Sunday, August 1, 2021

English 101 reflection paper

English 101 reflection paper

english 101 reflection paper

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The Smith chartinvented by Phillip H. Smith — [1] [2] and independently [3] by Mizuhashi Tosaku, [4] is a graphical calculator english 101 reflection paper nomogram designed for electrical and electronics engineers specializing in radio frequency RF engineering to assist in solving problems with transmission lines and matching circuits.


However, the remainder is still mathematically relevant, english 101 reflection paper, being used, for example, in oscillator design and stability analysis. Thus most RF circuit analysis software includes a Smith chart option for the display of results and all but the simplest impedance measuring instruments can plot measured results on a Smith chart display.


The Smith chart is plotted on the complex reflection coefficient plane in two dimensions and is scaled in normalised impedance the most commonnormalised admittance or both, using different colours to distinguish between them. These english 101 reflection paper often known as the Z, Y and YZ Smith charts respectively. The most commonly used normalization impedance is 50 ohms. Once an answer is obtained english 101 reflection paper the graphical constructions described below, it is straightforward to convert between normalised impedance or normalised admittance and the corresponding unnormalized value by multiplying by the characteristic impedance admittance.


Reflection coefficients can be read directly from the chart as they are unitless parameters, english 101 reflection paper. The Smith chart has a scale around its circumference or periphery which is graduated in wavelengths and degrees. The wavelengths scale is used in distributed component problems and represents the distance measured along the transmission line connected between the generator or source and the load to the point under consideration.


The degrees scale represents the angle of the voltage reflection coefficient at that point. The Smith chart may also be used for lumped-element matching and analysis problems. Use of the Smith chart and the interpretation of the results obtained using it requires a good understanding of AC circuit theory and transmission-line theory, both of which are prerequisites for RF engineers.


As impedances and admittances change with frequency, problems using the Smith chart can only be solved manually using one frequency at a time, the result being represented by a point. Provided the frequencies are sufficiently close, the resulting Smith chart points may be joined by straight lines to create a locus. A locus of points on a Smith chart covering a range of frequencies can be used to visually represent:.


The accuracy of the Smith chart is reduced for problems involving a large locus of impedances or admittances, although the scaling can be magnified for individual areas to accommodate these. The SI unit of impedance is the ohm with the symbol of the upper case Greek letter omega Ω and the SI unit for admittance is the siemens with the symbol of an upper case letter S.


Normalised impedance and normalised admittance are dimensionless, english 101 reflection paper. Actual impedances and admittances must be normalised before using them on a Smith english 101 reflection paper. Once the result is obtained it may be de-normalised to obtain the actual result, english 101 reflection paper. Using complex exponential notation:.


All terms are actually multiplied by this to obtain the instantaneous phasebut it is conventional and understood english 101 reflection paper omit it. For the loss free case therefore, the expression for complex reflection coefficient becomes. This equation shows that, for a standing wave, the complex reflection coefficient and impedance repeats every half wavelength along the transmission line. The complex reflection coefficient is generally simply referred to as reflection coefficient.


The outer circumferential scale of the Smith chart represents the distance from the generator to the load scaled in wavelengths and is therefore scaled from zero to 0.


and the normalised impedance of the english 101 reflection paper represented by the lower case zsubscript T. These are the equations which are used to construct the Z Smith english 101 reflection paper. They both change with frequency so for any particular measurement, the frequency at which it was performed must be stated together with the characteristic impedance. Any actual reflection coefficient must have a magnitude of less than or equal to unity so, at the test frequency, this may be expressed by a point inside a circle of unity radius.


The Smith chart is actually constructed on such a polar diagram. The Smith chart scaling is designed in such a way that reflection coefficient can be converted to normalised impedance or vice versa. Using the Smith chart, the normalised impedance may be obtained with appreciable accuracy by plotting the point representing the reflection coefficient treating the Smith chart as a polar diagram and then reading its value directly using the characteristic Smith chart scaling.


This technique is a graphical alternative to substituting the values in the equations. By substituting the expression for how reflection coefficient changes along an unmatched loss-free transmission line.


for the loss free case, into the equation for normalised impedance in terms of reflection coefficient. yields the impedance-version transmission-line equation for the loss free case: [11]. Versions of the transmission-line equation may be similarly derived for the admittance loss free case and for the impedance and admittance lossy cases.


The path along the arc of the circle represents english 101 reflection paper the impedance changes whilst moving along the transmission line. In this case the circumferential wavelength scaling must be used, remembering that this is the wavelength within the transmission line and may differ from the free space wavelength.


If a polar diagram is mapped on to a cartesian coordinate system it is conventional to measure angles relative to the positive x -axis using a counterclockwise direction for positive angles. The magnitude of a complex number is the length of a straight line drawn from the origin to the point representing it.


The region above the x-axis represents inductive impedances positive imaginary parts and the region below the x -axis represents capacitive impedances negative imaginary parts.


If the termination is perfectly matched, the reflection coefficient will be zero, represented effectively english 101 reflection paper a circle of zero radius or in fact a point at the centre of the Smith chart. If the termination was a perfect open circuit or short circuit the magnitude of the reflection coefficient would be unity, all power would be reflected and the point would lie at some point on the unity circumference circle.


The normalised impedance Smith chart is composed of two families of circles: circles of constant normalised resistance and circles of constant normalised reactance. In the complex reflection coefficient plane the Smith chart occupies a circle of unity radius centred at the origin. Substituting these into the equation relating normalised impedance and complex reflection coefficient:. This is the equation which describes how the complex reflection coefficient changes with the normalised impedance and may be used to construct both families of circles.


