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awan
Joined: 11 Jun 2004
Posts: 104
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 22 Jun 2004 8:42 microwave |
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| please tell me the phenomenon behind smith chart
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rudane
Joined: 26 Mar 2004
Posts: 38
Helped: 5
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23 Jun 2004 6:10 Re: microwave |
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| There is no phenomenon behind a smith chart. It's simply a plot of the valid equations for microwave systems. This allows us to draw on the chart instead of using math to figure out the problem. I'm sure the people who use smith charts daily appreciate not having to resort to Maxwell's equations (an electrical engineer's nightmare, as I'm told).
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zanov
Joined: 09 Jun 2004
Posts: 61
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23 Jun 2004 7:13 Re: microwave |
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| awan wrote: |
| please tell me the phenomenon behind smith chart |
even if you search google for Smith Chart tutorial I bet you would receive hundred of websites. Look there.
cheers.
zanove.
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Google
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23 Jun 2004 7:13 Ads |
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dicket
Joined: 04 Jun 2004
Posts: 23
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24 Jun 2004 11:23 Re: microwave |
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| It's a kind of expression of the transmission line theory.
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a_aziz
Joined: 04 Jan 2005
Posts: 73
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13 Jan 2005 10:38 microwave |
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hi.
The smith chart is not a phenomenon.This chart can very simply the calculations in microwave such as the impedance, admitance, and S parameters.
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Borber
Joined: 01 Jan 1970
Posts: 1561
Helped: 117
Location: Slovenia
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13 Jan 2005 11:00 Re: microwave |
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Smith chart is nothing but transformation of cartesian coordinate system for positive real axe of impedance or reflexion coeficient plane in to diagram where zero and infinite values of real and imaginary axes are presented on single drawing. This is achieved by using transformation formula.
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aboozar.hamidipoor
Joined: 21 Dec 2004
Posts: 192
Helped: 29
Location: Iran
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13 Jan 2005 16:58 Re: microwave |
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Smith chart is used generally for simplification of solving the transmition lines problems . the best advantage of it is visualization solving . the phenomenon behind it is summerized in wave length calculation . in smith chart you can calculate all problems in field of transmition lines only in a circle which has a unit
radius and enviroment = λ/4π .
you can find more explanations in text book .
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jinhaozi
Joined: 08 Jul 2002
Posts: 47
Helped: 1
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15 Jan 2005 15:29 Re: microwave |
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| awan wrote: |
| please tell me the phenomenon behind smith chart |
The best way to understand smith chart is refer to a classic microwave book, such as "Microwave engineering" wirrten by D.M.Pozar, or use google
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xxargs
Joined: 28 Jul 2002
Posts: 231
Helped: 44
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16 Jan 2005 3:47 Re: microwave |
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| awan wrote: |
| please tell me the phenomenon behind smith chart |
One of very usefull chart in engineering world simular lin/log-chart
but little more advanced 'shrinking' of chart-axes
Smith chart using (if rember rigth) möbius-transform
(moebius-transform for english) for 'distording' axes from
Z-plane (impedance plane) to a representation in the reflection
coeffecient plane called Γ- plane (gamma-plane) on the relation:
Γ = ( (Z - Zo) / (Z + Zo)) [1.1]
Γ = gamma
Z = Impedances
Zo = referens Impedance
and all this a complex value simular
Z = R + jX in impedance plane
and
Γ = U + jV in gamma plane
(but you can try real value on Z and finding value 0 < Z < Zo
going from -1 to 0, and value Zo < Z < ∞ from 0 to 1 on real axis)
ie:
Zo = 50
if Z = 100 => 0.33333....
if Z = 25 => -0.33333...
if Z = 50 => 0 (middle of chart)
ie whole positive real number resistance between zero and infinity
going into -1 to +1 interval on real axis and 0 to +/- infinity on
imaginary axes build a unit circle around ' -1 to +1' real axes.
negative impedances (=gain) give point a outside
on unit circle and uses for example stability circle...
(if you have advanced calculator with complex support or
use mathcad or mathematica on PC, can try this with complex
argument to make at sense how equations work)
And easly convert from Γ-plane to Z-plane with
Z = Zo * ( (1 + Γ ) / ( 1 - Γ) ) [1.2]
and operations tricky to make on impedance plane
is a easy make on Γ-plane and vice verse
and uses lot of this calculate inside vector network
analyser
for example is as easy to rotate value in Γ-plane with
delay with Γ * e^j2d, d = insert pice of Zo coaxial cable
between measure port and complex load, measured in electrical
phase shift lengd (radians) and convert back to Impedance-plane
and recive new value on R and X on load after change.
example (calculate with hp42s...)
