Intrinsic impedance of a resistor

[iVenky]

Hi,
What's the intrinsic impedance of a resistor?
The intrinsic impedance defined as η=E/H ratio of Electric field to Magnetic field? Is it the same as the resistance 'R'? Does it depend on μ,ε of the resistor material or free-space?
Also, do we have any electric field surrounding a current carrying wire (assuming DC current and it's not changing with time)?

 

[anorlunda]

If you are asking about an ideal resistor, then it is the resistance R.

Non-ideal components can have R, L and C, as well as nonlinearities which can not be characterized by R, L, or C.

Then there is resistivity, which has to do with bulk materials.

Can you be more specific as the the intent of your question?

 

[CWatters]

Hi,
What's the intrinsic impedance of a resistor?

Context please. Are you referring to resistance or resistivity?

A material has an intrinsic or specific resistivity. This property allows you to compare the properties of different materials.

Once you have fabricated the material into a resistor it has resistance.

 

[iVenky]

If you are asking about an ideal resistor, then it is the resistance R.

Non-ideal components can have R, L and C, as well as nonlinearities which can not be characterized by R, L, or C.

Then there is resistivity, which has to do with bulk materials.

Can you be more specific as the the intent of your question?

Yes, I am talking about ideal resistors. The intent is I understand that EM waves reflect when there is a difference in the intrinsic impedance between two media. I was wondering how this would apply when an EM wave traveling along a transmission line with an intrinsic impedance η hits a resistor (for which I don't know the intrinsic impedance). If η=E/H (ratio of Electric to Magnetic field) =R for an ideal resistor, can you tell me why that's the case?

 

[sophiecentaur]

You are referring to wave propagation here and to discuss a "reflection" with a resistor, you need to specify the situation that the wave interacts with the resistor. If you have a 50Ω coax cable and you solder a resistor across the end it then the reflection from a 'regular' resistor can be calculated fairly easily. You can also calculate the reflection when the resistor is bridged across a cable that is carrying a signal from point A to point B, with whatever impedances you choose to be connected at source and load. That is everyday transmission line theory; steer clear unless you really have to get involved.
Resistors can be made as near to the required Resistance value with as small parasitic components as you want to pay for. Once you get up into the UHF regions and above, resistors need to be very carefully designed and mounted into circuits. For audio and 'lower' Radio Frequencies, the parasitics are usually of no bother - but you can never say never, here.

 

[iVenky]

You are referring to wave propagation here and to discuss a "reflection" with a resistor, you need to specify the situation that the wave interacts with the resistor. If you have a 50Ω coax cable and you solder a resistor across the end it then the reflection from a 'regular' resistor can be calculated fairly easily. You can also calculate the reflection when the resistor is bridged across a cable that is carrying a signal from point A to point B, with whatever impedances you choose to be connected at source and load. That is everyday transmission line theory; steer clear unless you really have to get involved.
Resistors can be made as near to the required Resistance value with as small parasitic components as you want to pay for. Once you get up into the UHF regions and above, resistors need to be very carefully designed and mounted into circuits. For audio and 'lower' Radio Frequencies, the parasitics are usually of no bother - but you can never say never, here.

I do understand based on TL theory we can calculate reflection coefficient as Γ=(Z-Z0)/(Z+Z0), where Z is the resistor impedance and Z0 is the characteristic impedance of the TL line.
I am trying to understand this using EM waves and my understanding is that reflection can be explained by solving maxwell's equations with boundary conditions at the interface, which demands a difference in intrinsic impedance between two media for the reflection to happen. Hence, I want to know the intrinsic impedance of an ideal resistor.

 

[sophiecentaur]

Hence, I want to know the intrinsic impedance of an ideal resistor.

The "Intrinsic Impedance" means the resistance that you can put in a transmission (perfectly terminated or infinitely long) line or a medium that will replace the downstream part of the line will have the same effect as the medium. If the resistor is "ideal" then you can replace it with a copy of itself.

