SBE
certification is the emblem of professionalism in broadcast
engineering. To help you get in the exam frame of mind, Radio World
Engineering Extra poses a typical question in each part of this
series. Although similar in style and content to the exam questions,
these are not from past exams nor will they be on future exams in
this exact form.
Oh, to Be 50
Again
Question from the
June 12 issue
(Exam level: CBRE)
Your radio station
transmitter is a perfect 50 ohm source connected to pure 50 ohm line
that feeds an ideal 50 ohm antenna. What are the current and voltage
characteristics along the transmission line?
a. Since the line is
merely a big capacitor, current will lead voltage.
b. Since the line is
mainly an inductor, voltage will lead current.
c. Voltage and
current obey wavelength concepts and are offset by sine and cosine
values as a function of whether the line length is more than 180
degrees or less than 180 degrees of a wavelength at the load
respectively.
d. Copper losses
will reduce the voltage proportionately but the current will diminish
asymptotically as it is liberated only in the load.
e. The current and
voltage will be the same at all points on the transmission line.
In
previous Certification Corner columns, we have promulgated that a
large part of our job as broadcast engineers is power conservation.
It is a major goal to get as much of the power we buy from the
utility into the antenna and onto our listeners.
Maximum
power transfer always occurs when the generator matches the load in
impedance. In our hypothetical question here, we outline the perfect
case (with the line and antenna in this case representing the load).
Part
of the purpose of this column is to get your brain (we have some of
the best in the world in our profession, and yours is probably one of
them) into the examtaking frame of mind. An element of that is to
help you to read the question and then ask yourself:
• What
am I actually being asked;
• What
useful/important information am I being provided; and
• Which
is the best answer of the choices I am given.
Although
the circumstances in our question assume an ideal match between
transmitter, line and antenna, that’s not always the case. One
aspect of broadcast engineering is creating the perfect match by
design and proper installation.
POWER
TRANSFORMER
What
is an antenna system but a special sort of transformer to couple RF
energy into electromagnetic waves that can travel long distances
wirelessly? When the antenna “output impedance” matches the
electromagnetic characteristics of free space (around 377 ohms), the
maximum energy will become radio waves. To make this match, impedance
transformation networks are implemented, which use lump constants of
capacitive and inductive reactance. At AM frequencies these are
discrete components. At FM, quite often the reactive aspect of
coaxial components is utilized.
We’re
not going to divert today to network design or any of the related
graphic aids such as Smith charts (we’ll get to these in the
future), but merely note that if improperly used coax can take on
reactive qualities as alluded to in answer (a) and (b). However, this
reactance presents a large problem in a series circuit such as your
main run to the antenna. The goal is to get the power to the antenna,
not present a resonant circuit. Answers (a) and (b) are out.
We
have to have some Buc gobbledygook in these columns somewhere, and
that is what answer (c) is. As above, all reactance has a phase
component in it someplace and that’s why the uninitiated might
think (c) was our best answer.
Your
distinguished editor and I have constantly reinforced that a good
grounding in basic electrical science is probably the best
preparation for success in our field. Here in answer (d) is a
classic, mini case of that. The transmitter, coax line and antenna
are essentially a twowire series circuit. In this situation, voltage
drops to zero around the circuit, but current must remain constant,
according to Kirchoff’s laws. Hence (d) is easily dismissed.
READ
IT CAREFULLY
Now
onto answer (e) and at this point, possibly our most correct answer.
One of our greatest leading lights in communications engineering,
Major Howard Armstrong, was an extremely literate and perceptive
gentleman. During his long and tenuous court battle with RCA to
recognize his patents, he said something prescient about that legal
experience:
Lawyers
reduce ideas to words and then argue over the words.
Well,
engineers struggle for precision in ideas and descriptions as well,
but we’re paid a lot less for it and we’re usually a lot more
genial and mannerly in our discussions. Our distinguished editor and
your humble writer have had “discussions” about “the words”
and whether answer (e) is accurate.
