LAB331 - familiarisation with osciloscope PDF

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familiarisation with osciloscope...

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DEPARTMENT OF ELECTRICAL ENGINEERING

EEB 331

ELECTRICAL NETWORK THEORY LAB 1 NAMES STUDENT ID COURSE CODE

MOSES SEEPI 201702328 EEB331

DATE

09/06/2020

MAXIMUM POWER TRANSFER THEOREM

PAGE \* MERGEFORMAT 11

TABLE OF CONTENTS 1. …1 2. … 3. 4. 5. 6. 7. 8. 9.

Objectives………………………………………………………… Apparatus………………………………………………………… Introduction Theory Procedure Results and analysis Discussion Conclusion References

OBJECTIVES OF THE EXPERIMENT: The aim of this experiment is understand and prove that Thevenin’s and Norton`s Theorems actually satisfy their theoretical statements. This experiment also serves to prove the authenticity of maximum power theorem. This experiment utilises the use of computer simulated circuits called Pspice therefore part of this experiment serves to familiarise the student with such softwares.

APPARATUS: 1.

PC/ Laptop equipped with Pspice software.

INTRODUCTION: Linear circuit theorems are theorems of assessing linear circuits and effectively being able to simply the circuits and explore the behaviour of various components in a circuit. There exists 3 Linear circuit theorems, Superposition Theorem which is useful in finding the influence of individual current or voltage sources in a linear circuit, Thevenins and Norton`s Theorems which are useful in simplifying a linear circuit into 2 components, a voltage source and corresponding resistance in Thevenins Theorem and a current source and resistance in Norton`s theorem. Thevenins Theorem and Norton`s Theorem are also effectively the source transformations of each other. The idea is to be able to understand how a load would behave when connected through the terminals to the linear circuit.

THEORY: Thevenins Theorem states that any linear circuit with two terminals can be simplified to or represented with an equivalent circuit consisting of a Voltage source (Vth) in series with a resistance (Rth). The Voltage source(Vth) is taken as the voltage across the open circuit terminals and the resistance (Rth) is the resistance of the circuit when looking at the circuit through the terminals while all independent sources are shutoff. Figure a.

Figure b.

Figure a shows a linear circuit and figure b shows the Thevenin equivalent of the circuit. Thevenins equivalent circuit is useful in analysis of power systems and circuits more especially when interested in the varying load resistance in terms of the current passing through it and the voltage drop across it. Although Thevenins theorem is useful it also has limitations as it only applies to linear circuits only, meaning it could be useful in simplifying a complex circuit that might contain linear portions and none linear portions but it can only apply to the linear portions of the circuit. Nortons Theorem as already mentioned is basically the source transform of a Thevenin equivalent circuit i.e a current source(IN) connected in parallel with a resistor(Rn) where Rn = Rth and as such IN = Vth /Rth .The same limitations of Thevenins theorem apply to Norton`s Theorem as it is only functional or only applies to linear circuits, similarly a complex circuit could contain linear portions and none linear portions and Norton`s theorem would apply to the former portions of the circuit. Figure 1

Figure 2

Figure 1 shows a linear circuit and figure 2 is the Norton`s equivalent circuit of the circuit. Norton`s Theorem and Thevenins Theorem are used often by circuit designers and are also useful in troubleshooting fault currents. The maximum power transfer theorem states that in a Thevenin equivalent circuit the maximum amount of power that can be dissipated through a load resistance will be dissipated at the point where the load resistance(RL ) is equal to thevenins equivalent resistance i.e RL = Rth.

Using ohms law Power(P)= current(I)2 * resistance ( RL) this is the power dissipated across the load resistance At the point of maximum power, P=( Vth/(Rth + RL))2 * RL Pmax= Vth2/4Rth. If a graph of power against varying resistances is made it will display the behaviour shown in figure c.

Figure c.

