Is electrical engineering's "Smith Chart" relevant to sound waves?

[neRok]

I just watched the Veritasium video Why is This the Scariest Chart in Electrical Engineering?

It starts off talking about radio waves and electricity transmission lines, and shows how the waves can reach their destination and then reflect back to the source causing standing waves - just like sound bouncing off the walls of our rooms.


I didn't pay enough attention to the next bits, but it said some stuff about tweaking the overall length and/or material properties in order to get the phases inline. It then described these possible tweaks as being either inductive or capacitive.
They then showed the example in the following screenshot, which shows something like the default wave leaning to 1 side, and by adding some inductance it can be brought back to neutral.


Then they showed how some math is applied to wrap these and more properties together in to the Smith Chart.


Then they showed an example problem that the smith chart can solve, and as per my simplistic understanding;
* the center of the circle along the horz line is the waves resistance or something.
* the blue diamond is something related to the default state (perhaps the simply calculated/measured reflection point).
* the red circle represents other places the wave (blue diamond) could exist if the circuits length/resistance/etc was slightly different.
* the yellow circle shows what I guess are harmonious inductive/capacitive values relative to the resistance (center of red circle).
* wherever the red and yellow lines cross are places whereby the yellow and red will combine in a way that creates a neutral result (the desired outcome).
* the angle between the points is relevant to phase shift or something.


Now I clearly didn't understand the maths/science in this video properly - but it seems that basically you locate your current "outcome" on the chart, and then the chart will show you what to do to get a "neutral outcome"? And so I wonder if this chart is the secret-sauce for doing "active cancellation" like what Dirac ART is doing? Because to me the problems seems similar, whereby the blue diamond is the measured SPL in room, which means all reflections are included - and then perhaps the yellow dots are the cancellation tones, the yellow circle is the strength of those tones, and the angle between blue and yellow dots is the phase-shift/time-delay of the cancellation tones?

 

[sam_adams]

It has no bearing at all on analog audio cable interconnects. Audio interconnect cables are far too short to be transmission lines—where signal reflection in the cable might be of concern. Characteristic impedance of RF cabling means nothing to us at our frequencies of interest. Our greatest concern is with resistance, capacitance, and inductance of the cable. By-and-large, capacitance is the major concern for those cabling a phono preamp to a turntable where the interconnect's capacitance may load the circuit and change the frequency response.

Resistance would be of concern in the shield of a shielded, twisted pair cable because we want the lowest resistance possible to prevent chassis circulating currents from generating noise in the signal conductors. We also want a good low resistance shield conductor to reduce radiated RFI from being coupled to the signal conductors. This is where a balanced line, differential pair interconnect provides the most benefit.

Inductance can be offset in an interconnect by controlling impedance through cable geometry and construction so that the cable capacitance will offset the rising inductance at the higher frequencies in the audio band and keep the frequency response flat.

Read these:

Jensen Transformers Application Notes

Bill Whitlock - An Overview of Audio System Grounding and Interfacing - Indy-AES-2012 (PDF)

Effects of Cable, Loudspeaker,and Amplifier Interactions - Fred E. Davis (PDF)

 

[Redacted]

It's exactly like this for any means whereby waves are propagated, at least mathematically. The key thing is how much is going to be audible.

The conduction of current down a wire is fantastically complicated but can easily be made to work for anything a human cares about.

In a nutshell, apart from LCR (where L & C store energy) any change in any transmission medium can cause reflection, phase changes and all sorts of "effects". In a room, it's the fact that the air suddenly becomes walls, firnuture edges etc that gives you the need for Dirac etc, which just identifies peaks and troughs in certain parts of the room and applies filtering to reduce the effect. You could achieve similar with speaker arrays playing phase-varied signals around the room, but it's less practical.

Many systems use phased arrays to shape signals - not quite what we're talking about, but related when you do the sums!

Also, for those interested, look up "inerters" (sic) in suspension systems too.