I have been trying to think what you actually have a problem with here. The above is a bit glib, I admit but it is the literal answer to your literal question. If you wanted to take that transmission line context into a traveling wave, you are considering the Fields in space or in a waveguide of some kind. You cannot 'connect' any resistor which will perfectly terminate a wave in free space - how would you do that? You would have to connect an antenna of some sort (which would transform any lumped resistor, at its feed point) and which would gather all the energy that's radiated. Etc. Etc. It doesn't make sense to go too far in that direction so you just have to talk in terms of the Impedance Of Free Space as the ratio of E and H fields (= about 377Ω and yes "how does the ratio of two fields become a Resistance?" is a fair question. Maths alone can justify that!) and accept that you can't actually replace space with a 'resistor'.

The same thing applies in a Wave-Guiding structure but where, in the waveguide would you place a resistor to produce a perfect termination? All you can do there is to pick off the power with a loop (or something else), placed at a certain point in the guide and feed that signal to a (perfect) Resistor that absorbs all the Power. But the value of the resistor required will depend on where you pick off the signal. Near the wall, the E field is low and the H field is high is the Impedance is Low and , in the middle, the H is low and the E is high so the Impedance is high). You can tinker with the geometry at the end of any guide in such a way as to eliminate the reflection from the Load, wherever you couple it but that only means you have transformed the load in such a way as to match it to the Intrinsic Impedance of the guide. The resistor doesn't need to be any particular value (not even purely resistive.

Does that make any sense?

 

[alan123hk]

Hi,
What's the intrinsic impedance of a resistor?
The intrinsic impedance defined as η=E/H ratio of Electric field to Magnetic field? Is it the same as the resistance 'R'? Does it depend on μ,ε of the resistor material or free-space?
Also, do we have any electric field surrounding a current carrying wire (assuming DC current and it's not changing with time)?

I believe that the intrinsic or wave impedance of a ideal resistor is equal to its characteristic impedance, namely "R" in the units of ohms, although resistor is usually referred to an element in lumped circuit working in low frequency.

 

[sophiecentaur]

I believe that the intrinsic or wave impedance of a ideal resistor is equal to its characteristic impedance, namely "R" in the units of ohms, although resistor is usually referred to an element in lumped circuit working in low frequency.

I really don't see how a lumped (="ideal"?) resistor as any Intrinsic Impedance. I think the term is being mis- applied.

The intrinsic impedance defined as η=E/H ratio of Electric field to Magnetic field?

A resistor will have an Impedance which will be just resistive if it is mounted appropriately in a transmission line but that is to do with the line itself and not the resistor.
This is yet another example of people worrying about terms and classification rather than the Physics of a situation.

@iVenky Perhaps if you were to draw a diagram which includes your Ideal Resistor and show what you mean by its Intrinsic Resistance in a particular context and which E and H come into it..

 

[alan123hk]

I really don't see how a lumped (="ideal"?) resistor as any Intrinsic Impedance. I think the term is being mis- applied.

My previous statement "resistor is usually referred to an element in lumped circuit working in low frequency" is inaccurate, lumped resistor is just a model for simplifying the description of the behaviour of spatially distributed physical system of the resistor into an entities that approximate the behaviour of the distributed system under certain assumptions, it's convenient and useful for engineering design and analysis, and it is intended for either high or low frequency down to DC, it can also be used to model ideal resistor and non-ideal (having capacitive or(and) inductive effect) resistor as well.
https://en.wikipedia.org/wiki/Lumped_element_model

wave impedance (intrinsic impedance) is defined for a wave (ratio of transverse components of electric and magnetic field) and usually apply to the situation of wave traveling through a medium, whereas characteristic impedance is given for finite transmission line (terminated by a matched load) defined as a ratio of amplitudes of voltage to current.

People seldom apply the term "intrinsic impedance" for resistor in electrical engineering.

 

[sophiecentaur]

People seldom apply the term "intrinsic impedance" for resistor in electrical engineering.

I'm not surprised because I haven't seen a (your) definition. How would I recognise one if you handed it to me?