Wavelengths along a Smith Chart

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LambdaIn summary, the question is about finding the input impedance and return loss of a loaded line at a specific distance. The solution involves deducting multiples of λ/2 and only analyzing λ/8. The purpose of this is to avoid spinning around the Smith chart multiple times. The number 4 in the solution comes from the fact that 5λ/8 - λ/2 = 4λ/8. With this understanding, the person asking the question is now clear on the solution.
  • #1
OnceMore
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Hello,

This may be something that is more mathematical than electrical, but I figured here was the best place.

I am going through a worked example, and there is something I don't understand. The question is as follows

Find the imput impedance and return loss (in dB) of the loaded line in the last question as seen at the distance l = 5λ/8 from the load

The solution states that "because the input impedance is a periodic function of the line lenth, we need to decuct all multiples of λ/2 and analyse only the remainder (λ/8)..."

Now, I understand that λ/2 is a full rotation of the Smith chart, but why is that deducted? And, if you remove λ\2, how are you left with λ\8 ...from an origianl length of 5λ/8?

The last part may just be some mathematics that is escaping me at the moment, but I just cannot get past this part.

Thanks for any advice.

-S
 
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  • #2
5/8 - 4/8 = 1/8.

You deduct it so you don't spin around the chart 4 times for nothing.
 
  • #3
Hello.

Ok, that makes sense ...but, where is the 4 coming from? I mean, why not 6 times?

-S
 
  • #4
1/2 Lambda = 4/8 Lambda.
 
  • #5
Ahh, okay ...I am with you now!

That's fantastic. Thanks for your help.

-S
 

1. What is a Smith Chart?

A Smith Chart is a graphical tool used in radio frequency (RF) engineering to analyze and design transmission lines and other RF components. It is a polar plot that represents the complex impedance of a device, allowing engineers to easily visualize and manipulate RF circuits.

2. How are wavelengths represented on a Smith Chart?

Wavelengths are represented on a Smith Chart as circles. Each circle represents a specific wavelength, with the center of the chart representing the shortest wavelength and the outer edge representing the longest wavelength.

3. What does the location of a point on a Smith Chart represent?

The location of a point on a Smith Chart represents the complex impedance of a device. The horizontal axis represents the real part of the impedance (resistance) and the vertical axis represents the imaginary part of the impedance (reactance).

4. How can a Smith Chart be used to match impedances?

A Smith Chart can be used to match impedances by adjusting the position of the point on the chart. By moving the point along the constant resistance or constant reactance circles, the impedance can be adjusted to match the desired value.

5. Can a Smith Chart be used for all types of RF circuits?

No, a Smith Chart is most commonly used for single-ended circuits. It can also be used for some types of differential circuits, but it may not accurately represent the impedance of these circuits in all cases. In these cases, other tools such as a TDR (time domain reflectometer) may be more suitable.

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