PROCEDURE: Circuit A

Circuit B

On the schematics page of the program, the Pspice program was opened and circuit A was drawn. A variable load resistance starting from 1k (ohms) ending at 100k (ohms). To observe the voltage drop through the load resistance and the current through the load resistance for all RL values, the circuit was then compiled and stored in the program and simulated. To observe once again the voltage drop through RL and the current through RL, the circuit was redrawn to circuit B compiled and simulated. The power dissipated by the resistance was then computed and tabulated for all circuit A and B RL values.

RESULTS AND ANALYSIS For Circuit A Disconnecting the load and Shutting off all soucres, and looking at the circuit through the terminals Ω R th=1+(2.2 /¿ 5.7 )k ¿ ) R th=3.58Ω k (Ω)

Using mesh analysis thevenins Voltage will be equal to the voltage drop across the resistor of value 2.2k(Ω). For circuit A Va th=−14.52 V

For circuit B Vb th=1.39 V

The maximum power output is then found by the relation P max=V th 2/ 4 R th. Pb max=134.92 µW −Circuit B

Pamax=14.7 mW −Circuit A

Circuit A Table of Results R LOADk(Ω)

Voltage(VL)(V)

Current(A)

POWER(mW)

1 1.5

6.12 8.28

6.12m 5.52m

37 46

2 2.5 3 3.5 4 5 10 20 30 40 50 60 70 80 90 100

10.05 11.53 12.78 13.86 14.79 16.34 20.64 23.77 25.04 25.72 26.15 26.44 26.66 26.82 26.95 27.05

5.03m 4.61m 4.26m 3.96m 3.70m 3.27m 2.06m 1.19m 834.50µ 643.00µ 522.98µ 440.72µ 380.82µ 335.26µ 299.43µ 270.52µ

51 53 54 55 55 53 42.6 28.2 20.9 16.5 13.7 11.7 10.2 9 8.1 7.3

Circuit B Table of results R LOADk(Ω) 1 1.5 2 2.5 3 3.5 4 5 10 20 30 40 50 60 70 80 90 100

Voltage(VL)(V) Current(A) POWER( W) 326.64m 326.64µ 107µ 423.51m 282.34µ 120µ 497.24m 248.62µ 123µ 555.2m 222.10µ 123µ 602.05m 200.69µ 121µ 640.64m 183.04µ 117µ 672.98m 168.25µ 113µ 724.18m 144.84µ 107µ 854.11m 85.41µ 72.9µ 938.29m 46.91µ 44µ 970.16m 32.24µ 31.4µ 986.92m 24.67µ 24.4µ 0.997 19.95µ 19.9µ 1.004 16.74µ 16.8µ 1.009 14.42µ 14.5µ 1.015 12.67µ 12.9µ 1.016 11.29µ 11.5µ 1.019 10.19µ 10.4µ

DISCUSSION

Using Thevenins Theorem we can express the Circuit A in terms of a voltage source in series with a resistance connected to two open terminals. Where Rth= 3.58Ωk(Ω), when a load resistance is connected there is power dissipated by the resistor. The maximum power that can be dissipated by the circuit will be reached when RL = Rth. According to the measurements taken in the experiment the maximum power dissipated by circuit A and B are Pamax = 55mW Pbmax =123µW Those values are very different from the theoretical values of 1.47mW and 0.13mW respectively this maybe due to previous calculation errors and the mathematics might require reviewing. In spite of this the type of graph of Power against Load Resistance, we expected to see a behaviour similar to that portrayed in figure c and the resulting graphs from the 2 part experiment is similar to that in figure c essentially proving the maximum transfer theorem. The Resistance calculated to have the circuit deliver the maximum amount of power 3.58k(Ω) from the measurements the value of this load resistance. Although the 2 circuits differ they share the same value of Rth but vary at Vth . From observing the table of circuit A it can be noted that the resistance that corresponds with maximum power output fall is the range 3.5-4.0Ωk(Ω) , the theoretical value Rth falls in that range.

CONCLUSION Linear circuit theorems have proven to be useful in power analysis of varying load resistance, with Thevenins Theorem and The Maximum power Theorem being the most useful in that manner. The theorems are therefore important topics to be explored in engineering as they can help in understanding complex circuits and the theorems have proven effective in those regards....