======================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 = N-channel 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 24-22) 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 high-frequency 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 open-wire 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 100-200 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. 30-ohm Maximum power-carrying capability occurs at a diameter ratio of 1.65 corresponding to 30-ohms 60-ohms Optimum diameter ratio for voltage breakdown is 2.7 corresponding to 60-ohms 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 30-ohm 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 low-loss 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 77-ohm air line is reduced to 51 ohms when filled with polyethylene. Fifty-one 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 power-carrying 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) / (Z1-Z2) 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.