How is impedance matched with RF connectors?

[Mzzed]

I am just a bit confused as to how impedance is matched with RF connectors such as type-N or BNC connectors. I know Coaxial cabling and RF connectors come in common impedance ratings like 50 or 75 ohm but how is this all matched properly? For example many people have told me that when using coax, you would have a 50 ohm female and male connector at one end, a 50 ohm coax cable, and then another 50 ohm female and male connector and this will be properly matched.

I know in order to match two impedances each impedance must be the complex conjugate of the other in order to cancel and leave only the real resistance value. Do male and female rf connectors have complex conjugate impedances to always match properly at their connections?

 

[davenn]

I know Coaxial cabling and RF connectors come in common impedance ratings like 50 or 75 ohm but how is this all matched properly?

The characteristic impedance of a coax cable is determined by 3 main factors
1) the diameter of the inner conductor
2) The dielectric constant of the dielectric used
3) the internal diameter of the outer shield

https://www.pasternack.com/t-calculator-coax-cutoff.aspxA coax connector is designed with the same 3 factors in mind.
So that in a perfect world, if you have 2 lengths of coax of the same impedance and you joined them with a male and female connector.
Those 2 connecters in the middle would look "invisible" under test and the full length of the coax would test as one uniform length.

But in a real world, even though those connectors are made with very good precision* … They are not perfect ( not as good as a continuous length of coax)
They will exhibit small impedance bumps under test and produce small losses into the coax transmission line.
* and be very aware … if you ever get into RF in a serious way …. not all connectors are made the same …. there are some really crappy brands out there. Some exhibit large impedance bumps because of poor manufacturing

Amphenol, Radiall, Times Microwave, Pasternack, Trompeter and Tajimi are the top brandscheers
Dave

 

[Mzzed]

The characteristic impedance of a coax cable is determined by 3 main factors
1) the diameter of the inner conductor
2) The dielectric constant of the dielectric used
3) the internal diameter of the outer shield

https://www.pasternack.com/t-calculator-coax-cutoff.aspxA coax connector is designed with the same 3 factors in mind.
So that in a perfect world, if you have 2 lengths of coax of the same impedance and you joined them with a male and female connector.
Those 2 connecters in the middle would look "invisible" under test and the full length of the coax would test as one uniform length.

But in a real world, even though those connectors are made with very good precision* … They are not perfect ( not as good as a continuous length of coax)
They will exhibit small impedance bumps under test and produce small losses into the coax transmission line.
* and be very aware … if you ever get into RF in a serious way …. not all connectors are made the same …. there are some really crappy brands out there. Some exhibit large impedance bumps because of poor manufacturing

Amphenol, Radiall, Times Microwave, Pasternack, Trompeter and Tajimi are the top brandscheers
Dave

Thankyou, that makes a lot of sense. So I was correct in assuming that one connector has positive reactance and the other connector has negative reactance so that when the are connected together, they cancel impedance and are essentially invisible to any signals?

 

[davenn]

. So I was correct in assuming that one connector has positive reactance and the other connector has negative reactance so that when the are connected together, they cancel impedance and are essentially invisible to any signals?

no that isn't correct

As I said (maybe not clearly enough) in my previous post …..

The connectors are manufactured so that they as closely as possible represent the impedance of the coax in which they are to be used.
That's why they are close to invisible in their use when testing the length of cable

look at it this way ……

A … normal length of cable

B … a male and female connector used to join 2 lengths and keep the impedance and losses figures as close as possible
to that of "A"

C … take the 2 separate lengths butt them together and solder/join the centre conductors and the shields at closely as possible
without producing impedance / losses bumps

OR you can look at C as the same as taking a short length of same type of coax and inserting it as accurately as possible between the 2 ends

This is what your connectors are representing/replicating

Dave

 

[CWatters]

Perhaps have a look at some F Series connectors to see how they are assembled. They use the solid core of the coax cable as the male/pin.

 

[berkeman]

I know in order to match two impedances each impedance must be the complex conjugate of the other

So I was correct in assuming that one connector has positive reactance and the other connector has negative reactance so that when the are connected together, they cancel impedance and are essentially invisible to any signals?

A good transmission line (and any good connectors used as part of that TL) will have a real Zo, so no conjugate matching is needed.

 

[GrahamN-UK]

I know in order to match two impedances each impedance must be the complex conjugate of the other in order to cancel and leave only the real resistance value.

True. However if an impedance is purely real - that is, it is just a resistance and has no imaginary component from a reactance - then the matching impedance is that resistance.

Perhaps some numerical examples will help:
Consider a source with internal impedance consisting of a 50 Ω resistance in series with a 40 Ω inductive reactance (an inductor). So the source impedance, written in rectangular form, will be 50 + j40 Ω.

For a complex conjugate impedance match we will need a load impedance with an equal real (resistive) component and an imaginary (reactive) component of the same magnitude but opposite sign. So the matched load impedance will be 50 - j40 Ω - a 50 Ω resistor in series with a 40 Ω capacitive reactance (a capacitor).

So what happens if the source impedance is purely resistive, say a 50 Ω resistance again and no reactance? In rectangular form this is written as 50 + j 0 Ω.

The rule for the matched load impedance is the same as above so this is 50 - j 0 Ω. But that's the same as 50 + j 0 Ω and is more usually written just as 50 Ω. This is also true for other values of resistance. So the matched load for a pure resistance is just that resistance again.

Phew. So now we can answer your actual question:

Do male and female rf connectors have complex conjugate impedances to always match properly at their connections?

No. As berkeman pointed out in post #6 rf transmission lines and connectors are designed to have real characteristic impedances (Zo). That is, they are purely resistive with no reactive component. So a 50 Ω line and connector has an impedance of 50 + j 0 Ω. The matching impedance is also 50 + j 0 Ω. Hence matching connectors don't have positive and negative reactances; they are designed to both have zero reactance.

This is also true for other impedances, such as the 75 Ω connectors you mentioned. The coaxial cable and the connectors need to have the same impedance to match properly, so you use 50 Ω connectors with 50 Ω cable, 75 Ω connectors with 75 Ω cable and so on. The equipment you are connecting with these cables and connectors will also have to have the same impedance.

 

[Baluncore]

The characteristic impedance of a coaxial cable is determined by the inductance and the capacitance per unit length; Zo = √(L/C). The impedance is maintained so long as L/C is maintained. Any change of L/C when passing through connectors results in a reflection of energy from the mismatch.

An RF connector does not have the specified impedance until it is properly coupled to the cable and to another connector. Only then do the dimensions of the dielectric and opposed conductors combine to provide the correct L/C and so correctly match Zo through the connection.

 

[sophiecentaur]

The characteristic impedance of a coaxial cable is determined by the inductance and the capacitance per unit length; Zo = √(L/C). The impedance is maintained so long as L/C is maintained. Any change of L/C when passing through connectors results in a reflection of energy from the mismatch.

An RF connector does not have the specified impedance until it is properly coupled to the cable and to another connector. Only then do the dimensions of the dielectric and opposed conductors combine to provide the correct L/C and so correctly match Zo through the connection.

The mechanical arrangement inside a connector is an attempt to produce a uniform Z₀ through the transition but there is a limit to the parasitics. Generally, you get what you pay for and the connectors (and cables) that are suitable for the very high frequencies in the tens of GHz range are made to very high tolerances. Dielectric loss is another problem.
The cable construction is pretty important too. There are always periodic variations in dimensions when a cable is made or stored on a reel. Tiny variations along a cable can add up at some wavelengths and a cable can produce significant reflections of signals that are well down in its nominal operating range.