# What is the Characteristic Impedance of a System?

1. Jul 24, 2013

### thegreenlaser

I'm just starting to read up on RF circuits, and I'm a little confused about what the characteristic impedance of a system is (not the characteristic impedance of a transmission line, I understand that pretty well). For example, in Pozar's book he talks about a 3 dB attenuator with a 50 Ω characteristic impedance (represented by a T configuration of resistors with a port on either side). Does that just mean that all the transmission lines connected to the ports have a 50 Ω characteristic impedance? Is that 50 Ω value determined by the lumped elements in between the ports in any way, or am I just deciding what all the connecting transmission lines will be? Basically, what is required for me to say "my system has a 50 Ω characteristic impedance?"

Hopefully what I'm asking is clear... I feel like this should be a fairly simple thing.

2. Jul 24, 2013

### Baluncore

Every EM signal has two components. Firstly, an electric field or voltage, and secondly, a magnetic field or current. The ratio of E/M or V/I is the impedance.

Characteristic impedance is a frequency independent (broadband) character of a port.

If the port has a frequency dependent impedance in the band of interest then it does not have a “characteristic” impedance.

3. Jul 24, 2013

### the_emi_guy

This simply means that the attenuator has nominal port impedances of 50 ohms (as opposed to, say, 75 ohms). In other words it is intended to interface with 50 ohm cables with nominally no reflections at the attenuator ports. Of course the actual impedances of the ports will vary from 50 ohms (as will the cable itself), and is a metric of the quality of the attenuator (and cable).

4. Jul 24, 2013

### the_emi_guy

E/H is field impedance in units of ohms.

5. Jul 25, 2013

### Averagesupernova

I can't say I have heard of anything except transmission line having a characteristic impedance. Devices such as attenuators, amplifiers and etc. certainly have an input impedance but I can't say I have heard it referred to as a characteristic impedance.
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At least in my mind, characteristic impedance of a transmission line is the impedance one would have if they hooked a DC source to the end of a transmission line that had no copper loss and extended infinitely in one direction. The voltage of the source divided by the current drawn from the source would of course be the characteristic impedance.

6. Jul 25, 2013

### the_emi_guy

Agreed.

Port impedance seems like the most likely interpretation of the Pozar reference (assuming it was not misquoted).

7. Jul 25, 2013

### Averagesupernova

I don't get very bent out of shape over wording until it causes confusion with something else.

8. Jul 25, 2013

### Baluncore

“Characteristic impedance” is a fundamental broadband “characteristic” of a transmission line's construction. It is independent of the far-end termination, the line length and the signal frequency.

Of all a transmission line's “characteristics”, the most critical parameter is it's characteristic impedance. A Smith Chart or Volpert Diagram is centred on the characteristic impedance of the transmission line being modelled. All other points on the diagram then represent apparent “input impedances”.

The apparent “input impedance” of a resistive attenuator is also dependent on the impedance of it's load. Not only does it attenuate the signal, but it also attenuates any terminal impedance mismatch towards the attenuator's “characteristic impedance”. This is quite a useful way to isolate reactive modules.

When designing RF systems, about half the components, or half the design time, is needed to match the various modules. The standard characteristic impedance of 50 ohm for functional modules greatly facilitates prototyping and experimental interconnections.

There is a very good argument for the use of the term “characteristic” to differentiate between a component's designed impedance parameter and the apparent input impedance when part of a reactive system.

9. Jul 26, 2013

### thegreenlaser

Hmm... I guess this isn't just a clear-cut terminology issue. Maybe I'll give a little more detail on the example in Pozar. His description of the circuit is that it's "A matched 3 dB attenuator with a 50 Ω characteristic impedance." He says that to calculate S11, we terminate the other port with a "matched load" (for which he uses what he calls the characteristic impedance, Z0 = 50 Ω). Then we find the input impedance at port 1 and calculate the reflection coefficient: S11 = (Zin - Z0)/(Zin + Z0).

He does pick his resistor values so that S11 works out to be zero, but I'm not understanding why, in principle, you couldn't just aribtrarily decide that the characteristic impedance of the attenuator is 75 Ω, and then do the calculation in exactly the same way to get a non-zero S11.

10. Jul 26, 2013

### Baluncore

If Pozar is designing a 3dB attenuator for use in a 50 ohm system, he must design it so the input looks like 50 ohm when it is terminated in 50 ohm.

If a 3dB, 75 ohm attenuator was used in a 50 ohm system, then additional 150 ohm resistors would need to be connected between both terminals and ground to make it look like a 50 ohm attenuator. The attenuation of the resulting network would no longer be 3dB.