In
a perfectly matched coaxial transmission system with RF conducted
through it, the values of voltage and current are constant at all
points. Obviously this is alternating current, so the instantaneous
values change but the average values remain constant. So, let the two
of us settle our “discussion” with an agreement that generally
the wording (e) is the most correct answer.
While
there may be a slight amount of loss to calculate in the real
(nonideal) case, this is one of the most amazing concepts of
electromagnetics: In a system where the generator output impedance is
matched to the transmission line impedance, which in turn is matched
to the load (antenna) impedance, essentially all
the power is transferred into the load. Transmission lines have
unique electromagnetic properties that allow us to completely ignore
the capacitive and inductive reactance. Thus they operate to move
highfrequency energy from generator to load without concern for the
operating frequency.
WHAT
MAKES A TRANSMISSION LINE?
As
we have previously written, the characteristic impedance of a
transmission line is based on the ratio of the inner to the outer
diameter. The classic formula for impedance of a line is:
Z_{line}
= square root of L/C, where L is the amount of inductance per unit
length and C is the capacitance per unit length. The unit comes out
as ohms if you do the math.
In
a line with a uniform cross section, these values of inductance and
capacitance can be easily calculated from the type of materials used
(typically copper), the distance between the inner and outer
conductors and the insulating material that separates them (often air
or a plastic foam). Now you know the rest of the story on how these
remarkable lines are built.
LESS
THAN PERFECTION
EQUALS REFLECTION
Our
perfect system might exist somewhere, but I’ve never encountered
it. We get close, but a perfect match is elusive. Mismatches in
coaxial transmission systems normally produce reflections of the
energy you’ve introduced. One way of expressing this mismatch is by
calculating the Standing Wave Ratio (SWR). Our constant values will
be affected by the phase and amplitude of the reflected wave as it
returns to the generator (our transmitter). This reflected wave,
depending on the length of the transmission line, will add or
subtract algebraically with the generator wave to produce a voltage
that varies with the distance on the transmission line. We define the
Standing Wave Ratio as simply the ratio of Emax / Emin.
As
a practical point, since the values of the forward and reflected
waves at FM frequencies are usually ascertained from a directional
coupler on the transmitter, these are the values at that point. Since
there is loss (albeit small in comparison to the total power)
the calculated SWR at
this point will, in fact, be less than the actual value.
Ideally the SWR should be determined at the far end, (the antenna
load) from the peak value of the reflected power measured there.
For
more on this subject, see “Transmission Lines” by Robert A.
Chipman, part of the Schaum’s Outline series, Chapter 8 starting at
page 156, and “Electronic and Radio Engineering” by Dr. Frederick
K. Terman, Chapter 4 Transmission Lines, centered around page 96.
The
next SBE certification exams will be given Feb. 7–17, 2014, in the
local chapters. Applications must be in by Dec. 31, 2013. Remember
a dream is just a dream … a goal is a dream with a plan and
a deadline! So
get yourself and your confreres motivated to become certified or
advance a grade today. Do not pass over this opportunity to learn and
advance.
Charles
“Buc” Fitch, P.E., CPBE, AMD,
is a frequent contributor to Radio World. Missed some Certification
Corners or want to review them for your next exam? See the
“Certification” tab under Columns at radioworld.com.
MR.
SMITH CHECKS HIS CHART
Question for next
time
(Exam
level: CPBE)
A
Smith chart is a graphic display of the orthogonal curvilinear
coordinates of the normalized impedance components on the voltage
reflection coefficient plane. With that in mind, what is the first
step necessary for meaningful results when using this chart?
a.
Annotate the cross field axis (susceptance, admittance, purveyance,
persistence).
b.
Assign the value of normalization (typically 50 ohms for ‘1’).
c.
Determine if you will be calculating a double or triple tuner.
d.
Determine if you will be using real or imaginary numbers.
e.
Decide whether negative or positive will be on the upper quadrant.
