We know the transmission of radio frequency needs aerial and coaxial cable, the transmission of radio frequency signal we always hope to transmit farther distance as far as possible, to transmit farther distance, we often hope to use very great power to go transmit facilitates cover bigger communication range. But actually, coaxial cable itself has loss, use lead is euqally usually with us, if transmit power too big, lead will be calorific even fusing. Such, we have a kind of hope, try to search a kind to be able to transmit high-power, at the same time loss very small coaxial cable.

 

 

Be in probably 1929, shellfish Er lab did a lot of tests, final discovery accords with this kind of high-power to transmit, the coaxial cable with small loss its feature impedance is 30 ohm are mixed respectively 77 ohm. Among them, the power that the coaxial cable of 30 ohm can transmit is the biggest, the loss that the coaxial cable of 77 ohm transmits signal is the smallest. 30 ohm and the arithmetical average of 77 ohm are 53.5 ohm, 30 ohm and the geometrical average of 77 ohm are 48 ohm, the impedance of 50 ohmic systems that we often say is the eclectic consideration on 53.5 ohm and a project of 48 ohm actually, consideration most high-power is transmitted and the smallest loss is satisfied at the same time as far as possible. And discover through practice, the systematic impedance of 50 ohm, to half wavelengh occasionally extremely child aerial and 1/4 wavelengh is extremely odd child the port impedance of aerial also matchs, the return loss that cause is the smallest.

 

In our common system, for instance TV TV and broadcast FM receive a system in, its system impedance basically is 75 ohm, in transmitting a system because of 75 ohmic radio frequency just about, the loss that signal transmits is the smallest, TV and broadcast FM receive a system in, the transmission loss of signal is main consideration factor. And to containing emissive broadcasting station character, 50 ohm are very common, because most high-power is transmitted is the main factor that we consider, loss is more significant also at the same time. This is why in our interphone system, what often see is the parameter index of 50 ohm.

 

If say impedance matchs 50 ohm, from maths, can accomplish strictly, but any component in applying actually, circuit, lead is put in loss, and any systematic components of the design are put in certain radio frequency bandwidth, match 50 ohm so, should make sure point of the frequency inside all belts drops around 50 ohm only on the project can. Will look on Smith circle graph, namely as far as possible the centre of a circle that approach pursues at the circle can, ensure the radio frequency inside the belt transmits signal to do not have return loss as far as possible, the energy that achieves the oldest rate is transmitted.

 

 

Why the transmission line impedance that most engineer likes to use 50 ohm to serve as PCB (the default that occasionally this value is PCB board even is worth) , why be 60 or 70 ohm?

 

  

 

Take a line to what width decides, 3 main factors can affect PCB to walk along the impedance of the line. Above all, it is the EMI that PCB takes field of line close division (electromagnetism is disturbed) the height that walks along a line to be apart from referenced plane with this is to become certain proportion to concern, height is lower mean radiation smaller. Next, the meeting that string together faze has marked change along with height taking a line, reduce height half, the meeting that string together faze decreases nearly 1/4. Finally, height is lower impedance is smaller, suffer capacitance sex load not easily to affect. 3 all elements can let an architect walk along a line to stand by referenced plane as far as possible. Preventing you to fall height taking a line to the reason of 0 is, most chip drive not the transmission line that impedance is less than 50 ohm. (this regular special case is OK drive the Rambus of 27 ohm, and of National BTL series, it is OK drive 17 ohm) not all circumstance is to use 50 ohm best. For example, the very old NMOS structure of 8080 processor, the job is in 100KHz, without EMI, string together faze and the problem with capacitance laden sex, it also cannot drive 50 ohm. To this processor, tall impedance means low power comsumption, you want as far as possible with fine, the tall line that has tall impedance so. The angle of pure machinery also wants to consider. For example, tell from density, multilayer the space between ply is very little, the line wide technology that place of 70 ohmic impedance needs is accomplished very hard. This kind of circumstance, you should use 50 ohm, its line is broad more wide, more make easily.

 

Is the impedance of coaxial cable how? In RF domain, the question with the consideration in PCB is different, but coaxial cable also has similar impedance limits in RF industry. The publication according to IEC (1967) , 75 ohm are a common coaxial cable (note: Air regards insulation as the layer) impedance standard, because you are OK,with a few common antenna configuration matchs. It also defined a kind of 50 ohmic cable that are based on solid state polyethylene, because fixed to the diameter exterior screen layer and dielectric constant are secured,be 2.2 (the dielectric constant of solid state polyethylene) when, loss of effect of skin of hasten of 50 ohmic impedance is the smallest.

