======================COMPONENTS_CABLE==============================
NEW CHEATSHEETS http://www.idea2ic.com/CheatSheet_2/CHEATSHEETS_2.html
These are my personal cheatsheets designed to make access to
detailed information much easier to find. They are being put
on the web mainly because for now it is easy to do. The new
rev of cheatsheets are the ones being continually upgraded.
Don Sauer 10/17/09 dsauersanjose@aol.com

K = Nchannel fet
Cable impedance The basic idea is that a conductor at RF frequencies no
longer behaves like a regular old wire. As length of
conductor (wire) approaches about
1/10 wavelength of signal it is carrying  good ol'
fashioned circuit analysis rules don't apply anymore.
How cable impedance Characteristic Impedance and is usually designated Zo or
"Zed nought". characteristic impedance formula can be
written in following format:
Zo = sqrt((R + 2*pi*f*L )/(G + j*2*pi*f*c) )
Where:
R = series resistance in ohms per length (DC resistance)
G = The shunt conductance in mhos per unit length
j = phase angle of +90 degres(imaginary number)
pi = 3.1416
L = Cable inductance per unit lenght
C = Cable capacitance per unit lenght
sqrt = square root function
For materials commonly used for cable insulation,
G is small enough that it can be neglected
At low frequencies, L is so small compared with R
that it can be neglected.at low frequencies,
Zo = sqrt ( R / (j * 2 * pi * f * L))
Polyvinyl chloride and rubber decrease somewhat in
capacitance as frequency increases, while
polyethylene, polypropylene, and Teflon* do not vary
significantly.
When f becomes large enough, two terms containing f
become so large that R and G may be neglected a
Zo = sqrt ( (j *2*pi*f*L) / (j*2*pi*f*C) )
Which can be simplified to form:
Zo = sqrt ( L / C )
coaxial cable: impedance = (138 / e^(1/2)) * log (D/d)
Where:
log = logarithm of 10
d = diameter of center conductor
D = inner diameter of cable shield
e = dielectric constant (= 1 for air)
In a nut shell characteristic impedance of a coax cable
is square root of (the per unit length inductance divide
by per unit length
capacitance). For coaxial cables characteristic
impedance will be typically between 20 and 150 ohms.
impadance of balanced pairs ?
Characteristic impedance is determined by size and
spacing of conductors and type of dielectric used between
them. Balanced pair, or twin
lines, have a Zo which depends on ratio of wire spacing
to wire diameter and foregoing remarks still apply. For
practical lines, Zo at high
frequencies is very nearly, but not exactly, a pure
resistance.
The following formula can be used for calculating
characteristic impedance of balanced pair near ground:
(formula taken from Reference Data for
Radio Engineers book published by Howard W. Sams & Co.
1975, page 2422)
impedance = (276 / e^(1/2)) * log ((2D/d) * (1 +
(D/2h)^2))^(1/2))
Where:
log = logarithm of 10
d = wire diameter
D = distance between wires in pair
e = dielectric constant (= 1 for air)
h = distance between balanced pair and ground
Not that this formula is only valid for unshielded
balanced pair when D and h are order of magnitude larger
than d. If twisted pair is far away from
ground (h is nearly infinite), effect of ground is
neglegtible and impedance of cable can be approximated
with simpler formula (my
own derivation from formula above):
impedance = (276 / e^(1/2)) * log ((2D/d)
For twin line Zo will be typically between 75 and 1000
ohms depending on intended application. The impedance of
typical old telephone pair in
telephone poles in air has characteristic impedance of
around 600 ohms. The telephone and telecommunication
cables in use have typically a
characteristic impedance of 100 or 120 ohms.
long coaxial cable If you know imductance and capacitance of certain lenght
of cable you can use following electrical model for it:
L L L / / L
+uuuu+++uuuu+++uuuu+/ ... /+uuuu+
   / / 
+ + + +
C + C + C+ C +
   / / 
+++/ ... /+
/ /
For this model it is a beneficial to know an useful
impedance equation which described relation of impedance,
capacitance and inducatance:
Z = sqrt ( L / C )
A relationship exists which makes determination of Zo
rather simple with proper equipment.
at a given frequency, impedance of a length of cable
is measure with far end open (Zoc),
and measurement is repeated with far end shorted (Zsc),
Zo = sqrt ( Zoc * Zsc )
Where:
Zoc = impedance of a length of cable is measure with far
end open
Zsc = impedance of a length of cable is measure with far
end shorted
Most wires 60 to 70 percent of speed of light,
Normal video signal rarely exceed 10 MHz.
minimize attenuation in coax ?
For a line with fixed outer conductor diameter, and whose
outer and inner conductors have same resistivity, and
assuming you use a dielectric with
negligible loss (such as polyethylene or Teflon in
highfrequency range at least), then you get minimum loss
in coax if you minimize expression:
(1/d + 1)/ln(1/d)
where d is ratio of inner conductor diameter to outer
conductor ID. A spreadsheet or calculator gets you close
pretty quickly: D/d = 3.5911 is close.
Thr formula was claimed to be derived from formula for
coax impedance versus D/d and a formula for loss that
