Voltage Reflection Coefficient Question

[Bitrex]

In Wes Hayward's book "Introduction to Radio Frequency Design" on page
116, the voltage reflection coefficient is given as gamma = V-/V+ =
(z-1)/(z+1) where z is the normalized impedance, Zin/Z_o. As an
example, the author then takes a circuit comprised of a 2 volt source
into a voltage divider to calculate the output voltage based on
reflected voltage waves. For example, with a source resistance of 1 ohm
and a load resistance of 0.5 ohm, gamma = (0.5 -1)/(0.5 +1) = -0.333.
The forward wave is said to be 1 and the reverse wave is -0.333 leaving
a sum of 0.667, which is the same thing you would get using the voltage
divider equation: (2*0.5)/(0.5+1) = 0.667.

My point of confusion is that this example only seems to work with a
source voltage of 2 volts. Why does a 2 volt supply cause the forward
wave to be 1? I'm probably missing something obvious, but could use some
insight.

 

[Andrew Holme]

"Bitrex" <bitrex@de.lete.earthlink.net> wrote in message
news:gPudnRJ1dJ5-M8bRnZ2dnUVZ_rydnZ2d@earthlink.com...

In Wes Hayward's book "Introduction to Radio Frequency Design" on page
116, the voltage reflection coefficient is given as gamma = V-/V+ =
(z-1)/(z+1) where z is the normalized impedance, Zin/Z_o. As an example,
the author then takes a circuit comprised of a 2 volt source into a
voltage divider to calculate the output voltage based on reflected voltage
waves. For example, with a source resistance of 1 ohm and a load
resistance of 0.5 ohm, gamma = (0.5 -1)/(0.5 +1) = -0.333. The forward
wave is said to be 1 and the reverse wave is -0.333 leaving a sum of
0.667, which is the same thing you would get using the voltage divider
equation: (2*0.5)/(0.5+1) = 0.667.

My point of confusion is that this example only seems to work with a
source voltage of 2 volts. Why does a 2 volt supply cause the forward
wave to be 1? I'm probably missing something obvious, but could use some
insight.

If there's a voltage V across a matched resistive load R connected via a
transmission line of characteristic impedance R to a generator with a source
impedance R, the Thevenin equivalent of the generator is a voltage soure of
e.m.f. 2*V in series with a source resistance R. The open-circuit voltage
across the generator output would be 2*V if you disconnected the load.

 

[Fred Abse]

On Fri, 06 Aug 2010 02:34:48 -0400, Bitrex wrote:

In Wes Hayward's book "Introduction to Radio Frequency Design" on page
116, the voltage reflection coefficient is given as gamma = V-/V+ =
(z-1)/(z+1) where z is the normalized impedance, Zin/Z_o. As an
example, the author then takes a circuit comprised of a 2 volt source
into a voltage divider to calculate the output voltage based on
reflected voltage waves. For example, with a source resistance of 1 ohm
and a load resistance of 0.5 ohm, gamma = (0.5 -1)/(0.5 +1) = -0.333.
The forward wave is said to be 1 and the reverse wave is -0.333 leaving
a sum of 0.667, which is the same thing you would get using the voltage
divider equation: (2*0.5)/(0.5+1) = 0.667.

My point of confusion is that this example only seems to work with a
source voltage of 2 volts. Why does a 2 volt supply cause the forward
wave to be 1? I'm probably missing something obvious, but could use some
insight.

I don't have access to a copy of the book you quote, but, assuming that
you've quoted correctly, I've never before seen such a poor "explanation".

The use of "gamma" for reflection coefficient, rather than the usual
"rho", casts doubt over the author's familiarity with the subject.

Transmission lines can have reflections, resistive voltage dividers don't,
and cannot have a reflection coefficient. The "example" is nonsense.

Reflection coefficient is simply the (complex) ratio of the reflected
voltage to the forward voltage. It is always >=zero <= unity.



--
"For a successful technology, reality must take precedence
over public relations, for nature cannot be fooled."
(Richard Feynman)