Why is impedance given as a simple Ohms unit when it's frequency dependent?

[Crimadella]

TL;DR Summary

The title nails it!

I've been trying to learn Impedance for over a year and this one thing is screwing me up. When they(any source) give an output or input Impedance it's always given in ohms. I went into learning about angular velocity, imaginary numbers, complex numbers- I haven't completed it but I feel I have it down to a point where I could calculate it with notes. Maybe there is something else I'm missing? Because a simple ohms unit is not a complex number yet Impedance is given in ohms- I feel like if it's simply in ohms that that's a measurement at a particular frequency because Impedance is frequency dependent. So it makes me think- what frequency is that assuming?

That's my curiosity but that kinda sounds ridiculous so very doubtful that's the case which begs the question, what am I missing?

Being I'm working with audio and guitar circuitry, how do you calculate the Impedance of a passive guitar pickup? Now that I think about it, I haven't read anything on how a transducers Impedance would be calculated, would it just be viewed as an inductor? (For this specific transducer, anyway)

And just one question on transformers. How is it that a transformer can pass audio frequencies with less windings/inductance than an inductor when the primary is an inductor.

Say I has an audio signal that passed through the primary coil and after the primary coil(aka not what transfers to the secondary via the core(or air)) I sent it through amplifier and speaker, would that audio signal be filtered as if it were an inductor? Can you have circuitry after a transformer primary, in series with the primary? I just thought of that one after coming up with the prior question, there is conservation of energy thus I would guess that there isn't going to be much, if any signal left after the primary, in series- but if there is, even a tiny signal, would it filter THAT signal as an inductor would?

Of course, a transformer is simply two inductors that are magnetically coupled, so it just seems weird that more audio frequencies would pass through a transformer for a given inductance than an inductor when a transformer literally is an inductor, as in its a coil, it passes fine through the transformer coil, that's how it's magnetic flux is superimposed on the core(or through the air onto the next coil), so how the H does that work?

Just an upfront notice, I'm Autistic and last completed grade was 7th at a horrifically lacking public school, so everything I've learned, pretty much, has been from curiosity and reading online.

 

[.Scott]

When dealing with audio frequency electronic signal, impedance measured in Ohms is used to describe the characteristic impedance of a cable, the impedance provided by a signal input, or the impedance expected by a signal output. What's important is impedance matching. So, if the output is expecting 75 Ohms, use 75 Ohm cables and 75 Ohm signal inputs. Similarly for 50 or 100 Ohm signals.
Mis-matching impedance can result in circuit overloads, clipping, or problems with gain (volume) control. For audio signals, the wavelengths are so large that other types of signal distortion are unlikely. But with video or telemetry signal, you can also get ghosting of the complete loss of sync information.

 

[Tom.G]

See if this article helps:
https://audiointerfacing.com/guitar-pickup-impedance/

(above, and many others, found with a Google search:
https://www.google.com/search?hl=en&q=output+impedance+of+guitar+pickup
You might also find some of the other articles found in that search useful.)

Cheers,
Tom

 

[Borek]

You are definitely right that impedance depends on the frequency, compare https://www.khanacademy.org/science...ic/ee-ac-analysis/v/ee-impedance-vs-frequency

(no, I don't know the answer to the question why it is listed as a single number then, but at least Khan academy shows your confusion has a merit)

 

[sophiecentaur]

TL;DR Summary: The title nails it!

When they(any source) give an output or input Impedance it's always given in ohms.

Not 'any source' but measurement equipment (sources or receivers / meters) are often designed to have a resistive impedance because that makes life easier. If you connect to a piece of measurement equipment with a complex impedance then you would need compensate for that if you want a proper answer. A signal source will often have an output amplifier with a low impedance and then have a good 50Ω resistor in series. Likewise, a measuring unit will have a high input impedance with 50Ω in parallel. Terminating signal lines like this avoids reflections at the end of a transmission line so it gives you the 'true' volts over a wide frequency range.

Matching is not always the best. Power amplifiers are usually designed to have a very low impedance so that most of the power gets to the load (likewise for the electricity supply system). Many loads do not have a resistive impedance. A nominally 8Ω loudspeaker will have significant Reactive components which vary all over the audio range but designers try to compensate for this in the loudspeaker and crossover units to give a reasonably flat response.

