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簽到天數: 1942 天 [LV.Master]伴壇終老
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Typical cable impedances
What are typical cable impedances ?
The most typical coaxial cable impedances used are 50 and 75 ohm coaxial cables. 50 ohm coaxial cables might be the most commonly used coaxial cables and they are used commonly with radio transmitters, radio receivers, laboratory equipments and in ethernet network.
Another commonly used cable type is 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 the wires comes out at about 120 ohms for the same mechanical reasons that the 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, the impedance is usually quite a bit lower, in the 100-200 ohm range typically.).
Why 50 ohm coax ?
Standard coaxial line impedance for r.f. power transmission in the U.S. is almost exclusively 50 ohms. Why this value was chosen is given in a paper presented by _Bird Electronic Corp._ Standard coaxial line impedance for r.f. power transmission in the U.S. is almost exclusively 50 ohms. Why this value was chosen is given in a paper presented by Bird Electronic Corp.
Different impedance values are optimum for different parameters. Maximum power-carrying capability occurs at a diameter ratio of 1.65 corresponding to 30-ohms impedance. Optimum diameter ratio for voltage breakdown is 2.7 corresponding to 60-ohms impedance (incidentally, the 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% higher at that impedance than at the minimum attenuation impedance of 77 ohms (diameter ratio 3.6). This ratio, however, is limited to only one half maximum power of a 30-ohm line.
In the early days, microwave power was hard to come by and lines could not be taxed to capacity. Therefore low attenuation was the overriding factor leading to the selection of 77 (or 75) ohms as a standard. This resulted in hardware of certain fixed dimensions. When low-loss dielectric materials made the flexible line practical, the 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 today though the standard for precision is 50 ohms.
The attenuation is minimum at 77 ohms; the breakdown voltage is maximum at 60 ohms and the power-carrying capacity is maximum at 30 ohms.
Another thing which might have lead to 50 ohm coax is that if you take a reasonable sized center conductor and put a insulator around that and then put a shield around that and choose all the dimensions so that they are convenient and mechanically look good, then the impedance will come out at about 50 ohms. In order to raise the impedance, the center conductor's diameter needs to be tiny with respect to the overall cable's size. And in order to lower the impedance, the thickness of the insulation between the inner conductor and the shield must be made very thin. Since almost any coax that *looks* good for mechanical reasons just happens to come out at close to 50 ohms anyway, there was a natural tendency for standardization at exactly 50 ohms.
Cable capacitance and characteristic impedance
Take a chunk of coax, connected to nothing. The center conductor and shield form a capacitor. If you charge that capacitor up to 100V, then short the shield to the center conductor, What is the current flow?
It is not infinite (or determined by parasitic resistance anc reactance ) like a "normal capacitor" but it is determined by the characteristic impedance of the line. If it is 50 ohm line charged to 100V then the current WILL be 2Amps. (100/50) It will be a square pulse, and temporal width (time duration, pulse width whatever you choose to call it) will be determined by the length of the line (around 1.5 nS/foot depending on line's velocity factor).
This method can be used for example to generate current pulses to semicondictor lasers. To get the pulse lengths longer than easily availabe with practical coaxial lines you can use use lumped impedance near-equivilant.
Using coaxial cables in applications
What happens if I use 50 ohm cable for vidoe application which needs 75 ohm cable ?
If 50 ohm cable sees a 75 ohm load (the receiver), a substantial part of the signal will be reflected back to the transmitter. Since the transmitter is also 75 ohm, this relected signal will be substantially reflected back to the receiver. Because of the delay, it will show up as a nasty ghost in the picture. Multiple ghosts like this look like ringing. Also, the reflections cause partial signal cancellations at various frequencies.
How can I convert cable impedance values ?
The cable impedance itself can't be converter unless you replace the whole cable with new one which has the right impedance. If you absolutelu need to use the existing cable for your application then there is one way to use the exiting cable: impedance converters. There are transformers which can make the cable look like different impedance cable when those are installed to both ends of the cable.
In some application it is possible to resistive adapers to convert the cable impedances. Those adapters are simpler than transformers but typically have a noticable signal loss in them (typically around 6 db for 75 ohm to 50 ohm conversion).
Impedance of circuit board traces
High speed signals can be routed on a circuit board if care is taken to make the impedance of the traces match the source driver impedance and the destination termination impedance. A microstrip line will exhibit a characteristic impedance if the thickness, width, and height of the line above the ground plane are controlled.
Characteristic impedance formula:
Z = (87 / sqrt( Er + 1.41 )) * ln( (5.98*h)/(0.8*w + t))
Where:
Er = dielectric constant (4.8 for typical fiberglass board)
h = height of the dielectric (fiberglass board thickness between trace nad ground plane)
t = thickness of the copper material in microstrip
w = width of the 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 the 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 the signal reflections in the place where the 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 the 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 the transformer voltage transferrign ratio between primaty and secondary. This means that when you know that ratio you can use the equation without knowing the 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 the 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 the table the cost of simple resistor based impedance matching is quite large signal level attenuation in the conversion process.
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Comments
I have received the following comment on the cable impedance equation:
I have read your document, which is I must say very well written. I found a small mistake there though in "How does coaxial cable chacteristics define the impedance ?". Your formula is *impedance = (138 / e^(1/2)) * log (D/d)*, but this is only true for ideal conductor. Speed of wave in copper is less than in vacuum, and it equals to about 248827740 m/s; this means that it should be multiplied by a factor of 0.83. So the formula should look like this:
impedance = ( (138/e^1/2) * log(D/d) ) * 0.83
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