ProSoundWeb Community

Please login or register.

Login with username, password and session length
Advanced search  

Pages: [1] 2  All   Go Down

Author Topic: The importance of Ohm's law-abiding caution advanced math geeking  (Read 2691 times)

Jay Barracato

  • Hero Member
  • *****
  • Offline Offline
  • Posts: 1993
  • Solomons, MD

A recent rfvenue blog post passed around on Facebook listed Ohm's law ( in it's most basic DC version) as something every audio professional should know.

My question is why? What does an audio professional use this for that is so important that it is one of the give most basic skills?

Caution math/science geeking ahead.

The original form of Ohm's law is that voltage and current are directly proportional. Voltage and current are macroscopic scalar properties. The constant of proportionality is what we now call resistance. In this form, we know that Ohm's law is a specific relationship that holds true for resistive circuits, in other words one for which resistance is constant.

Changing from DC to AC, introduces the capacitance, which while it doesn't change the outward form of Ohm's law does change the mathematics involved. Now instead of being a constant, resistance is replaced by impedance, a vector involving a complex number. (The resistance is the real portion of the complex number, and the reactance the imaginary part). Therefore, both voltage and current are complex scalars.

What this means is that the relationship between voltage and current is a differential equation that is both time and frequency (phase) dependant. As far as I can tell, in order to make this solvable you must decide if you want to consider either a time invariant or frequency invariant circuit but you can't have both.

That means a speaker, the most likely place for an audio tech to think about Ohm's law, is a loose approximation at best. This is further muddied by the fact that having the circuit moving in a magnetic field adds another indeterminate term due to the inductance.

Now an EE can help me out. It seems as a first approximation, since Ohm's law is linear with a zero intercept, actually measuring voltage and current and using a linear approximation would lump these deviations into the y intercept. Is this normal practice?

My other pondering is what about Kirchhoff's laws. Are they not just as fundamental?

For the record, my reference is University Physics by Young et.al.

On a side note, my chemistry side is tickled that I discovered a particle/ field level version of Ohm's law I was not familiar with.



Sent from my XT1254 using Tapatalk
« Last Edit: June 02, 2017, 10:01:58 am by Jay Barracato »
Logged
Jay Barracato

Dennis Wiggins

  • Hero Member
  • *****
  • Offline Offline
  • Posts: 684
Re: The importance of Ohm's law-abiding caution advanced math geeking
« Reply #1 on: June 02, 2017, 10:04:28 am »


...a speaker, the most likely place for an audio tech to think about Ohm's law, is a loose approximation at best.


Knowledge of Ohm's Law may not be not necessary for the average
consumer in the now-world of self-powered speakers and LED lighting.

However, Ohms Law, even when used with very broad approximations, still works. 

Treating all circuit loads as if they behave like DC is often used to approximate AC draw.

It will always be important have a grasp of P=IE, and all its variations.

It could be that it is being relegated to "theory" to the consumer, but real life (ohms, volts, and ampheres) is a lot easier to understand with that knowledge. 

I will not get on my soapbox (we, I guess I just did!) about how little our young people are being taught, or how little they need to "know", as technology replaces intelligence and critical thinking. 

The math is not hard.

-Dennis

« Last Edit: June 02, 2017, 10:26:20 am by Dennis Wiggins »
Logged

Mark Amber

  • Full Member
  • ***
  • Offline Offline
  • Posts: 108
Re: The importance of Ohm's law-abiding caution advanced math geeking
« Reply #2 on: June 02, 2017, 10:11:15 am »

I use the science to get my way when I need it. Say a broadcast type is trying to home run a mic to their grace preamp. I actually want it to show up in Dante and IDGAF about the folks at home listening over iPod headphones to a 1.5 mbps video stream. I can show them the science that my Yamaha mic pre is within spitting distance of their pre minus the 600 feet of snakage they want to put between it and the microphone.

Or maybe we are running some delays/ fills and it goes the other way: I just need those out fill amps to be at FOH where the power is. Sure let's use the science to justify the minimal losses in that 300' run.

It's whatever. For 99%

That last 1% is why specialist​s like you will get a call to help install an Olympic sized passive line array. Where every capacitance spec and ohm counts. Where quality matters.