(in 50 Ohm system)
We using impedanse of 100 Ohm and 45 degree on load
and after transform [1.1] to Γ = U + jV = 0.3832+j0.3613
in retangular notation (0.5267e^ j43.3139 degree in polar notation)
I using pice of 50 Ohm transmissionline for total delay
of 136.68 degree
and add delay angle to Γ in polar notation way
Γ * e^j136.68 degree = 0.5267e^j43.3139 * e^j136.68
= 0.5267e^j180 degree or -0.5267 + j0 in retangular mode
- ie pure real value
transform back to impedance plane with [1.2]
and give 15.5 Ohm and 0 degree
With 136.68 degree lenght of 50 ohm cable I transform
load impedance from 100 Ohm and 45 degree to 15.5 Ohm
real impedances.
after this in impedances moved to pure real axe, can use quarterwave
transformer to convert from 15.5 Ohm to 50 Ohm with
√ (50 * 15.5) = 27.83 Ohm quarterwave piece of transmission line
(Very common methode using delays and stub for ex.
impedance matching)
------------------------------------------------------------------
If you using a lossy line - use Γ * e^γd
d = distance fraktion of 'γ' - measure unit (m, km, ft etc.)
γ = α + jβ =√ ((r + jωl) * (g + jωc))
α = attenuation in neper (1 neper = 8.686 dB) per unit
β = propagation constant (phase shift) in radians per unit
and Z = Zo = √ (( r + jωl) / (g + jωc) )
example:
Γ * e^γd = Γ * e^d (α + jβ) = Γ * e^αd * e^jβd
d = 1
Γ = 0.5267e^ j43.3139
α = -0.1 (0.8686 dB loss)
β = 136.68 degree (2.39 rad)
Γ * e^α * e^jβ = e^-0.1 * e^j136.68 = Γ * 0.9048 * e^j136.68 =
= 0.4766e^-180
using [1.2] and give 17.72 Ohm real impedance and difference
between calculate on lossy free line and lossy line is a 2.2 Ohm
on result.
most of microwave litterature calculate only with lossless line
in example for simplify and clearty (and often missing completly
example with lossy line...)
- but in real world and experiment lab is always need thinking
with lossy line, special in high frequency also on short distance
transmissions line...
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Read microwave-books and most of these discuss transmissions
line and Smith Chart one or two chapter ie. essential tool for
practical microwave enginering.
HP:s application note '95' is more or less famous
in disscussion on S-parameters and Smithchart
(I have tidy typesetting book from 1968, but i know you can find
ugly, flashing, tasteless powerpoint-style version of this on
Agilent web... )
Find 'Microwave transistors Amplifiers, analys and design,
Guillermo Gonzalez' - I know discuss Smitchart inside book.
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Old - but still working and more or less most complete and high detailed
version of printable Smith chart - is written in commented Postsctript
if you want to analyse how do calculate and print out this.
(sending up here depend to harder and harder over time to find working
version on this type of file on Internet)
take only 22 kbyte in filesize and possibly to rescale in any size
and possible to modifying and/or convert to eps with GSview
to import document to LaTeX, MS-word etc. .
here in 3 versions , Z = RX (impedance chart), Y = GB (admittance chart),
RXGB (impedance/admittance on same chart)
Need Gsview and Ghostscript installed on computer to view
this chart or PS-printer if printing on paper - also possible
convert to pdf via acrobat distiller (i trying and this working).
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si14
Joined: 27 Sep 2006
Posts: 1061
Helped: 664
Location: North America
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05 Oct 2006 3:08 Re: microwave |
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says:
I am personally not a big fan of smith charts, but they have some historical value, are commonly used in
network analyzers, and they allow you to plot infinite change in impedance in a finite area.
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ihteshamhaider
Joined: 28 Sep 2006
Posts: 3
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05 Oct 2006 5:13 Re: microwave |
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| Smith chart is a polar plot of impedances, it is used to find stub , input impedance , reflection coefficient, swr, quickly without having to solve equations..
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