The Y Smith chart is constructed in a similar way to the Z Smith chart case but by expressing values of voltage reflection coefficient in terms of normalised admittance instead of normalised impedance. The normalised admittance y T is the reciprocal of the normalised impedance z Tso. The Y Smith chart appears like the normalised impedance type but with the graphic scaling rotated through °, english 101 reflection paper, the numeric scaling remaining unchanged. The region above the x english 101 reflection paper represents capacitive admittances and the region below the x -axis represents inductive admittances.


Capacitive admittances english 101 reflection paper positive imaginary parts and inductive admittances have negative imaginary parts. Again, if the termination is perfectly matched the reflection coefficient will be zero, represented by a 'circle' of zero radius or in fact a point at the centre of the Smith chart.


If the termination was a perfect open or short circuit the magnitude of the voltage reflection coefficient would be unity, all power would be reflected and the point would lie at some point on the unity circumference circle of the Smith chart.


A point with a reflection coefficient magnitude 0. The length of the line would then be scaled english 101 reflection paper P 1 assuming the Smith chart radius to be unity. For example, if the actual radius measured from the paper was mm, the length OP 1 would be 63 mm. The following table gives some similar examples of points which are plotted on the Z Smith chart. For each, the reflection coefficient is given in polar form together with the corresponding normalised impedance in rectangular form.


The conversion may be read directly from the Smith chart or by substitution into the equation. English 101 reflection paper RF circuit and matching problems sometimes it is more convenient to work with admittances representing conductances and susceptances and sometimes it is more convenient to work with impedances representing resistances and reactances.


Solving a typical matching problem will often require several changes between both types of Smith chart, using normalised impedance for series elements and normalised admittances for parallel elements. For these a dual normalised impedance and admittance Smith chart may be used.


Alternatively, one type may be used and the scaling converted to the other when required. In order to change from normalised impedance to normalised admittance or vice versa, english 101 reflection paper, the point representing the value of reflection coefficient under consideration is moved through exactly degrees at the same radius.


For example, the point P1 in the example representing a reflection coefficient of 0. To graphically change this to the equivalent normalised admittance point, say Q1, a line is drawn with a ruler from P1 through the Smith chart centre to Q1, an equal radius in the opposite direction.


This is equivalent to moving the point through a circular path of exactly degrees, english 101 reflection paper. Performing the calculation. Once a transformation from impedance to admittance has been performed, the english 101 reflection paper changes to normalised admittance until a later transformation back to normalised impedance is performed.


The table below shows examples of normalised impedances and their equivalent normalised admittances obtained by rotation of the point through °. Again, these may be obtained either by calculation or using a Smith chart as shown, converting between the normalised impedance and normalised admittances planes. The choice of whether to use the Z Smith chart or the Y Smith chart for any particular calculation depends on which is more convenient.


Impedances in series and admittances in parallel add while impedances in parallel and admittances in series are related by a reciprocal equation. Dealing with the reciprocalsespecially in complex numbers, is more time consuming and error-prone than using linear addition. In general therefore, most RF engineers work in the plane where the circuit topography supports linear addition. The following table gives the complex expressions for impedance real and normalised and admittance real and normalised for each of the three basic passive circuit elements : resistance, inductance and capacitance.


Using just the characteristic impedance or characteristic admittance and test frequency an equivalent circuit can be found and vice versa. Here the electrical behaviour of many lumped components becomes rather unpredictable. This occurs in microwave circuits and when high power requires large components in shortwave, FM and TV Broadcasting. For distributed components the effects on reflection coefficient and impedance of moving along the transmission line must be allowed for using the outer circumferential scale of the Smith chart which is calibrated in wavelengths.


The following example shows how a transmission line, terminated with an arbitrary load, may be matched at one frequency either with a series or parallel reactive component in each case connected at precise positions.


How may the line be matched? From the table above, the reactance of the inductor forming part of the termination at MHz is. This is plotted on the Z Smith chart at point P As the transmission line is loss free, a circle centred at the centre of the Smith chart is drawn through the point P 20 to represent the path of the constant magnitude reflection coefficient due to the termination. At point P 21 the circle intersects with the unity circle of constant normalised resistance at. Since the transmission line is air-spaced, the wavelength at MHz in the line is the same as that in free space and is given by.


To match the termination at MHz, a series capacitor of 2. An alternative shunt match could be calculated after performing a Smith english 101 reflection paper transformation from normalised impedance to normalised admittance. Point Q 20 is the equivalent of P 20 but expressed as a normalised admittance, english 101 reflection paper. Reading from the Smith chart scaling, remembering that this is now a normalised admittance gives. In fact this value is not actually used. The earliest point at which a shunt conjugate match could be introduced, moving towards the generator, would be at Q 21the same position as the previous P 21but this time representing a normalised admittance given by, english 101 reflection paper.


From the table it can be seen that a negative admittance would require an inductor, english 101 reflection paper, connected in parallel with the transmission line.




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english 101 reflection paper

A point with a reflection coefficient magnitude and angle 60° represented in polar form as, is shown as point P 1 on the Smith chart. To plot this, one may use the circumferential (reflection coefficient) angle scale to find the graduation and a ruler to draw a line passing through this and the centre of the Smith chart. The length of the line would then be scaled to P 1 assuming the It comes with instructions for how to use it, 6 months of daily, monthly and weekly review sheets, finance, savings, goals trackers and calendars. It also includes a sample pack of other pages that can be bought eg - Pomodoro planner, Cornell notes, blank, dot grid and graph paper. The paper Final Reflection - English Foundations of Writing -Wemple. Tweet. Kellie Nash. English ePortfolio: Final Reflection. Review. Profile. I learned to make sure to take certain audiences into consideration when writing a paper and to make sure I use reliable resources to support my ideas in each essay. There are also areas in writing

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