 

[amirm]

If you drive your car, time slows down for you relative to someone standing still. We don't care about that effect because it is extremely small. Same here. At audio frequencies and cable lengths we use, the effect is infinitesimal and hence, ignored.

In RF frequencies, the opposite is true making that field a specialty that not every engineer can master.

 

[MaxwellsEq]

I just watched the Veritasium video Why is This the Scariest Chart in Electrical Engineering?

It starts off talking about radio waves and electricity transmission lines, and shows how the waves can reach their destination and then reflect back to the source causing standing waves - just like sound bouncing off the walls of our rooms.
View attachment 545811

I didn't pay enough attention to the next bits, but it said some stuff about tweaking the overall length and/or material properties in order to get the phases inline. It then described these possible tweaks as being either inductive or capacitive.
They then showed the example in the following screenshot, which shows something like the default wave leaning to 1 side, and by adding some inductance it can be brought back to neutral.
View attachment 545820

Then they showed how some math is applied to wrap these and more properties together in to the Smith Chart.
View attachment 545824

Then they showed an example problem that the smith chart can solve, and as per my simplistic understanding;
* the center of the circle along the horz line is the waves resistance or something.
* the blue diamond is something related to the default state (perhaps the simply calculated/measured reflection point).
* the red circle represents other places the wave (blue diamond) could exist if the circuits length/resistance/etc was slightly different.
* the yellow circle shows what I guess are harmonious inductive/capacitive values relative to the resistance (center of red circle).
* wherever the red and yellow lines cross are places whereby the yellow and red will combine in a way that creates a neutral result (the desired outcome).
* the angle between the points is relevant to phase shift or something.
View attachment 545826

Now I clearly didn't understand the maths/science in this video properly - but it seems that basically you locate your current "outcome" on the chart, and then the chart will show you what to do to get a "neutral outcome"? And so I wonder if this chart is the secret-sauce for doing "active cancellation" like what Dirac ART is doing? Because to me the problems seems similar, whereby the blue diamond is the measured SPL in room, which means all reflections are included - and then perhaps the yellow dots are the cancellation tones, the yellow circle is the strength of those tones, and the angle between blue and yellow dots is the phase-shift/time-delay of the cancellation tones?

Hi I'm an Electronic Engineer who has worked in the broadcasting world.

When you are transmitting radio (which includes TV) waves, understanding propagation, reflections, attenuation is absolutely vital. This also includes high frequency signal movement over wires (including data). Smith Charts are a classic way to model this. It's all standard stuff you need to be able to answer exam questions on to get a degree.

Irrelevant at HiFi, music, audio frequencies and domestic cable lengths.

Domestically, where it's relevant: WiFi or Cat5 data, cable TV, traditional and digital radio and TV.

 

[Berwhale]

@neRok Watch this bit again (starting 5:58)...

 

[SSS]

Haha, a radio frequency engineer will laugh when asked smith chart for audio. It is totally irrelevant. Except you may have audio lines as long as over land telephone lines.

 

[neRok]

I should have clarified further that I'm not asking about the electrical signal side of the music (cables/interconnects/etc), but actually the physical sound pressure waves in room. So I'm pondering if the EE Smith Chart is "an analogy" of sound waves? And as both discussion domains are effectively "waves" (electricity is electrons shuffling about in a wire, and sound is particles of air shuffling about), both have phase etc, and the physics is all "intertwined" in this 1 universe - then perhaps its not so much of an analogy, but the same thing just in different realms?! Or perhaps at least the "charts" are the same shape.

So when I mentioned "sound bouncing off the walls of our rooms", the way the waves reflect in EE seems just like they do along 2D planes in room. Consider the visualisations in this thread: Visualizing How Different Loudspeaker LF Directivity Patterns Couple to Room Modes

Monopole located near the left wall

In that GIF you can see how the waves propogate from the red dot, go forwards and backwards, and eventually reflect off the far wall. This seems to be the same phenomenon?!
Edit: also in the Veritasium video, they showed waves moving along slinkys, and you can obviously see that the wave emanates from the source, and that reflections can occur for various reasons like if there are changes in the transmission medium.