Im not saying quality doesn't matter. I'm just saying 99% of the time it's gonna be a ULX-D Dante into your digital console with a 15 foot XLR going from your stage box to a powered speaker. And when it matters you will still be there to save the day. 

Sent from my Pixel using Tapatalk

Logged

Chris Grimshaw

  • Hero Member
  • *****
  • Offline Offline
  • Posts: 914
    • Grimshaw Audio
Re: The importance of Ohm's law-abiding caution advanced math geeking
« Reply #3 on: June 02, 2017, 10:21:35 am »

I think you're over-thinking it.

Knowing and understanding Ohm's Law would stop someone trying to put 16x 4ohm speakers in parallel on one side of an amplifier. In our industry, that's important.

The impedance curve doesn't matter much if the nominal rating is derived sensibly: if an 4ohm-rated cabinet drops below 2ohm in places, something has gone wrong and the rating should be changed. If it stays above 3ohm for the majority of it's range, any half-decent amplifier will drive it all day. Sure, there'll be a little more current here and a little less there. It'll average out just fine (depending on the program material etc etc).

Chris
Logged
Sheffield-based sound engineering.
www.grimshawaudio.com

John Roberts {JR}

  • Hero Member
  • *****
  • Offline Offline
  • Posts: 16200
  • Hickory, Mississippi, USA
    • Resotune
Re: The importance of Ohm's law-abiding caution advanced math geeking
« Reply #4 on: June 02, 2017, 10:34:35 am »

Do the laws of physics still hold in sanctuary cities? (joke) Of course they do because the laws of physics can not be broken, unless replaced with a more accurate law.

Physical laws often can be translated into other disciplines. We often see water analogies for electrical current, understanding one helps understand the other, and larger world.

JR   

PS: STEM education is generally more valuable in the workplace.
Logged
On the internet people tell you everything "they" know, not the answer to "your" question.....  http://circularscience.com/

Frank Koenig

  • Hero Member
  • *****
  • Offline Offline
  • Posts: 602
Re: The importance of Ohm's law-abiding caution advanced math geeking
« Reply #5 on: June 03, 2017, 12:38:10 pm »

Quote
The original form of Ohm's law is that voltage and current are directly proportional.

This is correct. Ohm's law is but one of many formalizations of observed approximate linear behavior in the physical world. Hook's law for stress and strain and the ideal gas law are others.

Quote
The constant of proportionality is what we now call resistance.

Agree. This is the definition of resistance, for both linear and non-linear cases.

Quote
Changing from DC to AC, introduces the capacitance, which while it doesn't change the outward form of Ohm's law does change the mathematics involved. Now instead of being a constant, resistance is replaced by impedance, a vector involving a complex number.

Agree with this, too. The differential equations describe the behavior of approximately linear energy storage (stateful) elements. In the context where we call v=i*R the definition of resistance we should call v=L*di/dt and i=C*dv/dt the definitions of inductance and capacitance, respectively.

Quote
What this means is that the relationship between voltage and current is a differential equation that is both time and frequency (phase) dependant. As far as I can tell, in order to make this solvable you must decide if you want to consider either a time invariant or frequency invariant circuit but you can't have both.

Here's where I'm not getting what you mean. In the context of linear system theory "time invariant" usually means that the intrinsic properties of the the system (its elements, and how they are connected) do not change over time. The excitation and response of the system, however, may be time varying.

As for frequency, which I take to mean a spectral representation, it is an alternative way of looking at a time varying signal or a dynamic system that, in general, has energy storage and therefore state. The Laplace transform is such a view for both signals and systems, providing both a shorthand for the differential equations and a powerful means of visualization.

Quote
My other pondering is what about Kirchhoff's laws. Are they not just as fundamental?

Kirchoff's Laws are absolutely fundamental and are the basis for abstracting a system's topology into differential equations or other representations (such as the Laplace transform view).

Do audio engineers need to know this? I don't think it will help you mix a band or make a recording, but it's pretty much essential if you want to design gear. A fundamental (if only intuitive) understanding of Kirchhoff's laws and the definition of resistance is essential for working with electrical power and signal distribution. The water analogy works well at this level.

And some of us just like to agonize over definitions :)

Best,

--Frank
Logged
Yes, it is a giant stereo system!

