There are two factors that drive 50 Ohm impedance: losses and power. If we can plot transmission line loss versus characteristic impedance. It turns out that insertion loss is minimum at around 77 ohms. A good explanation for the choice of fifty ohms is given in Microwave Tubes , by A. Gilmour, Jr. The quick answer is that 50 ohms is a great compromise between power handling and low loss, for air-dielectric coax.
Let's look at the math that proves this, just for kicks. Another thing to consider for reason for why CATV systems use 75 ohm coax. A 2 turn to 1 turn balun changes the impedance of ohm twin lead from an antenna to 75 ohms very nicely and with a relatively broad band.
You've got folded dipole, you gotta have a balun, and baluns don't come any simpler than the hairpin balun and there isn't any easy way to get to 50 ohms from ohms. Though, I'm sure 75 ohm coax preceded choke baluns.
And that brings up the interesting topic of analyzing the folded dipole as standard dipole coupled to a transformer! For RF signals, resistance per unit length of coax cables is determined by circumferential area of the conductor surface due to skin depth effect, not cross-sectional area.
The details of this equation are derived on this page. The impedance of coax for a given outer diameter and dielectric is solely a function of the diameter of the inner conductor and the dielectric constant of the filler material:. In our example, we chose 10 mm inner diameter of the outer conductor, and calculated loss at 10 GHz. Note air dielectric provides the lowest loss as it eliminates dielectric loss, but it is not always practical.
You need at least some dielectric to support the center conductor, even if it is just occasional small chunks. Did you ever hear of heliax air dielectric cable? A spiral of dielectric material is used to pin the center conductor away from the outer conductor. The peak power handlin g for air coax is limited by voltage breakdown as opposed to heating effects which limit average power handling. You'd think that you'd want maximum separation between the opposing conductors inner wire and outer sheaf to avoid arcing, so you'd make the inner conductor as thin as possible, but you'd be wrong again!
The maximum voltage field in a coaxial cable if quite different than between parallel-plane conductors. Here's the equation for "field enhancement", which is a measure of how much worse the fields are than in parallel plate:.
Here a is the is the gap between the conductors and r is the radius of the inner conductor. We took this from Gilmour's book.
The way to calculate maximum power handling is to assume a critical electric field that can't be exceeded to avoid breakdown. Next, calculate the field that would be generated across the gap in the coax cable, without regard to the geometry assume the center and outer conductors are parallel plates.
How is the impedance of the coaxial cable? But in the Radio Frequency industry, coaxial cable has the same impedance range. According to IEC publications , 75 ohm is a common impedance standard for coaxial cables, because you can match some common antenna configurations. It also defines a ohm cable based on solid-state polyethylene, because the skin effect of ohm impedance is minimized for external shielding with a fixed diameter and a fixed dielectric constant of 2.
You can prove that 50 ohm is the best from basic physics. The skin effect loss L in decibels of the cable is proportional to the total skin effect resistance R unit length divided by the characteristic impedance Z0. The total skin effect resistance R is the sum of the shielding layer and the intermediate conductor resistance. The skin effect resistance of the shielding layer is inversely proportional to its diameter d2 at high frequencies.
The skin effect resistance of the inner conductor of the coaxial cable is inversely proportional to its diameter d1 at high frequencies. Combining these factors, given the dielectric constant ER of d2 and the corresponding isolation material, you can use the following formula to reduce skin loss.
In any basic books of electromagnetic fields and microwaves, you both can find Z0 is the function of d2, d1, and ER Note: relative dielectric constant of insulation layer. Put formula 2 into formula 1, multiply numerator and denominator by d2, we can get:. Assuming that the dielectric constant of solid polyethylene is 2. Long times ago, radio engineers used this value, approximately 50 ohms, as the optimal value for coaxial cable for the case of use. This proves that L is the smallest around 0 ohm.
For example, if you make a ohm cable with the same shielding layer diameter note: d2 and insulator note: ER. Other additions: the above derivation also explains why 75 ohm TV cable cut surface is lotus root hollow-core structure and ohm communication cable is solid core.
Why is 50 ohms the impedance standard of RF transmission line? One of the most popular versions of the story comes from Harmon Banning In the early days of microwave application, during world war ii, impedance selection was entirely dependent on the need for use. On the other hand, the impedance of the lowest loss air fill line is 93 ohms. In those years, for higher frequencies that were rarely used, there were no flexible cables, just rigid tubes that filled the air medium. Semi-rigid cables were invented in the early s, and true microwave flexible cables were around 10 years later.
As technology advances, impedance standards need to be given to striking a balance between economy and convenience. Europe chose 60 ohms. In fact, the most common conduit used in the United States is an existing rod and pipe connection, It is strange to see and use 50 ohms to The 50 ohms won out, and special tubes were made or the fitters changed the diameter of their tubes slightly.
Before long, Europeans were forced to change under the influence of dominant firms such as Hewlett-Packard. Impedance matching in RF circuit design.
Impedance matching is the basic requirement of RF design and testing. Reflection of signals caused by impedance mismatches can cause serious problems. Matching seems like trivial common sense when you are dealing with theoretical circuits that consist of ideal power supplies, transmission lines, and loads. Assume that the load impedance ZL is fixed. We need to do is include a source impedance ZS equal to ZL, and then design the transmission line so that its characteristic impedance ZO is also equal to ZL.
If the engineer has to modify each component and specify the size of each microstrip based on the impedance selected as the basis for all other impedances.
In addition, this assumes that the project has entered the PCB phase. What if we want to use discrete modules to test and characterize the system using off-the-shelf. In this case, compensating for mismatched impedance is more impractical.
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