Bonus idea: if "air" is main transmission medium of sound in our rooms, then perhaps you could add a volume of other-gas (like maybe a big balloon full of anything-but-air), then that "change" in the transmission medium could be used to reflect some sound at different times to the main reflection. So kind of like a diffuser?!

Now consider Double Bass Array, whereby you put a secondary array of subs on the back wall and feed them an altered signal, the result of which means new waves are output in the room that directly overlap the original waves that are now reflecting - and thus the new waves counter the original waves, which means there is in effect no reflections.

So consider any frequency in a DBA - 100Hz say. The front speakers output is going to have some relationship with the room, and thus the IR (impulse response) is going to be somewhere between good and bad - where "good" is "on the line" of the Smith Chart, and "bad" is above or below the line. What's the difference to "bad above" and "bad below" in terms of sound waves? Perhaps above is positive summation causing peaks, and below is negative summation causing nulls? And so if you put the front speakers on the chart as the blue diamond, then you can also put the rear speakers on the chart as the orange ("yellow") diamond.

And then through the process of imagination, you can see how the orange diamond can be moved along its circle until a point is reached that coincides "as good as possible" with the red circle. And then the size of the orange circle may indicate the relative power needed to be output by orange (rear speakers), and I guess being above or below could relate to polarity inversion, and the different diameter/center point of the circle is difference in dB, and the angle of the black lines could be the delay?

Because in a DBA you need those 3 things to be applied to the rear speakers - inverted polarity, slight delay, and slight volume reduction. And so is it this Smith Chart that is showing that relationship?

Regarding inductance and capacitance: my simplistic understanding of how those similarly named electrical components work is that they are like buffers that act more strongly when the waveform gets towards the its extremes - and so basically one of them takes power on occasion, and the other gives power on occasion? And so in that sense with regards to speakers in a room - one would "add power" by generating in-phase sound, and the other could "take power" by outputting off-phase sound?

The video said that the smith chart is geared around a singular target frequency, which makes sense in regards to electricity networks, where its a single frequency being transmitted on the wire. But it also said that you can plot the affects of other frequencies on the target frequency, and that those plots can be used to work out some combination of changes that give a "best fit" result. Like this;


So in the case of DBA, you have a nearly "perfect opposite" set of speakers - but in the case of Dirac ART, it just measures the IR's off the various speakers you have. Then I'm suggesting that for each speaker (the blue dot), you then plot the positions of all the other speakers (ie, orange dots), and then you can move those orange dots along their orange circles in ways that predictably impact the position of the blue dot.

So in that way, you can alter orange#1 along its circle a little, and orange#2 along its circle a little, and that hopefully results in blue dot moving along its circle and becoming closer to the line - the line representing a perfect IR...?

 

[neRok]

I just had a little bit more of a think and a then a re-read of my last post, and something twigged in my mind when I was looking at the GIF I quoted - AC vs DC. Because in a way "transmission lines" and "radios" are like DC, in that they output "one way" energy. IE, the energy goes down the line, and the subsequent reflections are just affecting other "DC" energy.

Now when you consider sound from a speaker, like the red dot in the quoted gif: it is more like AC energy, in that "reverse wave" is "quickly" back "in the mix" - and now it is opposite (alternate) because of the time-delay of the being a reflection. And so when you consider the "forward wave" and its summation with the "shortly delayed wave that may now be of opposite polarity" - well that sounds like an AC system!

Simplistic side note that explains my reasoning: AC oscillates over zero, whereas DC is wholly 1-sided?
And so perhaps "transmission lines" are "simplistic" in the sense that they are (in analogous terms) "only 2D", whereas "sound waves" are AC = "3D"?

 

[DonH56]

The Smith chart is referenced to a single impedance, not a single frequency. The chart is irrelevant to sound waves and low-frequency audio signals that do not require impedance matching. There is no practical analog to transmission impedance for audible sound waves. Sound waves do reflect and redirect, but their transmission through the air is a completely different mechanism than for RF signals. And unlike RF signals, sound waves do not invert when reflecting off a boundary. You are trying to force-fit something that simply does not fit.

