UEEA1253_LAB2

7/27/2019 UEEA1253_LAB2

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UEEA1253 – CIRCUITS, SIGNALS

AND SYSTEMS

LAB 2

NAME : RAJALAKSHMI NADARAJAN / HEMALATHA GANESAN

ID : 09UEB05159 / 09UEB07309

COURSE : EC/ MH

DATE OF EXPERIMENT : 28 MARCH 2012

CONTACT : 017-3608012 / 014-3258728

EMAIL : [email protected] / [email protected]

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mailto:[email protected]

mailto:[email protected]

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R g

~

R Lv

g

Signal Generator

v L

Introduction:

Impedance matching is a technique of impedance transformation so that the maximum

power transfer can be possible. Passive LC networks are used to match impedances

between the source (generator) and a load. These matching networks are designed

usingcombinations of inductors and capacitors.

Objectives:

a) To measure the power transfer coefficient of a circuit.

b) To show how impedance matching can improve the power transfer to the load for a

narrowband about the frequency of interest.

c) To understand theory and advantages of impedance matching.

Theory:

Maximum Power Transfer is used to ensuring the maximum amount of power that

going to dissipated in the load resistance, RL when value of the load resistance is

exactly equal to the resistance of the power source, Rg. The load impedance and the

internal impedance of the energy source have a relationship among themselves; the

different load impedance will give different value of power in the load.

The maximum power transfer can be seen by using a Thevenin equivalent circuit.

Generally, maximum power transfer theorem states that "the maximum amount of

power will be dissipated in the load resistance if it is equal in value to the Thevenin

or Norton source resistance of the network supplying the power ". Which mean when

, we can get the maximum power transfer for the circuit.

Impedance matching is a design to maximize the power transfer and minimize the

reflection of its corresponding signal source from the load by changing the input

impedance of an electrical load or in other word output impedance. Generally,

impedance matching is a design that making the load resistance, to get near to

internal resistance so that the maximum among of power can be dissipated in the

load resistance

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We going to do experiment on an LC circuit as an impedance transformer so that the

load resistor appears as R g to improve the power transfer ratio at an operating

frequency. By analyzing the Z(f) above, get its real part R(f) and imaginary part X(f)

in terms of L, C and R L .

R s = R LThe equation that can be derived is as shown below

Equipments and components:

• Signal generator and oscilloscope

• One each (10, 33, 56, 68, 100, 220, 330, 470 and 680 Ω) resistors, one 10mH

inductor and three 100nF capasitor

• Resistance box, Inductor box and Capacitor box.

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Vs

I

R L

R s

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R g

~

R Lv

g

Signal Generator

v L

Method:

Experiment 1: Measurement of the power transfer coefficient

NOTE: All the voltage measurement was done using the oscilloscope

a.)The sine wave f = 3kHz and v s = 16V pp(oscilloscope). Vs(peak value) = 8V p. The

calculated .

b) The R g value was measured. R g = 42.94 Ω

R L = 100.2

c) The maximum power available:

d) The Lv (rms) was measured for various values of resistor load R L given: 9.9Ω,

32.9Ω, 55.9Ω, 67.9Ω, 100.2Ω, 216.6Ω, 325.2Ω, 461Ω and 670Ω.

e) was calculated.

f) The power transfer coefficient was calculated.

No R L (Ω) VL(RMS)

1 9.9 0.892 0.0804 0.4232

2 32.9 2.157 0.1414 0.7442

3 55.9 2.885 0.1489 0.7837

4 67.9 3.146 0.1458 0.7674

5 100.2 3.640 0.1322 0.6958

6 216.6 5.020 0.1163 0.6121

7 325.2 5.360 0.0883 0.46478 461 5.570 0.0673 0.3542

9 670 5.820 0.0506 0.2663

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NOTE: After calculating if the t >1, the experiment was repeated again as the R g

value was wrongly measured or calculated.

g) The graph t against R L was plotted

Observation:

From the graph the maximum value of the t is 0.7837 when the R L value is equal55.9Ω.

