AdvancedTopic 95 of 106Electrical Engineering
Transmission line theory
Wave behaviour on lines with characteristic impedance and reflections.
In depth
Lines with distributed L and C support waves with characteristic impedance Z₀=√(L/C), velocity v=1/√(LC). Mismatch gives reflection coefficient Γ=(Z_L-Z₀)/(Z_L+Z₀) and standing waves (VSWR). Matched lines transfer all power; quarter-wave sections transform impedances.
Key points
- Lossless line formulas
- Stub matching
- Pulses reflect off open or short ends
ExampleA 50 Ω coax terminated in 75 Ω reflects 20% of voltage.
What is Transmission line theory?
Wave behaviour on lines with characteristic impedance and reflections.
Why is it important to understand transmission line theory?
Transmission line theory explains reflections and impedance matching at high frequency, where wires behave like waveguides.
Why do reflections matter?
When the load does not match the line's characteristic impedance, part of the wave reflects, reducing power delivered and causing signal distortion.
When does a line need transmission line analysis?
When the line length is a significant fraction of the wavelength, typically above about a tenth of a wavelength, so ordinary circuit rules fail.
How is Transmission line theory used in practice?
Typical applications include matching a 50 ohm antenna cable to a transmitter to avoid reflections, finding where the standing wave peaks on a long cable and designing a PCB trace with controlled impedance for a fast digital signal.
What should I learn before Transmission line theory?
Study "Poynting vector" first (topic 94 of 106 in Electrical Engineering). It covers the groundwork this topic builds on.
What are the key points of Transmission line theory?
Lossless line formulas. Stub matching. Pulses reflect off open or short ends.
Can you give an example of Transmission line theory?
A 50 Ω coax terminated in 75 Ω reflects 20% of voltage.
What comes after Transmission line theory?
The next topic is "Smith chart", which builds directly on this one.
How difficult is Transmission line theory?
It is classed as Advanced in Electrical Engineering (topic 95 of 106). It is an advanced topic. It assumes you are comfortable with the intermediate topics in Electrical Engineering.