Radio waves are not DC; they are AC signals alternating in phase, alternating, just as sound (pressure) waves alternate between compression and rarefaction. DC is something produced by a battery; AC is what comes out of your wall socket, or speakers. A "DC" audio signal would be silent.

 

[bmc0]

And unlike RF signals, sound waves do not invert when reflecting off a boundary.

An object that mostly reflects RF usually does so because of its low electrical impedance, thus the reflection coefficient is negative. In contrast, a solid object reflects sound because of its high acoustical impedance, thus the reflection coefficient is positive.

Acoustic pressure is analogous to electrical voltage and acoustic volume velocity to electrical current. An acoustic plane wave reflecting off a solid wall can be thought of as a transmission line with an open-circuit termination: the termination impedance is approximately infinite and the reflection is positive polarity. The RF reflection example above is like a transmission line with a short-circuit termination. An analogous example in the acoustical domain would be a plane wave propagating in an open-ended pipe: the termination impedance is approximately zero and the reflection is negative polarity.

 

[DonH56]

An object that mostly reflects RF usually does so because of its low electrical impedance, thus the reflection coefficient is negative. In contrast, a solid object reflects sound because of its high acoustical impedance, thus the reflection coefficient is positive.

That actually works for RF as well; open and short circuits using 1/4 and 1/2 wave tuning stubs are common, and reference opens and shorts for TDRs and such. I didn't figure it really mattered for this discussion.

Acoustic pressure is analogous to electrical voltage and acoustic volume velocity to electrical current. An acoustic plane wave reflecting off a solid wall can be thought of as a transmission line with an open-circuit termination: the termination impedance is approximately infinite and the reflection is positive polarity. The RF reflection example above is like a transmission line with a short-circuit termination. An analogous example in the acoustical domain would be a plane wave propagating in an open-ended pipe: the termination impedance is approximately zero and the reflection is negative polarity.

I am aware, but was trying to avoid reminders of my grad classes in acoustics. They were interesting but, let's just say, less "fun" than I expected. Much of the theory was useful in my later (non-acoustic) day job since a lot of the initial study was wave equations and such. My first intro to multidimensional FFTs as well, and one textbook was from Navy guys, so included some info on beamforming useful for radar and ultrasound systems that were part of my day job. This is useful additional information, though I suspect may be above the OP's technical level. And none of this makes using a Smith chart for acoustic analysis particularly relevant.

 

[bmc0]

That actually works for RF as well

Indeed. My point was to hopefully clarify for the OP (or other reader) that the phase of the reflection depends on the impedances rather than being some inherent "fixed" property of electromagnetic vs acoustic waves, which I thought some may misinterpret your comment as suggesting.

 

[kemmler3D]

I should have clarified further that I'm not asking about the electrical signal side of the music (cables/interconnects/etc), but actually the physical sound pressure waves in room. So I'm pondering if the EE Smith Chart is "an analogy" of sound waves? And as both discussion domains are effectively "waves" (electricity is electrons shuffling about in a wire, and sound is particles of air shuffling about), both have phase etc, and the physics is all "intertwined" in this 1 universe - then perhaps its not so much of an analogy, but the same thing just in different realms?! Or perhaps at least the "charts" are the same shape.

So when I mentioned "sound bouncing off the walls of our rooms", the way the waves reflect in EE seems just like they do along 2D planes in room. Consider the visualisations in this thread: Visualizing How Different Loudspeaker LF Directivity Patterns Couple to Room Modes


In that GIF you can see how the waves propogate from the red dot, go forwards and backwards, and eventually reflect off the far wall. This seems to be the same phenomenon?!
Edit: also in the Veritasium video, they showed waves moving along slinkys, and you can obviously see that the wave emanates from the source, and that reflections can occur for various reasons like if there are changes in the transmission medium.
View attachment 545852
Bonus idea: if "air" is main transmission medium of sound in our rooms, then perhaps you could add a volume of other-gas (like maybe a big balloon full of anything-but-air), then that "change" in the transmission medium could be used to reflect some sound at different times to the main reflection. So kind of like a diffuser?!