 

    

You can prove from elementary physics 50 ohm are best, the L of loss of hasten skin effect of cable (become an unit with decibel) with R of total resistor of hasten skin effect (unit length) except become direct ratio with characteristic impedance Z0. R of total resistor of hasten skin effect is screen layer and the sum of intermediate conductor resistor. The resistor of hasten skin effect of screen layer is in high frequency when, become inverse ratio with its diametical D2. According to understanding of filter public platform, the resistor of hasten skin effect of conductor of coaxial cable interior is in high frequency when, become inverse ratio with his diametical D1. R of gross series connection resistor, because this is mixed (1/d2 +1/d1) becomes direct ratio. Integrated these elements, give D2 and the corresponding dielectric constant ER that keep apart material, you can reduce loss of hasten skin effect with the following formula.

 

   

 

In any fundamental books about electromagnetism field and microwave, you can find Z0 is D2, d1 and ER (rich advocate note: The opposite dielectric constant of insulation layer) function

 

   

formula 2 belts enter formula 1 in, molecular denominator is multiplied at the same time with D2, arrange get

 

 

3 depart give formula invariable (/ 60)*(1/d2) , effective ((1+d2/d1)/ln(d2/d1)) is affirmatory most bit. Examine formula carefully the drop of the least value of 3 formula is controlled by D2/d1 only, have nothing to do with ER and fixed cost D2. It is parameter with D2/d1, make a plan for L, when indication D2/d1=3.5911 (note: Solution surmounts equation) , obtain the least value. Assume the dielectric constant of solid state polyethylene is 2.25, d2/d1=3.5911 reachs characteristic impedance is 51.1 ohm. Very long before, the radio engineer is used to go to the lavatory, regard coaxial cable as this value for 50 ohm approximately optimal value. This proved to be near 0 ohm, l is the smallest. But this does not affect you to use other impedance. For example, you make the cable of a 75 ohm, having same screen layer diameter (note: D2) with dielectric (note: ER) , loss of hasten skin effect can increase 12% . Different dielectric, the best impedance that arises with best D2/d1 scale can differ somewhat (note: Air insulation is for instance corresponding 77 ohm are controlled, the engineer takes a cost 75 ohm are convenient use) .

       

Other and compensatory: Afore-mentioned derivation also explained why tangent plane of cable of 75 ohmic TV is structure of empty core of lotus root shape and 50 ohmic telecommunication cable are solid core. Still have an important clew, want economic condition license only, choose cable of big external diameter as far as possible (rich advocate note: D2) , besides increasing strength, mainer reason is, external diameter is bigger, internal diameter is bigger also (optimal path compares D2/d1) , the RF loss of conductor is smaller of course.

       

Why the impedance standard that 50 ohm made radio frequency transmission line? A story version that circulates most, come from at Harmon Banning ” cable: About the antecedents of 50 ohm the likelihood has a lot of stories ” . In the initial stage of microwave application, during the World War II, the choice of impedance relies on use need completely. To the processing of high-power, 30 ohm often are used with 44 ohm. On the other hand, the impedance of the air fill line of lowermost loss is 93 ohm. In those years, to the taller frequency that uses rarely, without suppleness flexible cable, the tigidity that is fill air medium merely is tracheal. Half rigid cable is born at 50 time inchoate, true microwave flexible cable appears is after about 10 years. As technical progress, need gives out impedance standard, so that be on economy and convenient sex,acquire a balance. Be in the United States, 50 ohm are an eclectic choice; Solve these problems to combine army and navy, an organization that the name is JAN held water, with respect to the DESC that is later, by MIL of special development, according to filter public platform understanding arrives, europe chose 60 ohm. In fact, the vessel that uses at most in the United States is become by existing rear sight pole and hose connection, 51.5 ohm are very common. The adapter that see and uses 50 ohm to 51.5 ohm / converter, the feeling is very strange. Final 50 ohm won out, and special conduit is made come out (also may be the diameter that decorated worker appreciably to change their pipe) . Soon, below the influence that is in the company that takes regnant place in industry so like Hewlett-Packard, european also be forced to change. 75 ohm are the standard of long-range communication, because be medium fill line, lowermost loss is acquired in 77 ohm. 93 ohm are used at short continue all the time, be like join computer lead plane and monitor, its are low the characteristic of capacitance, reduced the load of circuit, allow longer continue; Filter public platform suggests, if interested friend can consult by oneself the 9th of MIT RadLab Series, there is more detailed description inside.