Re: relection coefficient?

From: Ray Anderson (reanderson_at_sbcglobal.net)
Date: 09/05/04 

Date: Sun, 05 Sep 2004 01:59:53 GMT

John Woodgate wrote:

.
>
> The reflection coefficient is always positive, and so the equation
> should be written R = |(Z1 - Zo)/(Z1 + Zo)|. |...| is the 'modulus'
> sign, indication that the answer is to be taken as positive, even if it
> isn't.
>

Consider a TDR, an instrument that measures the reflection coefficient
of a DUT.

If the DUT is, for example, a transmission line which is open circuited
at the far end then the reflected signal will be reflected from the open
circuit in phase with the incident signal and its amplitude will be a
function of the reflection coeeficient (a positive value in this case).

Now consider the same TDR connected to a the same transmission line that
is short circuited at the far end. The signal will be reflected from the
  short circuit out of phase with the incident signal (i.e. it will
exhibit a negative reflection coefficient).

The above example cite the extreme boundary conditions (open and short),
however you will see the same effects for intermediate cases where the
load is either > Zo or < Zo.

The sign of rho (the reflection coefficient) does make a difference and
it isn't common practice to only use only the absolute value of rho.

See http://cnx.rice.edu/content/m11379/latest/ for a graphic explanation
on how the reflection coefficient (both postive and negative values) are
used in a "Bounce Diagram" to illustrate how an incident signal's
amplitude varies as it bounces back and forth on a transmission line
with various source and load impedances. For Bounce Diagrams to work you
need to consider the sign of rho.

-Ray

Relevant Pages

  • Re: Analyzing Stub Matching with Reflection Coefficients
    ... in Reflections concerning the analysis of stub matching procedures using reflection coefficients are ... applicable only in cases where the transmission line is either lossless, ... SWR and the angle of the voltage reflection coefficient. ... Consider these two examples of a virtual short circuit: ...
    (rec.radio.amateur.antenna)
  • Analyzing Stub Matching with Reflection Coefficients
    ... in Reflections concerning the analysis of stub matching procedures using reflection coefficients are ... SWR and the angle of the voltage reflection coefficient. ... Consider these two examples of a virtual short circuit: ... between the source voltage wave incident on the input and the reflected voltage wave returning to ...
    (rec.radio.amateur.antenna)
  • Re: Convert reflection coefficient to Z
    ... Owen, for historical accuracy, at least in the US, prior to 1950, rho, sigma, and S were used to represent ... ASA Y10.9-1953, that rho is to replace upper case lambda as the standard symbol for reflection coefficient, ...
    (rec.radio.amateur.antenna)
  • Re: Convert reflection coefficient to Z
    ... Owen, for historical accuracy, at least in the US, prior to 1950, rho, sigma, and S were used to represent ... ASA Y10.9-1953, that rho is to replace upper case lambda as the standard symbol for reflection coefficient, ...
    (rec.radio.amateur.antenna)
  • Re: Convert reflection coefficient to Z
    ... reflection coefficient, and SWR to represent standing wave ratio. ... I write Gamma to mean ... rho for the magnitude of Gamma, lambda for wavelength, don't use Lambda ...
    (rec.radio.amateur.antenna)
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