Now consider Double Bass Array, whereby you put a secondary array of subs on the back wall and feed them an altered signal, the result of which means new waves are output in the room that directly overlap the original waves that are now reflecting - and thus the new waves counter the original waves, which means there is in effect no reflections.

So consider any frequency in a DBA - 100Hz say. The front speakers output is going to have some relationship with the room, and thus the IR (impulse response) is going to be somewhere between good and bad - where "good" is "on the line" of the Smith Chart, and "bad" is above or below the line. What's the difference to "bad above" and "bad below" in terms of sound waves? Perhaps above is positive summation causing peaks, and below is negative summation causing nulls? And so if you put the front speakers on the chart as the blue diamond, then you can also put the rear speakers on the chart as the orange ("yellow") diamond.
View attachment 545850
And then through the process of imagination, you can see how the orange diamond can be moved along its circle until a point is reached that coincides "as good as possible" with the red circle. And then the size of the orange circle may indicate the relative power needed to be output by orange (rear speakers), and I guess being above or below could relate to polarity inversion, and the different diameter/center point of the circle is difference in dB, and the angle of the black lines could be the delay?

Because in a DBA you need those 3 things to be applied to the rear speakers - inverted polarity, slight delay, and slight volume reduction. And so is it this Smith Chart that is showing that relationship?

Regarding inductance and capacitance: my simplistic understanding of how those similarly named electrical components work is that they are like buffers that act more strongly when the waveform gets towards the its extremes - and so basically one of them takes power on occasion, and the other gives power on occasion? And so in that sense with regards to speakers in a room - one would "add power" by generating in-phase sound, and the other could "take power" by outputting off-phase sound?

The video said that the smith chart is geared around a singular target frequency, which makes sense in regards to electricity networks, where its a single frequency being transmitted on the wire. But it also said that you can plot the affects of other frequencies on the target frequency, and that those plots can be used to work out some combination of changes that give a "best fit" result. Like this;
View attachment 545849

So in the case of DBA, you have a nearly "perfect opposite" set of speakers - but in the case of Dirac ART, it just measures the IR's off the various speakers you have. Then I'm suggesting that for each speaker (the blue dot), you then plot the positions of all the other speakers (ie, orange dots), and then you can move those orange dots along their orange circles in ways that predictably impact the position of the blue dot.

So in that way, you can alter orange#1 along its circle a little, and orange#2 along its circle a little, and that hopefully results in blue dot moving along its circle and becoming closer to the line - the line representing a perfect IR...?

I think you are thinking along kind of the right lines, but as others have mentioned, transmission line calculations are not a great model for room acoustics. Possibly a good model when you are building a transmission line speaker.

From my limited knowledge of both, the mechanics of sound waves in rooms have more in common with optics than RF engineering. The waves are always moving in 3D, the reason you can sort of maybe not really model a DBA as a transmission line within the room is the approximation of the sound wave moving through the room as a plane is close enough to reality at very low frequencies to work such that a 2D approximation is OK. At high frequencies unfortunately it is nothing like that.

Speakers / room acoustics are tricky in general because the size of the waves is similar to or even larger than the size of the room. As such it is hard to get things right using simplified models. Example: In optics, a useful diffuser for LED light can basically just be a lens with a random shape. We don't care that some wavelengths are diffracted more than others in a diffuser for an LED lamp because the size of the variation is much smaller than what we care about.

In contrast, acoustic diffusers can't just be a random shape to scatter sound evenly, since the size of the wave has a meaningful interaction with the size of the features of the diffuser.

etc.

 

[amm]

Hello All,

I hope you do not mind a few facts and clarifications from someone who teaches the Smith chart in electromagnetics (EM) and RF courses and whose research includes microwave acoustics. (By the way, we introduce the Smith chart in our first EM course for sophomores, so it is not particularly difficult to learn.) I am sure many contributors here are already familiar with these concepts, but readers may become confused by some of the parallel discussions and conclusions in this thread.

