INSTITUTO POLITÉCNICO NACIONAL

ESCUELA SUPERIOR DE CÓMPUTO

FUNDAMENTAL CIRCUITS ANALYSIS LABORATORY

FUNDAMENTAL CIRCUITS ANALYSIS

GROUP: 1CV11

Professor: Raúl Santillán luna

TEAM 1

Team Members:

Castro Maya Cristopher

Cadena Martínez Fernando

Javier Alejandro Andrade

Internship 8 Superposition Theorem

1

|

me

asu

rem

en

t in

str

um

en

ts

INDEX

Objective…………………………………………………….2

Introduction………………………………………………....2

Development………………………………………………...3

Quiz …………………………...……………………….…5

Conclusions…………………………………………………6

2

me

asu

rem

en

t in

str

um

en

ts |

Superposition Theorem The strategy used in the Superposition Theorem is to eliminate all but one source of power within a network at a time, using series/parallel analysis to determine voltage drops (and/or currents) within the modified network for each power source separately. Then, once voltage drops and/or currents have been determined for each power source working separately, the values are all “superimposed” on top of each other (added algebraically) to find the actual voltage drops/currents with all sources active. Let’s look at our example circuit again and apply Superposition Theorem to it:

Since we have two sources of power in this circuit, we will have to calculate two sets of values for voltage drops and/or currents, one for the circuit with only the 28 volt battery in effect. . .

. . . and one for the circuit with only the 7 volt battery in effect:

When re-drawing the circuit for series/parallel analysis with one source, all other voltage sources are replaced by wires (shorts), and all current sources with open circuits (breaks). Since we only have voltage sources (batteries) in our example circuit, we will replace every inactive source during analysis with a wire. Analyzing the circuit with only the 28 volt battery, we obtain the following values for voltage and current:

3

|

me

asu

rem

en

t in

str

um

en

ts

Analyzing the circuit with only the 7 volt battery, we obtain another set of values for voltage and current:

When superimposing these values of voltage and current, we have to be very careful to consider polarity (voltage drop) and direction (electron flow), as the values have to be added algebraically.

Applying these superimposed voltage figures to the circuit, the end result looks something like this:

Currents add up algebraically as well, and can either be superimposed as done with the resistor voltage drops, or simply calculated from the final voltage drops and respective resistances (I=E/R). Either way, the answers will be the same. Here I will show the superposition method applied to current:

4

me

asu

rem

en

t in

str

um

en

ts |

Once again applying these superimposed figures to our circuit:

Quite simple and elegant, don’t you think? It must be noted, though, that the Superposition Theorem works only for circuits that are reducible to series/parallel combinations for each of the power sources at a time (thus, this theorem is useless for analyzing an unbalanced bridge circuit), and it only works where the underlying equations are linear (no mathematical powers or roots). The requisite of linearity means that Superposition Theorem is only applicable for determining voltage and current, not power!!! Power dissipations, being nonlinear functions, do not algebraically add to an accurate total when only one source is considered at a time. The need for linearity also means this Theorem cannot be applied in circuits where the resistance of a component changes with voltage or current. Hence, networks containing components like lamps (incandescent or gas-discharge) or varistors could not be analyzed. Another prerequisite for Superposition Theorem is that all components must be “bilateral,” meaning that they behave the same with electrons flowing either direction through them. Resistors have no polarity-specific behavior, and so the circuits we’ve been studying so far all meet this criterion. The Superposition Theorem finds use in the study of alternating current (AC) circuits, and semiconductor (amplifier) circuits, where sometimes AC is often mixed (superimposed) with DC. Because AC voltage and current equations (Ohm’s Law) are linear just like DC, we can use Superposition to analyze the circuit with just the DC power source, then just the AC power source.

5

|

me

asu

rem

en

t in

str

um

en

ts

Development

Students will obtain the values requested in Table 1, with reference to the circuit of Figure

1 and applying the concept of overlap seen in class, also carried out simulating the circuit

using any software tool and include in its report the full development of mathematical

analysis.

I. Without even turning on the voltage sources, connect the circuit shown in Figure 1. Figure 1

II Since the armed circuit, power source voltage and measure the values requested in Chart 1.

measurements

theoretical value

measured value

simulated value

IAB 4mA 3.98mA 4.03mA

VAB 880.91mV 880.41mV 887.53mV

PR5 3.52*10-3W 3.5024*10-3W 0.0003502W

III In the circuit under analysis. Turn off voltage sources disconnect t E2 and E3 replacing them with a short, leaving only E1, as shown in Figure 2. Once this amendment is made to activate said voltage source and taking measurements as requested in the table 2.

For the previous circuit, turn off and disconnect voltage E1 source and replace and by short circuit. Connect only E2, as

shown in figure 3, and made such modification check to said voltage and proceed to take to measures asked in table 3.

Measures for E1 Theatrical value Value measures Simulated value

IAB 18.51 mA 18.4 mA 18.51 mA

VAB 4.08 mV 4.03 mV 4.08 mV

PAB 6.55 x10-5 w 7.41x10-5 7.55 x10-5 w

A B

6

me

asu

rem

en

t in

str

um

en

ts |

Considering again the previous circuit, now turn off the power and disconnect voltage E2 and replaced by a short circuit. Connect only to E3, as show in figure 4, and once made such active to say voltage source to take appropriate measures asked in the table 4.

Finally calculated and measure the following values:

Measures for E1 Theatrical value Value measures Simulated value

IAB 3.98 mA 3.78mA

VAB 875.83 mV 874.83mV

PAB 3.48 x10-5 3.303x10-5

Measures for E1 Theatrical value Value measures Simulated value

I’’’AB -2.70mA -2.70mA -2.70mA

V’’’AB -0.70v -0.67v -0.70v

P’’’AB 1.89 x10-3 1.79 x10-3 1.89 x10-3

Superposition with Theatrical value Value measures Simulated value

I’AB +I’’AB+ I’’’AB 4mA 4mA 4mA

V’AB +V’’AB+ V’’’AB 880.91mV 880.91mV 880.91mV

P’AB +P’’AB+ P’’’AB 1.56*10-3W 3.52*10-3W 3.52*10-3W

7

|

me

asu

rem

en

t in

str

um

en

ts

Quiz: 1. What Superposition Theorem Says?

The voltage across (or current through) an element in a linear circuit is the algebraic sum of the voltages across (or currents through) that element due to each independent source acting alone.

2. What’s the purpose of disconnect RL and measure into point a and b?

Review the venin current and voltage

3. Which is the reason of the difference between calculated and measurements values?

The difference between values it’s produced because we are not using ideal components

4-which is the utility of the venin reduction?

It allows to simplify a very complex component into a simple resistance and voltage supply

Conclusions

The Thevenin’s theorem it’s an important tool for the circuit analyses it allows to reduce a complex circuit

into a very simple one --Castro Maya Cristopher

The venin’s theorem greatly facilitates the analysis of a circuit, because we can get a reduced equivalent circuit.

The calculations are less and get better results.-Fernando Cadena Martinez

The venin 's theorem is very helpful as we used to make a big circuit having two terminals, one containing only

simple voltage source or voltage in series with a resistor-Andrade Guzman Javier Alejandro