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# Engineering Order (Essay Sample)

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A research paper about fundamental elements of microwave engineering.

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Engineering Order

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Impedance Matching

Impedance matching is hugely important in various engineering aspects particularly microwave engineering. It, therefore, implies that the circuitry of the two portions of the original network is required for matching to be achieved.

The elements of a communication networks should be designed and constructed in such a way that they can allow maximum power transfer to take place between the source and the load. This is in cycle with the maximum power transfer that states that maximum power is absorbed by a network from another network joined to it at its two terminal if the impedance of network is a complex conjugate the other. This can otherwise be interpreted as maximum power takes place between the source and the load if the resistance of the source is equal to the resistance of the load and more so, when the reactance of the load should be equal to the reactance of the source but in opposite direction. This means that if the source is inductive, the load should be capacitive and vice versa. This condition is what is known as impedance matching and the techniques used to attain these are called impedance matching devices (Rizzi 1988).

Ideally, single sources or a generator can be referred to as impedance devices. For a specified load, a given specified load needs to be transferred to proper load impedance for maximum power transfer to be achieved by a given single source. This phenomenon in a network is called to matching network.

Impedance matching is of great importance in any network since it enables efficient power transfer between the source and load which are at a single frequency. When the transmission line is matched at the load and the source ends, maximum power is delivered to a given load whenever the configuration fulfills the condition of conjugate match. More so, much signal power can be transferred to a load in matched transmission line which does increase the sensitivity of an electronic device. Another advantage is that it eliminates the need of a specified reference plane. Moreover, the power handling ability of a transmission line is at its maximum when working at a low SWR. Lines terminated by its characteristic impedance Z0 possess R and transmits power at low peak voltage. Additionally, various components in a system can be interconnected by constraining the reflection coefficients at various interfaces. This is achieved through impedance matching. Multiple reflections could yield to group delay variations that can result to unwanted intermodulation in broadband systems. Amplifiers could be damaged in case much power is reflects back to the source (Rizzi 1988).

There exist a number of factors that affect the choice of matching a given network. This includes the type of design, for instance need for simple design. Additionally, an impedance match at single frequency is easy to achieve but it is, consequently, difficult to achieve a wide bandwidth matching. Another factor to consider is that the matching network should perform ultimately despite the load changes.

There exist various methods of impedance matching namely L networks, quarter wave transformers and single stub tuners (David 1998).

Measures of Impedance Matching

Impedance matching measures include the return loss, VSWR, and the reflection coefficient.

Reflection coefficient is the measure of how much power or signal is reflected back from a terminal. It is the ratio of reflected voltage to incident voltage or the ratio of reflected current to incident current.

Return loss is obtained as a result of expressing the power reflection coefficient and voltage reflection coefficient in logarithms or logarithmic forms (David 1998).

LRT(l)=-20log10(magnitude of Ó¶(l)) = -10log10 (Ó¶(l)) (David 1998)

The table below show how measures are related.

ZL/Z0

Ó¶

LRT(dB)

VSWR

Note

Infinity

+1

0

Infinity

Open circuit

5.8470

0.7079

3

5.8470

Half power returned

3.0096

0.5012

6

3.0096

1.9248

0.3162

10

1.9248

Close to VSWR=2

1.2222

0.0100

20

1.2222

1.0653

0.0316

30

1.06253

1.0202

0.0100

40

1.0202

1

0

Infinity

1

Matched

0.9802

-0.0100

40

1.0202

0.9387

-0.0316

30

1.0653

0.8182

-0.1000

20

1.2222

0.5195

-0.3162

10

1.9248

Close to VSWR=2

0.3323

-0.5012

6

3.0096

0.1710

-0.7079

3

5.8470

Half power returned

0

-1

0

Infinity

Short circuit

If ZL is a real number, then when:

ZL/Z0Ëƒ1, ZL/Z0=VSWR;

Moreover, when ZL/Z0Ë‚1, ZL/Z0=1/VSWR (David 1998)

If ZL is a complex number, its imaginary part is not equal to zero and therefore the relationships between ZL/Z0 and VSWR do not exist (David 1998).

The Smith Chart

This chart has a number of coordinate grids which are essential in the calculation of electrical characteristics of circuits.

In smith charts, calculation of the electronic devices values required to construct an impedance matching network needs an understanding of characteristic impedance of both the load and the generator impedance. Moreover, factors like componentsâ€™ power limitations and componentsâ€™ packaging effects should be put into consideration in actual design. A device value could be determined using either numerical analysis of circuit or graphical analysis which uses a smith chart. Numerical analysis method is complex and time consuming whereas graphical analysis is easier and time saving (Tri 1981).

The original graph is shown above

Each line on a smith chart has a purpose. For instance, the straight horizontal line in the above displayed chart represents the circuitâ€™s real resistance. It, therefore, implies that the constant circles that cross the center line stand for the circuitâ€™s constant real resistance. These are the vertical reference lines in the original graph.

The arcs that are adjacent to center line represent capacitance and inductance in the circuit which are the imaginary value of the reactance. These lines are the horizontal lines of the original graph.

The smith chart has a unit circle that occupies the center of the chart. When you work with specified characteristic impedance, all reference points need to be multiplied by the impedance value and calculations computed using the new reference points.

The figure indicates the specific locations on t...

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