Before I begin, let me emphasize that I am not suggesting the Smith chart can be used to solve room acoustics problems. My goal is simply to clarify some fundamental concepts for those following the discussion. For example, the suggestion that the Smith chart is a tool only RF engineers can use is incorrect. Moreover, the original poster has raised several valid ideas that are worth exploring and should not be dismissed out of hand.

Sound waves and EM waves exhibit many similar behaviors. Both undergo reflection, refraction, and transmission as they propagate through different media. Analogies between acoustics and EM propagation can be valid when discussing wave phenomena.

The Smith chart is a transformation (conformal mapping to be precise) of the (normalized) impedance onto (complex) reflection coefficient plane (coordinates). Reflection occurs whenever a wave encounters a discontinuity, whether it is an EM wave propagating in free space, on a transmission line, or a sound wave propagating through a medium.

Just as the Smith chart can be applied to EM “plane waves” incident on a wall or another impedance discontinuity, it can also be applied to acoustic plane waves propagating through a medium and bouncing off a wall for example, where reflection phenomena occur. The underlying principles of impedance mismatch and wave reflection are the same in both cases.

The impedance read on the Smith chart does not need to be electrical impedance it can be acoustic impedance, The chart itself is agnostic to the physical nature of the wave, EM or acoustics, does not matter.

The scale on the periphery of the Smith chart is graduated in fractions of wavelength. Wavelength is the relevant quantity because the phase variation of a propagating wave is determined by distance measured in wavelengths.

In summary, the Smith chart is fundamentally a tool for analyzing wave propagation and reflection. Whether the wave is acoustic or EM is irrelevant. The underlying mathematics remains the same. Also, the Smith chart is not tied to a particular range of frequencies.

As I read the various comments and replies to the original post, I feel that some misunderstanding appears to stem from the assumption of electrical signals at audio frequencies traveling on transmission lines. These are not sound waves; they are bound electromagnetic waves. It should be noted that the original poster indeed has sound waves in mind.
Related to sound waves undergoing a 180° phase shift upon reflection in air, acoustic metamaterials are engineered to exhibit an effective acoustic impedance approaching zero, even in air, over specific frequency ranges.

As it has been noted in previous posts, Smith chart is designed for one-dimensional (1D) wave propagation, where waves travel along a one direction (say +/-z). For example, Smith chart can be used analyzing acoustic propagation in a pipe or duct.

A loudspeaker radiating into a room, however, generates approximately spherical waves, whose power density decreases as 1/r2. The Smith chart is not intended for this type of three-dimensional propagation. Note that Smith chart can be used to compare the acoustic impedance at two nearby points far from the speaker (where the wavefront is nearly planar). For example, it is commonly used to design layered sonar absorbers and other impedance-matching structures, where wave propagation is essentially is in one dimension (plane waves).

Returning to room acoustics, the acoustic impedance of a loudspeaker varies significantly with frequency and depends on its physical characteristics. In an enclosed room, reflections from the walls, ceiling, and floor produce standing waves and a highly complex three-dimensional sound field. The Smith chart cannot be sued to track these effects.

Now, here is an important application of the Smith chart that is often overlooked. One does not need to be dealing with wave propagation, reflections, or impedance matching to benefit from the Smith chart. The impedance of a complex netwrok can be plotted on a Smith chart as a function of frequency, providing valuable insight into the circuit's behavior. From such a plot, one can identify the equivalent circuit, resonant frequencies, parasitic resonances, losses, quality factor (Q), bandwidth, and other important characteristics. For this reason, the Smith chart is an extremely powerful tool for the analysis and design of AC circuits, even when transmission-line effects are negligible.

Phillip H. Smith, at Bell Telephone Laboratories, was truly a genius. Nearly ninety years after its invention, the Smith chart remains an indispensable tool in RF and microwave engineering, as well as circuit analysis—and acoustics (when appropriate). For example, please see: https://pmc.ncbi.nlm.nih.gov/articles/PMC7411934/

Sorry for the length of this post. I hope you find it useful.