I just realised I have launched out on a limitless field of information. Just work steadily at this and you will eventually get near enough to a working knowledge. Read as much as you can but avoid glib 'make it work' web pages which can mislead you.

 

[berkeman]

TL;DR Summary: The title nails it!

Maybe there is something else I'm missing? Because a simple ohms unit is not a complex number yet Impedance is given in ohms

Of course it is. In general an impedance will not be purely real, and will have a Real and an Imaginary component. These are each a ratio of the Voltage and Current, so each component has units of Ohms.

There are two common ways to express this complex impedance -- With complex numbers:
$$ \mathbf{Z(f)} = Z_r(f) + jZ_i(f) $$
where both the Real and Imaginary impedances have units of Ohms, and with Magnitude and Phase notation:
$$ \mathbf{Z(f)} = Z_{mag}(f) < \theta (f) $$
where the Magnitude is in Ohms and the Phase angle $\theta$ is in radians or degrees.

The Magnitude and Phase notation is commonly used in logarithmic impedance plots from Impedance Analyzers like the HP 4194 and similar...

https://www.researchgate.net/figure...ical-impedance-element-Figures_fig13_38006544

 

[DaveE]

The unit of Ohms is simply the ratio of Volts and Amps. At any instant in time there is a Real scalar Value of Volts and Amps in any component.

We extend this to waveforms that vary in time, usually focusing on sinusoids of a fixed frequency. This simplifies situations where the circuit response varies in frequency and is the basis for more advanced analysis techniques like Fourier or Laplace transforms. Many circuits will cause a shift in the phase of sinusoidal waveforms as well as changes in amplitude. This phase shift is important in the behavior, so we then need to represent sinusoidal behavior with a pair of values representing both magnitude and phase. This leads to mathematical techniques based on vectors or complex numbers and such. For convenience in this analysis we extend the concept of resistance to impedance which can be represented with complex numbers but still maintain the Ohms unit. In this case it is the ratio of a sinusoidal voltage and it's associated sinusoidal current and, of course, could be frequency dependent.

In cases where we aren't dealing with a single frequency waveform, like a step or impulse response, the concept of Ohms doesn't make much sense and isn't used.

 

[The Electrician]

TL;DR Summary: The title nails it!

I've been trying to learn Impedance for over a year and this one thing is screwing me up. When they(any source) give an output or input Impedance it's always given in ohms. I went into learning about angular velocity, imaginary numbers, complex numbers- I haven't completed it but I feel I have it down to a point where I could calculate it with notes. Maybe there is something else I'm missing? Because a simple ohms unit is not a complex number yet Impedance is given in ohms- I feel like if it's simply in ohms that that's a measurement at a particular frequency because Impedance is frequency dependent. So it makes me think- what frequency is that assuming?

That's my curiosity but that kinda sounds ridiculous so very doubtful that's the case which begs the question, what am I missing?

Being I'm working with audio and guitar circuitry, how do you calculate the Impedance of a passive guitar pickup? Now that I think about it, I haven't read anything on how a transducers Impedance would be calculated, would it just be viewed as an inductor? (For this specific transducer, anyway)

And just one question on transformers. How is it that a transformer can pass audio frequencies with less windings/inductance than an inductor when the primary is an inductor.

Say I has an audio signal that passed through the primary coil and after the primary coil(aka not what transfers to the secondary via the core(or air)) I sent it through amplifier and speaker, would that audio signal be filtered as if it were an inductor? Can you have circuitry after a transformer primary, in series with the primary? I just thought of that one after coming up with the prior question, there is conservation of energy thus I would guess that there isn't going to be much, if any signal left after the primary, in series- but if there is, even a tiny signal, would it filter THAT signal as an inductor would?

Of course, a transformer is simply two inductors that are magnetically coupled, so it just seems weird that more audio frequencies would pass through a transformer for a given inductance than an inductor when a transformer literally is an inductor, as in its a coil, it passes fine through the transformer coil, that's how it's magnetic flux is superimposed on the core(or through the air onto the next coil), so how the H does that work?

Just an upfront notice, I'm Autistic and last completed grade was 7th at a horrifically lacking public school, so everything I've learned, pretty much, has been from curiosity and reading online.

Are we to understand that you are now in eighth grade? If you are self educating about all this, you would be well repaid in knowledge gained by going through this free online book: http://www.dissidents.com/resources/ACElectricalCircuitAnalysis.pdf

The very first chapter will answer a lot of your questions.

