated

2R V

Calculated 3R

V Calculated

1R V

% Error 2R

V % Error

3R V

% Error

1 V

2 V

1 2 V V

Exercise E2.3 – Thévenin’s Theorem.

1. Construct the circuit in Figure E2.8.

Figure E2.8. Circuit to be Reduced.

2. Measure and record the current L

I and the voltage L

V in Table E2.4.

3. Calculate the Thévenin voltage and the Thévenin resistance for the network to the left of points a-b in Figure E2.8.

4. Keep the circuit of Figure E2.8 set up for Exercise E2.4. Build the circuit in Figure

E2.9 using T

V and T

R from step 3.

Figure E2.9. Thévenin Equivalent Circuit.

5. Measure and record the current L

I and the voltage L

V in Table E2.4.

 What is the percent error between the original circuit and the equivalent circuit’s

current L

I and voltage L

V ? Use Table E2.4 to summarize your answers.

 Does Thévenin’s Theorem hold true? Explain?

EE 3342

E2 – 7

Table E2.4 – Thévenin Data

L

I L

V T

R T

V

Circuit

Equivalent

Circuit

% Error

Exercise E2.4 – The Maximum Power Transfer Theorem.

1. Construct the network shown in Figure E2.10.

Figure E2.10. Maximum Power Transfer Circuit.

2. Theoretically calculate the value of L

R that will absorb the most power from the

circuit.

3. Fill in Table E2.5 with the measured values for R

V and calculate R

P as the resistance

varies.

 How does the theoretical value of L

R compare to T

R calculated earlier?

 Compare the experimental results with the PSpice results obtained in the Pre-Lab Exercise.

Table E2.5 – Maximum Power Transfer Data

L R

R V

R P

10

50

100

150

200

250

300

350

400