 

[sam_adams]

A loudspeaker radiating into a room, however, generates approximately spherical waves, whose power density decreases as 1/r2. The Smith chart is not intended for this type of three-dimensional propagation.

This is one reason why it is of little use to us.

I feel that some misunderstanding appears to stem from the assumption of electrical signals at audio frequencies traveling on transmission lines. These are not sound waves; they are bound electromagnetic waves.

That is an assumption on your part not contained in statements in the record. The below is why I linked to the presentation by a respected individual who has spent forty years of his life trying to educate an industry on audio cabling issues:

From (PDF).

In an enclosed room, reflections from the walls, ceiling, and floor produce standing waves and a highly complex three-dimensional sound field. The Smith chart cannot be sued to track these effects.

Again, outside of a purely academic exercise, it is of little value when applied to acoustics in 'normal' sized listening rooms or to analog interconnects of 'average' use length.

You have to ask yourself the question; if the Smith Chart was of any value from either an acoustics or general audio cabling perspective, why hasn't it been used since its creation for these purposes?

 

[terryforsythe]

Haha, a radio frequency engineer will laugh when asked smith chart for audio. It is totally irrelevant. Except you may have audio lines as long as over land telephone lines.

I was an RF engineer (RF filters), but I admit to having a brain fart some time back and mentioning characteristic impedance. I was quickly corrected, which is evidence of the brain power in this forum.

 

[NTK]

The headphone - ear canal - eardrum system is sometimes modelled as a transmission line. But being a mechanical engineer, I have no idea where Smith chart may fit in.

https://www.researchgate.net/publication/272681209_Headphone_Fundamentals_and_Comparison_with_Loudspeakers_Tutorial_AES_Paris_2006

 

[MaxwellsEq]

As I read the various comments and replies to the original post, I feel that some misunderstanding appears to stem from the assumption of electrical signals at audio frequencies traveling on transmission lines. These are not sound waves; they are bound electromagnetic waves. It should be noted that the original poster indeed has sound waves in mind.

You are correct in that some of the feedback to the OP (including mine) is that Smith Charts are not needed for electrical propagation at audio frequencies in domestic rooms. The poster was talking about acoustic waves and I did not read the post properly, for which I apologise to @neRok I think others are in the same boat.

I accept your argument that Smith Charts are not the exclusive domain of RF electromagnetic signals and could be applied to an acoustic plane wave.

Where I think the application would not work is that each speaker develops a spherical wave at lower frequencies and a progressively more beamed wave at higher frequencies, and all waves at all frequencies encounter complex boundaries. For this reason it seems you would need a near infinite number of Smith Charts in a normal reflective room. Perhaps I'm misunderstanding the benefits.

 

[amm]

The headphone - ear canal - eardrum system is sometimes modelled as a transmission line. But being a mechanical engineer, I have no idea where Smith chart may fit in.
View attachment 546635

https://www.researchgate.net/publication/272681209_Headphone_Fundamentals_and_Comparison_with_Loudspeakers_Tutorial_AES_Paris_2006

Indeed, this is such a great find. Thanks for sharing it.

Although Philips does not disclose the details, they appear to have analyzed the cascaded acoustic network using ABCD (chain) matrices (as well as circuit simulators) to determine its overall frequency response. Since the impedance of each individual element and the terminating load (ERP in the figure) are known to them, the same network can also be analyzed using a Smith chart to determine the input impedance and explore impedance-matching strategies between the acoustic network and the source. Starting from the load, the Smith chart can be used to successively transform the impedance through each cascaded transmission-line section as well as the lumped elements, ultimately yielding the input impedance at a given frequency. Plotting the impedance as a function of frequency on the Smith chart can provide valuable insight into the system's frequency response, resonance behavior, and impedance-matching, perhaps in hearing-aid applications. Such an approach also offers an intuitive graphical interpretation that complements the ABCD matrix analysis.