Experiment 2: Impedance Matching for maximum power transfer

When R g is as measured and the load resistor R L = 670 Ω a mismatching occurs. The

calculated power transfer ratio is:

In this experiment an LC circuit was an impedance transformer so that the 670 Ω load

resistor appears as R g to improve the power transfer ratio at an operating frequency.

Assumption made was that a 10mH inductor was provided.

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After Z(f) was analyzed, the real part R(f) and the imaginary part X(f)was found in

terms L, C and R L as shown below

i) By using the L = 10mH, R g = 42.94 Ω and R L = 670 Ω and substituting the values

into the equation to find the f 0.

ii) After obtaining f 0 substitute into the next equation to get C.

The nearest capacitor value that can be used to conduct this experiment according to

the calculated value of the capacitor is = 357nF

iii) Using the Ohm meter provided the internal resistance of the inductor was

measured. The value is = 15.2 Ω

a) The v s = 7Vrms, sine wave f = 100Hz and R L = 670 Ω was set. b) The v L was measured

c) The was calculated.

d) The power transfer coefficient

e) The steps were repeated for the other frequencies and the R L was measured. The

results are as shown in the table below:

No f (Hz) V L(RMS)

1 100 6.29 0.0591 0.2038

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2 500 6.52 0.0634 0.2186

3 1000 6.99 0.0729 0.2513

4 2000 9.09 0.1233 0.4252

5 2500 10.30 0.1583 0.5459

6 3000 10.18 0.1547 0.5334

7 3500 7.53 0.0846 0.29178 4000 4.97 0.03686 0.1271

9 5000 2.22 7.3558x10-3 0.0254

10 6000 1.40 2.9254x10-3 0.0101

11 7000 0.976 1.4218x10-3 4.90x10-3

12 8000 0.718 7.6944x10-4 2.65x10-3

g) The graph t against f was plotted

Observation:

From the graph the maximum value of t is 0.5459 when the frequency is 2500Hz.

When the frequency is increasing, we can see that the power transfer coefficient ,t is

increasing until one point which is the peak of the curve, the power transfer

coefficient , t decreasing after that point .

Discussion:

In the first experiment,the value of t isnot more than 1.Therefore the value of R gobtained is correct.Based on the graph it can be seen that the value of t is increasing

for the value of R L 9.9Ω to 55.9Ω. Then as the value of R L increases from 67.9Ω to

670Ω the value t is decreasing gradually. From the table we can say that the VL(RMS)

increases as the R L value increases. The PL value also shows the same characteristic asthe t value that is when the R L value is 9.9Ω to 55.9Ω it is increasing and as the R L

value increases from 67.9Ω to 670Ω it decreases.

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R g

~

R Lv

g

Signal Generator

v L

For the second experiment from the table itself it can be seen and concluded that the

value of t , VL(RMS) and the PL value is increasing for the value of the frequency starting

from 100Hz to 2500Hz. All the three values starts to decrease when the frequency is

increasing from 3000Hz to 8000Hz

After each experiment, the power transfer coefficient, t is calculated.It should not bemore than 1 for both experiments.This is because the power that transfers will not

bigger than the maximum power available. If the coefficient, t is bigger than 1, it

simply means the circuit is generating or amplifying the power from the input.

Unfortunately, in the experiment 3.1 and experiment 3.2, the circuit that we connected

is not one of an amplifying type. Hence, the power transfer coefficient, t will be 1 and

will not more then 1. Or in other word, the power transfer coefficient, t is showing the

remaining power after the power loss from the input power.

There are few precautionary steps we need to check. First, all the apparatus should be

tested to make sure there was not any apparatus was not functioning or functioning in

a good condition. Besides that, the materials that we use such as resistors, capacitors

and also the inductors are needed to be checked. This may save up time in doing theexperiment so that we will not keep getting the wrong result and force to redo the

experiment as we do not know the apparatus and material that we used is not

functioning.

The position of the eyes must be correct when reading the scale.This is to avoid

parallax error.In both experiments we need to measure the VL ,if the value were

measured wrongly it will effect the whole experiment results.

Analysis and Confirmation of Experimental Results:

Experiment 1: Measurement of the power transfer coefficient

By using the equation we can obtain the theoretical values for the

experiment 1.

