Impedance Matching Coaxial Cables

In summary: As for the calculation part, it looks like you have the right idea. Just make sure you are using the correct values for the dimensions and units. In summary, we discussed the question of how to connect two coax cables with the same dielectric but different dimensions in order to match two lines. The solution involves calculating the radius of the outer conductor of the second line using the characteristic impedance equation Zc=sqrt(μ/ε)((ln(b/a))/(2∏)). We also considered how the velocity of wave propagation and characteristic impedance would change if the dielectric was removed. It was determined that the velocity would decrease and the characteristic impedance would increase. It was also clarified what is meant by two transmission lines being "matched".
  • #1
DODGEVIPER13
672
0

Homework Statement


We need to connect two coax cables with the same dielectric (εr = 9) but
with different dimensions as shown. How big must be the radius of the
outer conductor of the second line in order to match two lines?

How would the velocity of the wave propagation change, if we remove
the dielectric? What’s about the characteristic impedance?


Homework Equations


Zc=sqrt(μ/ε)((ln(b/a))/(2∏))
μ=μrμ0
ε=εrε0

The Attempt at a Solution


I so far have uploaded my answer to the radius part am I right? For the last conceptual parts I am not sure and need a bit of help.
 

Attachments

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  • #2
For the conceptual part I am thinking that the velocity would decrease because Vp=C/(sqrt(με) so if the dielectric is removed the denominator will decrease and will lead to a faster propaagation. Furthermore the characteristic impedance is sqrt(μ/ε) so it will increase too.
 
  • #3
First, what is implied when two transmission lines of different characteristic impedance are "matched"? In regards to the conceptual question, it looks like you have the right idea.
 
  • #4
Zl=sqrt(μ/ε)(((ln(b/a))/(2∏))=sqrt(μ/ε)((ln(b2/a2))/(2∏)) so I can cancel 2 pi and sqrt(μ/ε) and both natural logs giving b1/a1=b2/a2 solving for b2 I get 12 mm is it still wrong I am lost?
 
  • #5
I wasn't implying that it was wrong I was just seeing if you understood what was meant conceptually by impedance matching.
 

1. What is impedance matching in coaxial cables?

Impedance matching in coaxial cables refers to the process of ensuring that the impedance of the cable matches the impedance of the source and the load. This is important for minimizing signal loss and maximizing the efficiency of the transmission.

2. Why is impedance matching important in coaxial cables?

Impedance matching is important in coaxial cables because it helps to prevent signal reflections, which can cause interference and reduce the quality of the transmitted signal. It also helps to minimize signal loss and ensure that the maximum amount of power is transferred from the source to the load.

3. How is impedance matching achieved in coaxial cables?

Impedance matching is achieved in coaxial cables by using components such as resistors, capacitors, and inductors to adjust the overall impedance of the system. This can be done by selecting the appropriate cable and connectors, as well as using impedance matching devices such as baluns or transformers.

4. What are the consequences of not having impedance matching in coaxial cables?

If impedance matching is not achieved in coaxial cables, it can result in signal reflections, which can cause interference and reduce the quality of the transmitted signal. It can also lead to increased signal loss and reduced efficiency, as well as potential damage to the equipment or components involved in the transmission.

5. How do I know if my coaxial cables have proper impedance matching?

To determine if your coaxial cables have proper impedance matching, you can use a network analyzer or a reflectometer to measure the return loss or standing wave ratio (SWR) of the cable. If the return loss is low and the SWR is close to 1, then the cable has good impedance matching.

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