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The Mysterious 50 Ohm Impedance: The place It Got here From and Why We Use It | Weblog

The Mysterious 50 Ohm Impedance: The place It Got here From and Why We Use It | Weblog

2023-05-28 14:50:21

After we speak about S-parameters, impedance matching, transmission strains, and different basic ideas in RF/high-speed PCB design, the idea of fifty Ohm impedance comes up again and again. Look by way of signaling requirements, element datasheets, utility notes, and design tips on the web; that is one impedance worth that comes up repeatedly. So the place did the 50 Ohm impedance commonplace come from and why is it vital? Taken in isolation, deciding on 50 Ohm impedance would appear completely arbitrary: why not 10 Ohms or 100 Ohms?

The reply largely relies on who you ask. The RF neighborhood, and significantly cable designers, have one of the best reply, and their evaluation of coaxial cables backs up their rationalization. I’ve by no means seen this mentioned when it comes to what occurs on a PCB besides from one knowledgeable reference, however the reply for PCBs relates again to the inner construction and electrical traits of frequent logic circuits. If you happen to’re prepared for a historical past lesson the 50 Ohm impedance worth, then maintain studying. We’ll even look into the 75 Ohm commonplace to see what we will study sign and energy switch on RF interconnects.

The historical past of fifty Ohm impedance goes again to the late Twenties/early Thirties, when the telecom trade was in its infancy. Engineers had been designing air-filled coaxial cables for radio transmitters designed to output kW price of energy. These cables would additionally span lengthy distances, reaching tons of of miles. This implies the cables have to be designed with highest energy switch, highest voltage, and lowest attenuation. Which impedance needs to be used to fulfill all three aims?

Because it seems, it’s not possible to steadiness all three aims, similar to in lots of different design issues. 

  • Lowest loss: This relies on losses within the inner dielectric in a coaxial cable. For the air-filled coaxial, this happens at roughly 77 Ohms, or at roughly 50 Ohms for sure dielectric-filled cables (extra on this beneath).
  • Highest voltage: That is primarily based on the electrical subject between the middle conductor and sidewalls within the air-filled coax cable. The electrical subject within the TE10 mode is maximized when the conductor is constructed such that its impedance is roughly 60 Ohms.
  • Highest energy switch: Coaxial cables of any dimension is perhaps lengthy sufficient to behave like transmission strains and assist wave propagation. The facility carried by a coaxial cable is proscribed by the breakdown subject and the impedance of the cable: V2/Z. It seems that, for the air-filled coax working beneath the TE11 cutoff, energy switch is maximized at about 30 Ohms.

The graph beneath reveals the tradeoff between losses and energy. The file beneath is offered by Wikimedia, however you will discover comparable graphs from many different references. It’s also possible to calculate the losses utilizing the impedance, copper roughness/skin effect, and dielectric absorption and generate an identical graph particularly for coaxial cables. The facility calculation requires utilizing the total resolution for the basic propagating mode and the attribute impedance.

50 Ohm impedance

One level to know in regards to the above graph is that dielectric dispersion is usually not included and can have an effect on the outcomes at larger frequencies. Dispersion (each Dk worth and loss tangent) are taken to have flat dispersion when calculating these curves, which can not match actuality inside your frequency vary. Nonetheless, the curve provides us a good suggestion as to why there’s the deal with 50 Ohm impedance.

Compromise or Dielectric?

The fast reply to this query is that fifty Ohms is the least dangerous compromise between the impedance equivalent to minimal loss, most energy, and most voltage. Certainly, 50 Ohms is fairly near the imply between 77 and 30 Ohms, and it’s near 60 Ohms, so it appears pure to imagine that is the explanation for the 50 Ohm impedance commonplace. Nonetheless, one may discover that the impedance with minimal loss in a PTFE-filled coaxial cable is nearly 50 Ohms, so this looks like one other pure rationalization!

What About 75 Ohm Impedance?

Because it seems, the voltage worth is of much less significance; both you’re fearful about carrying energy, minimizing loss, or attempting to steadiness the 2. Low-cost coaxial cables with air or low-Dk dielectric filler can shoot for 77 Ohm impedance for lengthy cables runs, however the purpose for rounding off to 75 Ohms as a substitute of utilizing 77 Ohms remains to be a thriller to me. One would suppose that 75 Ohms is a pleasant rounded quantity that’s simple to recollect, whereas an exterior article on Microwaves 101 claims this was an intentional design. In coaxial cables with metal core, the diameter is simply barely outsized to offer some additional flexibility, so the impedance would come out to 75 Ohms. Whether or not or not that is true, I can’t affirm, however I’d welcome anybody contact me on LinkedIn with the answer!

When working with high-speed or high-frequency channels, we typically use S-parameter measurements as vital sign integrity metrics. These are outlined when it comes to some reference impedance, which is often taken as one of many above values (50 or 75 Ohms) because you is perhaps interfacing with one in all these media in your high-speed/RF system. I choose to think about reference impedance when it comes to your required termination impedance; you’re taking pictures for 75 or 50 Ohm impedance at every port, and S-parameter measurements present you ways you’ve deviated from this objective in your design.

When you’ve got a measured S-parameter matrix for an interconnect in your PCB, you may remodel it to a brand new S-parameter matrix with the next transformation:

See Also

50 Ohm impedance S-parameter transform
Transformation between S-parameter matrices with two completely different reference impedances.

That is helpful for understanding how your S-parameters may change whenever you swap your reference media (e.g., between 75 and 50 Ohm impedance cable). Through the use of the time period “reference media”, we’re making a comparability between our DUT/interconnect and an idealized 50/75 Ohm cable, 50/75 Ohm port, or one other element with 50/75 Ohm enter impedance.

Whether or not you want to design to 50 Ohm impedance or another worth, the PCB format options in Altium Designer® embody the instruments you want for high-speed design and RF design. You may entry the built-in 3D field solver from Simberian within the Layer Stack Supervisor to implement impedance control in your PCB stackup.

While you’ve completed your design, and also you need to share your venture, the Altium 365™ platform makes it simple to collaborate with different designers. We’ve got solely scratched the floor of what’s doable to do with Altium Designer on Altium 365. You may examine the product page for a extra in-depth function description or one of many On-Demand Webinars.

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