"Roy Lewallen" wrote in message
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Owen wrote:
I note that any textbook I pick up shows that VSWR=(1+rho)/(1-rho) where rho
is the magnitude of Gamma (Gamma=(Z-Zo)/(Z+Zo)); rho=abs(Gamma)).
Now, reading TL theory texts can be confusing because of the sometimes subtle
swithes to and from an assumption of lossless line (under which rho cannot
exceed 1).
To complicate matters, roughly half the textbooks use rho instead of Gamma for
the complex reflection coefficient. You've got to be careful.
Since VSWR is the ratio of the magnitude of the voltage at a maximum in the
standing wave pattern to the magnitude of the voltage at a minimum in the
standing wave pattern, if we are to infer SWR at a point on a line (if that
makes sense anyway) from rho (which is a property of a point on a lossy
line), isn't the formula VSWR=abs(1+rho)/abs(1-rho) correct in the general
case (lossy or lossless line)?
The whole concept of VSWR gets flakey on a lossy line, and really loses its
meaning. It's often analytically convenient to define a quantity at a point
and call it "VSWR", although in the presence of loss it no longer means the
ratio of maximum to minimum voltage on the line. Since it's lost its original
meaning, it comes to mean just about anything you'd like. And the generally
accepted definition then is the equation you gave in your first paragraph.
That is, in the presence of loss, VSWR is something which is *defined* by that
equation, rather than the equation being a means of calculating some otherwise
defined property.
Under the right conditions and if loss is large enough, rho can be greater
than 1, in which case the VSWR as defined by the equation in the first
paragraph becomes negative. Again, this is no longer a ratio of voltages along
a line, but a quantity defined by an equation. If you alter the equation,
you're defining a different quantity. Now, there's no reason that your "VSWR"
definition isn't just as good as the conventional one (first paragraph
equation). But the conventional one is pretty universally used, and yours is
different, so if you're interested in communicating, it would be wise to give
it a different name or at least carefully show what you mean when you use it.
Given that rho cannot be negative (since it is the magnitude of a complex
number), the general formula can be simplified to VSWR=(1+rho)/abs(1-rho).
But it can be greater than one. See above.
Seems to me that texts almost universally omit the absolute operation on the
denominator without necessarily qualifying it with the assumption of lossless
line.
If VSWR=(1+rho)/abs(1-rho), then doesn't it follow that rho is not a function
of VSWR (except in the lossless line case where VSWR=(1+rho)/(1-rho) and
therefore rho=(VSWR-1)/(VSWR+1))?
Rho is never a function of VSWR. VSWR is a function of rho. Unlike actual VSWR
(that is, the ratio of maximum to minimum voltage along a line), the
reflection coefficient can be and is rigorously and meaningfully defined at
any point along a line, lossy or not.
Roy Lewallen, W7EL
Good response, Roy, but concerning rho and gamma to represent reflection
coefficient, I refer you to Reflections, Sec 3.1,
"Prior to the 1950s rho and sigma, and sometimes 'S' were used to represent
standing wave ratio. The symbol of choice to represent reflection coefficient
during that era was upper case gamma. However, in 1953 the American Standards
Association (now the NIST) announced in its publication ASA Y10.9-1953, that rho
is to replace gamma for reflection coefficient, with SWR to represent standing
wave ratio (for either voltage or current), and VSWR specifically for voltage
standing wave ratio. Most of academia responded to the change, but some
individuals did not. Consequently, gamma is occasionally seen representing
reflection coefficent, but only rarely."
Hope this clarifies any misunderstanding concerning the use of gamma for
reflection coefficient.
Incidentally, Roy, I recently mailed you a CD containing Laport's book, "Radio
Antenna Engineering." I'm wondering if you received it, or did it go astray?
Walt, W2DU
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