You might also find this thread answers some of your transformer questions: https://groupdiy.com/threads/mic-preamp-input-impedance-and-transformer-impedance.67649/

 

[Crimadella]

Thanks for the responses, it's going to take a minute for me to grasp them, I'm having difficulty following them right now(ADHD). I'll look into the links and additional reading when I can read better. Obviously I need to do more reading on angular velocity. When I get bombarded with too much new information it becomes hard to follow/comprehend. The formulas supplied will help.

You don't have to assume anything about what grade I'm in, I'm 43yo, I left school decades ago. The point of including my highest grade completed was to make people aware that I haven't learned anything about electronics via a formal school, coupled with ADHD, the way I learn is by being all over the place, figuratively speaking, which adds ample opportunity to miss small things that had I not I would have a better understanding.

I have several E-books, a ton of lengthy PDF'S, a problem I encounter with following a book is running into problems understanding due to how things were phrased, explained or in many cases an absence in knowledge that the author expected the reader to know. For example, it took months for me to find someone actually explaining what the j(imaginary number) and the little "w" meant because for unkown reasons what the j and w represented was left out of the explanation of formulas. I read hundreds impeadance formula explanations before someone finally mentioned what those two variables are/were. It's kinda annoying how so many people wrote materials on formulas, explaining literally what every variable except for the imaginary number and radians symbol represented, thus for like half a year when they popped up in formulas that pretty much stopped me from figuring it out because these two variables just pop into the equation with no explanation of what they are.

From what I gather, due to autism, I tend to interpert things abnormally, or differently, and this causes problems following a book because it's not going to take long to run into a situation where I don't understand what they are explaining and would have to have questions answered to proceed any further. I'll keep coming back to read over this stuff, maybe I'll understand it eventually, my mind is kinda in a funk right now and the responses were a lot more expanded and complex than expected.

Something I noticed in the past, a long time ago I needed to learn some algebra to pass GED so my Grandpa gave me his old college algebra book and I couldn't help but not how much easier it was to understand because they used more simple words to explain things, it was far easier to follow and understand than anything modern. Anyway, I'll keep at it- I won't ask anymore questions until I can understand these answers.

I'm trying to learn enough to design and make my own audio circuitry(preamp and effects) for my guitar, maybe an amp to- eventually. I don't want to just copy someone else's design but understand how to create my own design and topologies.

 

[DaveE]

Anyway, I'll keep at it- I won't ask anymore questions until I can understand these answers.

There is an issue with these forums, I think. The people that respond to questions know the material and probably learned it years ago. We typically learned it in conventional educational structures: HS, universities, work experience...

Then when people ask questions it's easiest for us to parrot back the learning process we followed and give the information in a form that makes the most sense for us, after we've learned the basics. So, a natural focus on what WE THINK are the interesting, complex, parts develops. Those are the parts that interest us and that WE THINK you are asking about.

Don't give up on us, we want to help. But sometimes we don't know how to do that the best way. One of the things that I find difficult in answering questions is understanding what the questioner knows, at what level should I respond, what can I assume you already know. Tell us what you need. Tell us if our answers don't make sense to you, this is a normal process of teaching. If you don't understand our answers, it's not all your issue. It also means we didn't explain things appropriately. If you think we can help, stay engaged, give us feedback.

Also, remember that you need to learn to walk before you can run. Some questions just can't be answered well without some more basic understanding. You will not get a simple answer if you start asking about very difficult subjects. But we should be able to explain that if we understand where you're coming from. We should always be able to describe the "next step".

 

[sophiecentaur]

it's easiest for us to parrot back the learning process we followed

The word "parrot" implies a lot of things about attitudes to education. I'm afraid it raised my hackles a bit.

No pain, no gain applies to any field of learning and learning stuff by rôte is often the only way into a Science. I think I understand why your post contained that term and there are many replies to beginners which ignore the declared level of a starter question and plunge into Integral and vector equations with no help with their message.

The OP has asked a very open question and there is no closed answer except :"You'll have to do an lectronics course if you really want to know". There is certainly no answer that doesn't contain Maths and there's an awful lot of 'Parrot' in dealing with Algebra and Calculus. So I don't feel that an apology is due; the OP needs to be prepared for a hard road.