Jay Barracato

  • Hero Member
  • *****
  • Offline Offline
  • Posts: 1993
  • Solomons, MD
Re: The importance of Ohm's law-abiding caution advanced math geeking
« Reply #6 on: June 03, 2017, 05:01:49 pm »

Frank by time invariant I was thinking about the inductance die to the coil moving in the magnetic field in a speaker.

It may be the transform is the reduction in the number of variables I was missing as I was rolling this thought problem around in my head.

In class I only cover true resistive  DC circuits but I started wondering about real world examples and how they differ.

Call me the new spokesperson for the committee for the correct use of Ohm's law. Join the resistance.

Sent from my XT1254 using Tapatalk

Logged
Jay Barracato

Stephen Swaffer

  • Hero Member
  • *****
  • Online Online
  • Posts: 2120
Re: The importance of Ohm's law-abiding caution advanced math geeking
« Reply #7 on: June 03, 2017, 09:31:02 pm »

Arguably, in every facet of physics we use aproximations.  Take the most basic measurement of length/distance.  To the traveler, an aproximation of a 1/4 mile is usually plenty accurate, to the rough carpenter an aproximation to the 1/4" may well work, the machinist may need accuracies to the thousandths of an inch.  The fact that a carpenter doesn't know a stud length to 3 decimal places doesn't make the measurement any less useful.

For AC, we commonly refer to voltage-usually meaning RMS, or the number that gives the equivalent potential to a DC voltage of equal value.  A true absolute average measurement will yield a value of 0, and an instaneous vlaue is constantly changing, so we work with the effective value.  It is a functional and useful measurement.

We assume resistance is constant-but even that is not true.  All materials have a temperature coefficient, as soon as voltage is applied and current flows the resistance generates heat which changes the resistance. Granted measuring this change would be a very sophisticated measurement.

Understanding ohms law helps one understand that wire length will affect power transmission from an amp to a speaker-and this affect is directly proportional to the wire resistance.  Technically, the wire inductance would change with length and diameter-but again a neglible difference in the grand scheme of things.

Ohms & Kirchoff's laws may not include all of the elements affecting a circuit-but an understanding of these relationships is fundamental to understanding how electricity works.
Logged
Steve Swaffer

Scott Bolt

  • Hero Member
  • *****
  • Offline Offline
  • Posts: 1326
Re: The importance of Ohm's law-abiding caution advanced math geeking
« Reply #8 on: June 03, 2017, 09:42:27 pm »

Hi Jay,

When I was in college, they used to teach the ME's electrical circuits by replacing the electrical parts with mechanical parts.  Most people can get their head around mechanical parts and how they will behave.

The resistance of a circuit (the DC impedance) can be represented in a fluid system by an orifice placed in a pipe.  The orifice simply restricts water flow ... just like a resistor restricts current flow .... current = water flow.

Capacitance can be represented by an accumulator and an inductor is represented by a paddle wheel:  https://en.wikipedia.org/wiki/Hydraulic_analogy

A speaker is not a simple thing to model (my hat is off to Ivan ;) ).

First, the impedance of a speaker is frequency dependent.  Since the frequency content of music is ever-changing, the impedance is also changing.

Second, as a speaker moves in and out, the capacitance and inductance of the speaker change.

Third, when the speaker moves in and out of the magnetic field, a counter electromotive force is created.  What this means is the act of moving the speaker out creates a force that wants to move the speaker back.

Fourth, each driver in the speaker has widely varying physics that govern it.  My points above are for a woofer with a coil wound driver.

Treating a speaker like a DC resistance seems like it would not be that close in real life.  The simple version of Ohm's law
Logged

Stephen Swaffer

  • Hero Member
  • *****
  • Online Online
  • Posts: 2120
Re: The importance of Ohm's law-abiding caution advanced math geeking
« Reply #9 on: June 04, 2017, 12:01:07 am »


Treating a speaker like a DC resistance seems like it would not be that close in real life.  The simple version of Ohm's law

Perhaps why speaker impedances are often quoted as nominal impedances?  Perhaps that is the technically correct term?
Logged
Steve Swaffer
Pages: [1] 2  All   Go Up
 


Page created in 0.043 seconds with 22 queries.