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No R L (Ω) VL(RMS)

1 10 1.0691 0.1143 0.6016

2 33 2.4596 0.1833 0.9648

3 56 3.2036 0.1833 0.9645

4 68 3.4693 0.1770 0.9316

5 100 3.9597 0.1568 0.8252

6 220 4.7357 0.1019 0.5365

7 330 5.0083 0.0760 0.4000

8 470 5.1862 0.0572 0.3012

9 680 5.3238 0.0417 0.2194

The graph t against R L was plotted.

Observation:From the graph the maximum value of the t is 0.9648 when the R L value is equal

33Ω.When we compare the theoretical and the experimental graph,it is almost the

same.Even if there is a slight difference it may be because due to the technical

problem exist in the experimental tools used.

Experiment 2: Impedance Matching for maximum power transfer

For this experiment we analyze it in two which in the first case where it is an ideal

inductor and the second case inductance with the internal resistance.

Case 1: Ideal inductor

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---------- 1

-------- 2

-------- 3

-------- 4

By substituting equation 2 into 1 we obtain:

By substituting 2 into 3 we obtain:


In terms of

Substituting into the equation we obtain:

By solving we obtain:

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By using the values below and substituting into the equation above we ob tain the

results as shown in the table below:

No f (Hz) V L(RMS)

1 100 628.31854 5.66 0.047 0.230

2 500 3141.5927 6.36 0.059 0.289

3 1000 6283.1854 7.07 0.074 0.363

4 2000 12566.370

8

8.49 0.106 0.520

5 2500 15707.963

5

9.55 0.134 0.657

6 3000 18849.556

2

10.61 0.166 0.814

7 3500 21991.148

9

9.55 0.134 0.657

8 4000 25132.741

6

7.07 0.074 0.363

9 5000 31415.927 3.54 0.018 0.088

10 6000 37699.112

4

2.26 0.007 0.034

11 7000 43982.297

8

1.56 0..004 0.020

12 8000 50265.483

2

1.10 0.002 0.009

The graph t against f was plotted.

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Observation:


Case 2: Inductance with internal resistance of 15.2Ω

----------1

---------- 2

---------- 3

---------- 4

By substituting equation 2 into 1 we obtain:



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In terms of

Substituting into the equation we obtain:

By solving we obtain:

By using the values below and substituting into the equation above we ob tain the

results as shown in the table below:

No f (Hz) V L(RMS)

1 100 628.31854 4.557 0.031 0.169

2 500 3141.5927 4.634 0.032 0.175

3 1000 6283.1854 4.887 0.035 0.191

4 2000 12566.370

8

6.015 0.053 0.290

5 2500 15707.963

5

6.786 0.068 0.372

6 3000 18849.556

2

7.071 0.074 0.404

7 3500 21991.148

9

6.223 0.057 0.311

8 4000 25132.741

6

4.817 0.034 0.186

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9 5000 31415.927 2.766 0.011 0.060

10 6000 37699.112

4

1.751 0.005 0.027

11 7000 43982.297

8

1.210 0.002 0.011

12 8000 50265.4832

0.890 0.001 0.005

The graph t against f was plotted.

Observation:


Comment:

Ideal inductor means having no resistance (impedance), is also known as inductance.

In ideal inductor case, the t value found that is slightly more than value t with internal

resistance of inductor. This proved that the impedance matching can improve the load

fornarrowband frequency. By plotting a graph, we can easily know the maximum power transfer.

Conclusion:

Based on the experiment, impedance matching techniques can known the electronics

design practice of setting the input impedance ( Z L) of an electrical load equal to the

fixed output impedance ( Z S) of the signal source to which it is ultimately connected,

usually in order to maximize the power transfer and minimize reflections from the

load. This only applies when both are linear devices

Reference:

John Bird. Revised edition(2003). Electrical Circuit Theory and Technology. Burlington,MA Newnes

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Impedance Matching Basics - Series L and C. (n.d.). Retrieved April 12, 2011, from Antenna-

Theory.com: http://www.antenna-theory.com/tutorial/smith/smithchart5.php

Impedance matching. (2011, April 3). Retrieved April 12, 2011, from Wkipedia:

http://en.wikipedia.org/wiki/Impedance_matching

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UEEA1253_LAB2