For air insulated line, corresponding
impedance is about 76.71 ohms, but if line is insulated
with solid polyethylene, then
minimum attenuation is at about 50.6 ohms.
The most typical coaxial cable impedances used are 50 and
75 ohm coaxial cables. 50 ohm coaxial cables might be
most commonly used coaxial 75 ohm ciaxial cable
which is used in video applications, in CATV networks, in
TV antenna wiring and in
telecommunication applications.
600 ohms is a typical impednace for openwire balanced
lines for telegraphy and telephony. A twisted pairs of 22
gage wire with reasonable insulation
on wires comes out at about 120 ohms for same
mechanical reasons that other types of transmission lines
have their own characteristic
impedances.
Twin lead used in some antenna systema are 300 ohms to
match to a folded dipole in free space impedance
(However, when that folded dipole is part
of a Yagi (beam) antenna, impedance is usually quite a
bit lower, in 100200 ohm range typically.).
Why 50 ohm coax ? Stand coaxial line impedance for r.f. power trans in U.S.
almost exclusively 50 ohms. value chosen given in paper
by Bird Electronic Corp.
Different impedance optimum for different parameters.
30ohm Maximum powercarrying capability occurs
at a diameter ratio of 1.65 corresponding to 30ohms
60ohms Optimum diameter ratio for voltage breakdown is 2.7
corresponding to 60ohms impedance (incidentally,
standard impedance in many European countries).
Power carrying capacity on breakdown ignores current
density which is high at low impedances such as 30 ohms.
Attenuation due to conductor losses alone
is almost 50 0gher at that impedance than at
77 ohms minimum attenuation impedance of 77 ohms
(diameter ratio 3.6).
This ratio,limited to one half maximum power of 30ohm
In early days, microwave power was hard to come by
and lines could not be taxed to capacity.
Therefore low attenuation was overriding factor
leading to selection of 77 (or 75) ohms as a standard.
resulted in hardware of certain fixed dimensions.
When lowloss dielectric materials
made flexible line practical, line dimensions remained
unchanged to permit mating with existing equipment.
The dielectric constant of polyethylene is 2.3.
Impedance of a 77ohm air line is reduced to 51 ohms
when filled with polyethylene. Fiftyone ohms is
still in use though standard for precision is 50 ohms.
attenuation is minimum at 77 ohms;
breakdown voltage is maximum at 60 ohms
powercarrying capacity is maximum at 30 ohms.
50 ohm coax 50 ohm coax mechanically look good, Since
almost any coax that looks* good for mechanical reasons
just happens to come out at close to 50 ohms anyway,
was natural tendency for standardization exactly 50 ohms.
board traces Impedance of circuit board traces
High speed signals can be routed on a circuit board
microstrip line Characteristic impedance formula:
Z = (87 / sqrt( Er + 1.41 ))*ln( (5.98*h)/(0.8*w + t))
Where:
Er = dielectric constant(4.8 for typ fiberglass board)
h = height of dielectric (fiberglass board thickness
between trace nad ground plane)
t = thickness of copper material in microstrip
w = width of copper material in microstrip
The dielectric constant, Er, for typical 0.062"
fiberglass board is 4.8. Using a trace thickness of
0.00134" gives a line width of 109 mils for a 50 ohm
microstrip.
When routing circuit board traces, differential pairs
should have same length trace. These trace lines should
also be as short as possible.
Impedance matching between different impedances
If two cables with different impedances are connected
togerther or a cable is connected to a source which has
different impedance then some kind of
impdance matching is needed to avoid signal reflections
in place where cables are connected together.
Using transformer for impedance matching
The most classical method for matching different
impedances is to use a matching transformer with proper
impedance tranfer ratio. The impednace
tranfer ratio of a transformer is determined by using
formula:
Za / (Na^2) = Zb / (Nb^2)
Where:
Za = input impedance
Na = number of turns on input coil
Zb = output impedance
Nb = number of turns on output coil
The equation can be converted to format:
Zb = Za * (Nb/Na)^2
From that equation you can see that Nb/Na is same as
transformer voltage transferrign ratio between primaty
and secondary. This means that
when you know that ratio you can use equation without
knowing exact turns ratio.
Impedance matching netweork usign resistors
The matching network shown below can be used to match two
unequal impedances, provided that Z1 is grater than Z2.
____
____+
R1 
 
Z1   R2 Z2
_

+
The resistor for this circuit can be calxulated using
following equations:
R1 = Z1  Z2*R2 / (Z2+R2)
R2 = Z2 * sqrt(Z1) / (Z1Z2)
The table below will show some precalculated values for
some most common interfacing situations:
Z1 Z2 R1 R2 Attenuation
(ohm) (ohm) (ohm) (ohm) (dB)
75 50 42,3 82,5 5,7
150 50 121 61,9 9,9
300 50 274 51,1 13,4
150 75 110 110 7,6
300 75 243 82.5 11,4
As you can see from table cost of simple resistor based
impedance matching is quite large signal level
attenuation in conversion process.