Editing Transmission line (section)

==General applications==

===Signal transfer===

Electrical transmission lines are very widely used to transmit high frequency signals over long or short distances with minimum power loss.  One familiar example is the [[down lead]] from a TV or radio [[Antenna (radio)|aerial]] to the receiver.

=== Transmission line circuits ===
{{main|Distributed-element circuit}}
A large variety of circuits can also be constructed with transmission lines including [[impedance matching]] circuits, [[distributed-element filter|filters]], [[power dividers and directional couplers]].

====Stepped transmission line====
{{see also|Waveguide filter#Impedance matching}}
[[Image:Segments.jpg|thumb|right|350px|A simple example of stepped transmission line consisting of three segments]]
A stepped transmission line is used for broad range impedance matching. It can be considered as multiple transmission line segments connected in series, with the characteristic impedance of each individual element to be <math>Z_\mathrm{0,i}</math>.<ref>{{cite journal |last1=Qian |first1=Chunqi |last2=Brey |first2=William W. |year=2009 |title=Impedance matching with an adjustable segmented transmission line |journal=Journal of Magnetic Resonance |volume=199 |issue=1 |pages=104–110 |bibcode=2009JMagR.199..104Q |doi=10.1016/j.jmr.2009.04.005 |pmid=19406676}}</ref> The input impedance can be obtained from the successive application of the chain relation

:<math>Z_\mathrm{i+1} = Z_\mathrm{0,i}\,\frac{\,Z_\mathrm{i} + j\,Z_\mathrm{0,i}\,\tan(\beta_\mathrm{i} \ell_\mathrm{i})\,}{Z_\mathrm{0,i} + j\,Z_\mathrm{i}\,\tan(\beta_\mathrm{i} \ell_\mathrm{i})}\,</math>

where <math>\beta_\mathrm{i}</math> is the wave number of the <math>\mathrm{i}</math>-th transmission line segment and <math>\ell_\mathrm{i}</math> is the length of this segment, and <math>Z_\mathrm{i}</math> is the front-end impedance that loads the <math>\mathrm{i}</math>-th segment.

[[Image:PolarSmith.jpg|thumb|The impedance transformation circle along a transmission line whose characteristic impedance <math>Z_\mathrm{0,i}</math> is smaller than that of the input cable <math>Z_0</math>. And as a result, the impedance curve is off-centred towards the <math>-x</math> axis. Conversely, if <math>Z_\mathrm{0,i} > Z_0</math>, the impedance curve should be off-centred towards the <math>+x</math> axis.]]
Because the characteristic impedance of each transmission line segment <math>Z_\mathrm{0,i}</math> is often different from the impedance <math>Z_0</math> of the fourth, input cable (only shown as an arrow marked <math>Z_0</math> on the left side of the diagram above), the impedance transformation circle is off-centred along the <math>x</math> axis of the [[Smith Chart]] whose impedance representation is usually normalized against <math>Z_0</math>.

==== Approximating lumped elements ====
At higher frequencies, the reactive parasitic effects of real world [[Lumped-element model|lumped elements]], including [[Inductor|inductors]] and [[Capacitor|capacitors]], limits their usefulness.<ref>{{Cite web |title=Microwaves101 {{!}} Parasitics |url=https://www.microwaves101.com/encyclopedias/parasitics |access-date=April 2, 2024 |website=Microwave Encyclopedia}}</ref>  Therefore, it is sometimes useful to approximate the electrical characteristics of inductors and capacitors with transmission lines at the higher frequencies using [[Richards' transformation|Richards' Transformations]] and then substitute the transmission lines for the lumped elements.<ref>{{Cite web |date=February 1, 2021 |title=2.12: Richards's Transformation - Engineering LibreTexts |url=https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electronics/Microwave_and_RF_Design_IV%3A_Modules_(Steer)/02%3A_Filters/2.12%3A_Richardss_Transformation |website=Engineering LibreTexts}}</ref><ref>{{Cite book |last=Rhea |first=Randall W. |url=https://archive.org/details/hffilterdesignco0000rhea/page/n5/mode/2up |title=HF Filter Design and Computer Simulation |date=1995 |publisher=McGraw-Hill, Inc. |isbn=0-07-052055-0 |pages=86–89}}</ref>

More accurate forms of [[multimode]] high frequency inductor modeling with transmission lines exist for advanced designers.<ref>Rhea, Randall W. "A Multimode High-Frequency Inductor Model", Applied Microwaves & Wireless, November/December 1997, pp. 70-72, 74, 76-78, 80, Noble Publishing, Atlanta, Georgia,</ref>

===Stub filters===
{{see also|Distributed-element filter#Stub band-pass filters}}
If a short-circuited or open-circuited transmission line is wired in parallel with a line used to transfer signals from point A to point B, then it will function as a filter. The method for making stubs is similar to the method for using Lecher lines for crude frequency measurement, but it is 'working backwards'. One method recommended in the [[Radio Society of Great Britain|RSGB]]'s radiocommunication handbook is to take an open-circuited length of transmission line wired in parallel with the [[feed line|feeder]] delivering signals from an aerial. By cutting the free end of the transmission line, a minimum in the strength of the signal observed at a receiver can be found. At this stage the stub filter will reject this frequency and the odd harmonics, but if the free end of the stub is shorted then the stub will become a filter rejecting the even harmonics.

Wideband filters can be achieved using multiple stubs.  However, this is a somewhat dated technique.  Much more compact filters can be made with other methods such as parallel-line resonators.

===Pulse generation===

Transmission lines are used as pulse generators. By charging the transmission line and then discharging it into a [[resistive]] load, a rectangular pulse equal in length to twice the [[electrical length]] of the line can be obtained, although with half the voltage. A [[Blumlein transmission line]] is a related pulse forming device that overcomes this limitation. These are sometimes used as the [[pulsed power]] sources for [[radar]] [[transmitters]] and other devices.