# What is Impedance Inversion in Transmission Line

1. Jun 1, 2014

### shayaan_musta

Hello to experts!

What is impedance inversion in quarter wave transformer?

I need definition not a concept, not explanation, not description. But a precise and point definition.

Thank you very much.

2. Jun 1, 2014

3. Jun 1, 2014

### shayaan_musta

These slides are made from the book electronic communication systems by keneddy and davis. I have already that book. I read but didn't understand. That book provides explanation directly without any definition. Let say, if someone ask me to define the what is impedance inversion by quarter-wave transformer then what should be my words to define it?

Did you get what I want sir?

Last edited by a moderator: May 6, 2017
4. Jun 1, 2014

### sophiecentaur

Are you trying to get answers to some weird question paper? There are not 'definitions' for these things. You seem to be seeking an answer and not an understanding, which seems a rather pointless exercise. What do you already know about transmission lines? You need to spend some time reading (and not just skimming for key words) some of the information in Wiki. No pain no gain.

PS that page Jim referred you to tells you plenty. Sometimes you need to accept information in terms other than what you are initially demanding. You have to make an effort at comprehension.

5. Jun 1, 2014

### jim hardy

The term comes from the standing wave traits of transmission lines, wherein the apparent impedance at any point is a function of two values:
the ratio of the line's characteristic impedance Z0 to its terminating impedance ZLoad
and one's position along the line.

The algebra involved is awful looking but i made my way through it decades ago (and changed my minor to Nuclear)

For a quarter wave ,

which is an inversion

note that a quarter wave open stub ( Zload = infinite ) behaves as a short circuit , Zin = 0
and that's the inversion.
Now - Smith Charts are the layman's way to solve transmission line problems.
It's not a one-minute task to learn their use.

But here's some reading:
http://www.rle.mit.edu/per/JournalPapers/JPtpejul07p1531.pdf
http://emcesd.com/pdf/zin-eqckt.pdf
http://www.authorstream.com/Present...ission-Lines-li-Entertainment-ppt-powerpoint/ slides 35 and 36 in particular
http://en.wikipedia.org/wiki/Quarter-wave_impedance_transformer

So were i asked for a brief description of "Impedance Inversion" i'd say

In my high school class we built a transmission line of two parallel wires maybe fifteen feet long and three inches apart. We built an instrumented trolley to ride on the wires with both capacitive and inductive pickups, so we could plot the standing waves of voltage and current.
We studied this 'transformer ' effect but called it by that name , not inversion.
Then we learned to use Smith charts.
So when we studied the same subject in 3rd year EE i had an advantage in visualizing those awful looking algebra equations .

It's important to visualize those standing waves along the line and realize that impedance DOES vary with position, but only if there's a standing wave. Each term in those ornate equations has a physical counterpart. At a point along the line where voltage is low and current high, Z is low and vice versa. That's how you "transform" - pick your spot.

It's not a one-minute subject.
I really urge you to get some Smith Charts and become proficient at using them. Because the phase inverts too. And remember - no mismatch, no standing wave to transform with.

Note to any educators reading this - our 'trolley' experiment really gave a lot of high school boys a head start.

old jim

Last edited: Jun 1, 2014
6. Jun 1, 2014

### jim hardy

When starting out with computers i was frustrated by the authors' habit of defining things in terms of other terms they hadn't bothered to define.

The trouble is it requires a certain amount of vocabulary, that is acquaintance with the basic concepts and the names for the basic principles, to speak meaningfully.

The briefest answer is zin= 1/zload at $\Lambda$ = $\frac{1}{4}$

which, lacking a decent introduction is pure jabberwocky.