Transmission Line Length for Real Input Impedance?

In summary, the conversation discusses a transmission line with a known characteristic impedance and an antenna with a complex impedance. The main concern is determining the minimum length of the line to achieve a real input impedance. The participant also mentions a formula involving the reflection coefficient and complex numbers. However, they were able to answer their own question in the end.
  • #1
sandy.bridge
798
1

Homework Statement


Hey guys. I have a transmission line with a known characteristic impedance (50 Ω) of length L that is connected to an antenna that has a complex impedance of (50-j25)Ω.

I am having extreme difficulty determining the minimum length (expressed in wavelengths) of line such that the input impedance is real.

Let τ denote the reflection coefficient.

I know that for the input impedance to have no complex component that (1+τ*e^(-jx))/(1-τ*e^(-jx)) should result in complex components vanishing. However, this is a rather complicated formula to solve in the state that it is in because both e^(-jx) and τ are complex numbers.

Am I missing something here?
 
Physics news on Phys.org
  • #2
Fortunately I was able to answer my own question. Thanks anyway!
 

FAQ: Transmission Line Length for Real Input Impedance?

What is a transmission line with load?

A transmission line with load is a type of electrical circuit that is used to transfer electrical energy from one point to another. The load is the device or system that consumes the energy, and the transmission line is the physical medium through which the energy is transferred.

How does a transmission line with load work?

A transmission line with load works by creating a flow of electrical energy from a source to a destination. The source generates the energy, and the transmission line carries it to the load, which then consumes it. The load can be any type of electrical device, such as a motor, light bulb, or computer.

What are the components of a transmission line with load?

A transmission line with load typically consists of three main components: a power source, a transmission line, and a load. The power source can be a generator or a battery, the transmission line is usually made of conductive material such as copper or aluminum, and the load can be any type of electrical device or system.

What is the purpose of a transmission line with load?

The main purpose of a transmission line with load is to efficiently transfer electrical energy from a power source to a load. It helps to minimize energy loss and maintain a stable flow of electricity, which is essential for the proper functioning of electrical devices and systems.

How can the performance of a transmission line with load be improved?

The performance of a transmission line with load can be improved by using higher quality materials for the transmission line, reducing the length of the transmission line, and properly matching the impedance of the load to the transmission line. Regular maintenance and monitoring of the circuit can also help to improve its performance.

Similar threads

Smith Chart: Find Input Impedance for Antenna Problem
Replies
2
Views
2K
Lossless transmission line question
Replies
4
Views
3K
Engineering Voltage pulse sketches for reflection on a lossless transmission line
Replies
18
Views
2K
Reflection factor for a microstrip transmission line
Replies
7
Views
2K
Transmission line input impedance
Replies
11
Views
8K
How to Simplify Backward Impedance Matching Equations?
Replies
1
Views
1K
How to Calculate Transmission Line Coefficients?
Replies
4
Views
3K
Transmission Line Homework - Determine Input Impedance
Replies
5
Views
3K
Electrical Engineering, power system, transmission line
Replies
10
Views
2K
A ##50\Omega## lossless transmission line impedance question
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top