Engineering Order (Essay Sample)

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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/Z0˃1, 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 components’ power limitations and components’ 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 circuit’s real resistance. It, therefore, implies that the constant circles that cross the center line stand for the circuit’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 the chart used to identify the type of devices and values.
A thorough examination of the above chart reveals that capacitors which usually have negative values of impedance on the impedance chart are represented below the center line. Inductors usually have positive values of impedance on the chart and are, therefore, represented above the center line.
In the essence, there exist two forms of smith chart namely admittance chart and impedance chart as figured below.
A close examination of the two charts indicates that an admittance chart is a mirrored image of impedance chart since the reciprocal of impedance is admittance and due to this reciprocal relation, "j" values signs are opposite.
In the design of circuits, it is good to overlay the admittance chart and the impedance chart as shown below.
The figure of overlain impedance and admittance charts.
In as much as it is convenient to overlay charts, it’s hard to work with this and in such cases transparencies are employed with the help of computer programs which enables the transferring of information.
Admittance and impedance charts are essential in the computation of component values for devices required in various impedance matching circuits. The admittance chart, usually, calculates the component values for shunt elements whereas the impedance charts calculates device values for series elements in an impedance matching circuit.
The use of admittance chart means using the shunt (parallel) devices whereas the use of impedance charts indicates the use of series components. For instance, in the figure below indicates that on an impedance chart, a clockwise direction move along the real axis implies that we need to add a series inductor. On the other hand, the anticlockwise direction movement along the real axis requires that we add a series capacitor.
Illustration of how to use Impedance chart
For further understanding of how the charts work, I would use an example of the figure shown below whose load impedance at point A is 10-j20Ω. To make this load a real and pure resistance of 10Ω, we could eliminate the capacitance value of - j20Ω by adding the inductance value of +j20Ω.
This is an example of how adding a series inductor value results in a clockwise direction movement of the chart.
In the figure below, point B has a load impedance of 10+j20Ω and addition of a series capacitor of- j20Ω results to impedance of 10+j0Ω.
The figure above shows how to add a series capacitor which results to anticlockwise direction movement in the chart.
Illustration of how to use admittance chart
Whenever an admittance chart is used, we focus on the shunt devices. If we move in an anticlockwise direction along the real axis, we will, consequently, add a shunt inductor. If we move in a clockwise direction, we will add a shunt capacitor.
To illust...