Complex Z0 mini-Compendium for Example Builders
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A lot of numerical examples have been appeared lately
which are related to the
Uniform Transmission Line "UTL" Theory
with a "Passive" Complex Z0.

After a try to follow a few of them,
I summoned up my courage
to suggest a mini-Compendium,
especially to those of the Example Builders
who maybe they don't feel any need for.


Table (R/C = Real/Complex. Angles in Degrees)
--:----:------------------------:---:--------------------------------|
0 1 2 3 4 5 6 7
12345678901234567890123456789012345678901234567890 12345678901234567890
--:----:------------------------:---:--------------------------------|
# :Symb: Quantity :R/C: Conditions
--:----:------------------------:---:--------------------------------|
01: w : Circular Frequency : R : 0 w
--:----:------------------------:---:--------------------------------|
A : UTL Analysis - Distributed Coefficients
--:----:------------------------:---:--------------------------------|
02: R' : Series Resistance : R : 0 = R'
03: L' : Series Inductance : R : 0 = L'
04: Z' : Series Impedance : C : Z' = R' + jw.L',(R',L')=/=(0,0)
--:----:------------------------:---:--------------------------------|
05: G' : Shunt Conductance : R : 0 = G'
06: C' : Shunt Capacitance : R : 0 = L'
07: Y' : Shunt Admittance : C : Y' = G' + jw.C',(G',L')=/=(0,0)
--:----:------------------------:---:--------------------------------|
B : UTL Design - Propagation Characteristics
--:----:------------------------:---:--------------------------------|
08: Ro : Char/tic Resistance : R : 0 Ro
09: Xo : Char/tic Reactance : R :|Xo|/Ro = 1
10: Zo : Char/tic Impedance : C : Zo = Ro + jXo
11:|Zo|: Magnitude of Zo : R : 0 |Zo|
12: to : Argument of Zo : R : -45 = to = +45
--:----:------------------------:---:--------------------------------|
13: a : Attenuation Factor : R : 0 = a
14: b : Phase Factor : R : 0 = b
15: g : Propagation Factor : C : g = a + jb, (a,b)=/=(0,0)
--:----:------------------------:---:--------------------------------|
C : UTL Fundamentals
--:----:------------------------:---:--------------------------------|
16: Z : Impedance [Passive] : C : Z = R + jX, 0 = R
17: T : Argument of Z : R : -90 = T = 90
18: z :"Normalized" Impedance : C : z = Z/Zo,
19: t : Argument of z : R : -90-to = t = -to+90
20: p : Reflection Coefficient : C : p = (Z -Zo)/(Z + Zo)
21:|p| : Magnitude of p : R :|p|=Sqrt[(1+Sin|to|)/(1-Sin|to|]
22: W : Average Power : R : 0 = W
--:----:------------------------:---:--------------------------------|

Some Applications of the mini-Compendium to Example Threads
-----------------------------------------------------------

I.
The following characteristic Impedance is proposed
in some Thread

Zo = 50 + j 200

But,
as it is readily seen from the Table,
these values are not obey the #09 -or its equivalent #12- condition
[as already has been noticed by David or Jo Anne Ryeburn, ex-W8EZE].

Therefore this Example is
_inconsistent_
with the UTL Theory.

II.
On the contrary,
the thread
"Complex Line Z0 : A Numerical Example"
by Roy Lewallen,
31 Aug 2003
forms a complete system
as far as both
the following Real values
which are given
either explicitly

Ro = 68 [Ohm]
Xo = -39 [Ohm]

or implicitly,
under the assumption that the involved calculations
have been carried out correctly,

w = 20,000 Pi [Hz]
a = 2.46526 10^-4 [Np]/[m]
b = 4.25879 10^-4 [rad]/[m]

since they are not violated any of the Tabled conditions,
all are
_consistent_
with the UTL Theoretical Design.

Indeed,
if we calculate
the design parameters,
we find

R' = 3.33731 10^-2 [Ohm]/[m]
L' = 3.07890 10^-8 [H]/[m]
G' = 2.51387 10^-11 [Mho]/[m]
C' = 9.99071 10^-11 [F]/{m]

which are all positive quantities
which of course
they don't violate any Tabled condition too.

Therefore
the UTL Theory applies,
at least in principle,
and we can attempt to check
any of the subsequent conclusions of this example,
although,
I am afraid,
a vaporization of this pseudo-RG-58
finally will happen...

Sincerely,

pez
SV7BAX

P.S.
Please feel free
to made any correction
or addition of your favorites,
as far as these are consistent
with the UTL Theory,
by yourselves alone.
Whether or not,
either welcomed or not,
comments do not appear...