Solve Smith Chart Q: Input Imp, SWR, Load Pwr

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In summary, using the Smith chart, we can find the input impedance on the lossless transmission line to be 1860 - j1350 (ohms), the standing wave ratio on the main line to be 9.5, and the input power to the line to be -242W, which may not seem correct. Further calculations may be needed to confirm the accuracy of this result.
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freezer
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Homework Statement


A lossless transmission line has a characteristic impedance Z0 = 300 ohms, is 5.3 wavelength long, and is terminated in a load impedance ZL = 35 + j 25 (ohms). Find the following using Smith chart.

a) The input impedance on the line
b) The standing wave ration on the main line.
c)If the load current is 1A, calculate the input power to the line.


Homework Equations





The Attempt at a Solution



a) Zin = 300(6.2 - j4.5) = 1860 - j1350 (ohms)
b) swr = 9.5
c) I am not finding a good equation to calculate part C and not sure how you can extract this information from the chart. P= i^2 R => 35W to the load then the input would need to be 35 /0.8^2= 54.6875W
 
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  • #2
So i can get VL = 35+j25(V)

Vl = V0+(1+gamma)
35+j25/(1.8)
V0+ = 19.44+j13.89(v)

Vin = V0+(exp(-j0.6pi) + 0.8exp(j0.6pi))
Vin = 18.89+j13.70

Iin = Vo+/Zo(exp(-j0.6pi) - 0.8exp(j0.6pi)
Iin = -1.12-j33.29
Iin* = -1.12+j33.29Pav = 0.5*Re(VI*)
1/2*Re(VinIin*)
then i get -242W (this does not seem correct)

Am i getting close?
 

FAQ: Solve Smith Chart Q: Input Imp, SWR, Load Pwr

1. What is a Smith Chart?

A Smith Chart is a graphical tool used in RF and microwave engineering to solve problems related to transmission lines and impedance matching. It is named after its inventor, Phillip H. Smith, and is used to visualize complex mathematical equations involving impedance, reflection coefficient, and standing wave ratio (SWR).

2. How do I use a Smith Chart to solve for input impedance?

To solve for input impedance on a Smith Chart, first plot the complex impedance of the load on the chart. Then, draw a line from the center of the chart (representing the normalized impedance of 1 + 0j) to the point representing the load impedance. The point where this line intersects the unit circle (the outermost circle on the chart) represents the input impedance.

3. Can a Smith Chart be used to determine SWR?

Yes, a Smith Chart can be used to determine SWR. To do so, plot the load impedance on the chart and draw a line from the center to the point representing the load. The point where this line intersects the SWR circle (a circle on the chart with a radius equal to the SWR) represents the reflection coefficient. The SWR can then be calculated using the reflection coefficient.

4. How can I use a Smith Chart to solve for load power?

In order to solve for load power on a Smith Chart, you will need to know the incident power and the reflection coefficient. Once these values are known, plot the reflection coefficient on the chart and draw a line from the center to the point representing the reflection coefficient. The point where this line intersects the unit circle represents the complex power at the load. The load power can then be calculated using the complex power and the reflection coefficient.

5. What are the limitations of using a Smith Chart to solve problems?

While Smith Charts are a useful tool for solving problems related to impedance matching, they have some limitations. They are only accurate for lossless transmission lines, and they do not take into account frequency-dependent effects such as dispersion and skin effect. Additionally, they may not be as accurate for highly mismatched loads or for frequencies outside of their design range.

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