# How is transmission line impedance selected?

I understand (roughly) why transmission line impedance has to be matched to the source and the load. What I don't understand is how different technologies have chosen to use different impedance. (USB is 90 ohms, Ethernet is 100 ohms, PCIe is 85 ohms, amateur radios and antennas are typically 50 ohms).

Was it related to natural impedances for the source or load? Is there some way to determine the optimal impedance for a whole system if I can control the source, load, and transmission line?

• – The Photon Jan 17 '18 at 6:41

Some impedances are more suited to higher power transmission and some are more suited to producing lower losses: -

Diagram taken from Techplayon but is available from other sources. The one below is taken from Beldon's website: -

So, 50 ohms is a compromise between low loss and decent ability to pass power.

USB is 90 ohms, Ethernet is 100 ohms, PCIe is 85 ohms, amateur radios and antennas are typically 50 ohms

USB (for instance) is a differential signalling system so it tends to have roughly twice the impedance of "standard" coax so, interestingly, there isn't much of a difference between it and twinax (dual coax): -

9207 Belden twinax cable: -

Thicker more robust cables tend to have a bigger core conductor and this tends to make the capacitance between inner and shield/screen bigger. It also tends to make the loop inductance smaller. So a cable having more power handling capability could be generally said to have more capacitance per metre and less inductance per metre. At RF frequencies the characteristic impedance of a cable is: -

$Z_0 = \sqrt{\frac{L}{C}}$

Hence, as L decreases and C increases, $Z_0$ gets lower.

• I'd be interested to see an explanation of the physics behind the curves you show in this answer. Do you know of any source that explains it? – Hearth Mar 31 at 12:43

The source impedance can be arbitrary but are based on physical constraints.

A transmission line is determined by the conductor, the physical dimensions of the conductor, spacing relative to other conductors (like a shield or another wire) and electric and magnetic permeability of materials around the wire.

The governing body that creates the standard will look at different physical limitations from the IC's to the wire and determine what impedance make sense and then design the spec around that.

Termination resistances are easy to come by, you can get resistors in any value you want.

Wire not so much, the capacitance, inductance and resistance of the wire determine the impedance, so the specs are probably built around the the best configuration for that.

Wire in my experience can be notoriously hard to get exactly what you want, and very expensive if you need a custom solution. If your designing a transmission line system you'd probably want to start with the transmission media, determine the impedance and design your system around that.

As you've said. you have to match the impedance of the load to the line impedance.

The reflection factor $$\Gamma = \frac{Z_{Load}-Z_{Line}}{Z_{Load}+Z_{Line}}$$ becomes 0 (no reflection) if the line and source impedance are the same. The input impedance of the line with load is not dependent on the length of the line in this case. It is constant:

$$Z_{in}=Z_{Line}=Z_{Load}$$

Regarding the source matching:

There are several ways to choose the source impedance: A line with some load has an input impedance of $$Z_{in}$$.

The maximum power transfer occurs if the Source impedance is the complex conjugate: $$Z_{source}=Z_{in}^{*}$$

In case of a 50 Ohm input impedance, the optimal source impedance is 50 Ohms as well. This is called power matching.

There are cases, you want to choose another source impedance. For example noise reduction. Usually noise and power matching require different source impedances.

Different Line Impedances:

The line impedance depends on the kind of transmission line you choose (coax, twisted pair, etc...). On a PCB the line impedance depends on the type of line (coplanar, microstrip, etc...) and the dimensions of the line and the substrate.

In order to connect different HF components, it is important to have a system with the same impedance everywhere. Therefore most HF systems are chosen to 50 Ohms.

Buses like PCIe, which use different line impedances, usually are not connected to typical HF stuff. Therefore, a different impedance is not that big of a deal. These impedances typically have some advantage for manufacturing and handling. 50 Ohm lines on a PCB can become quite wide. A higher impedance decreases the necessary width, for instance.

50 Ohms: Where does it come from?

The 50 Ohm system originates in a trade off between loss and power capability of a coaxial cable.

You get the minimal loss at approximately 75 Ohms Impedance. However, the maximum power capability is achieved with approximately 30 Ohms.

This is due to the different dimensions of the coaxial line at different impedances.

As a result 50 Ohms were chosen as a tradeoff.

You can look at it here.

In addition to that, coax cables for higher frequencies are usually thinner. This increases the loss of the cable, because the current density in the conductors increases. Thinner cables are chosen to suppress higher order propagation modes.

• Answer not well matched to question. – Heath Raftery Jan 17 '18 at 10:37
• He asked, how transmission line impedance is selected. i answered this question. However, the statement "I understand (roughly) [...]" made me write a bit more about it. – GNA Jan 17 '18 at 21:03