line inductance and coefficient of coupling

[panterafanatic]

ok guys. got an issue. i've been reading teach yourself electricy and electronics by stan gibilisco, and the one thing on inductance doesn't make much sense to me.

Line inductance- "short lengths of any type of transmission line behave as inductors, as long as the line is less than 90 elctrical degres in length. At 100MHz, 90 electrical degres, or 1/4 wavelength, in free space i just 75 cm, or a little morehan 2 ft. In general, if f is the freuency in megahertz, then 1/4 the wavelength (s) in free space, in centimters, is given by
s=7500/f"

where the **** does 7500 come from? is it always used or is it relative to something? also, what is an electrical degree? i read the book so far, but have i overlooked something?

by 1/4 wavelength does it literally mean the take the wavelngth and divide it by 4?


i'm gonna look up electrical degrees, so it isn't imperative to define it. anyone able to help me?

if this should be somewhere else let m know so i can delete it and post in another part of the forums. i assumed it belongs here as it is involved when designing circuits.

-Jared

also, with inductors, how do i find k? k is the coefficient of coupling, 0 is no coupling whereas 1 is maximum coupling.

[Ripthorn]

7500 is 1/4 the speed of sound in something like kilometers per second.  In general, c=f*lambda where c is speed of wave propagation, f is frequency and lambda is wavelength.  Works for both acoustical and electromagnetic (and thus optical) waves.

[R.G.]

Line inductance- "short lengths of any type of transmission line behave as inductors, as long as the line is less than 90 elctrical degres in length. At 100MHz, 90 electrical degres, or 1/4 wavelength, in free space i just 75 cm, or a little morehan 2 ft. In general, if f is the freuency in megahertz, then 1/4 the wavelength (s) in free space, in centimters, is given by
s=7500/f"

where the **** does 7500 come from? is it always used or is it relative to something? also, what is an electrical degree? i read the book so far, but have i overlooked something?

The 7500 is the crunching together of several other factors and units conversions to get the answer to come out in centimeters.

by 1/4 wavelength does it literally mean the take the wavelngth and divide it by 4?

Yes, literally. The speed of light in a vacuum is very close to 3x10E8 meters/sec; that's also the speed of propagation of any electromagnetic wave, which is a form of light. For EM waves of frequency 100MHz, the wavelength is L = C/F = 3*10E8/1*10E8 = 3 meters. So then 1/4 Wavelength is 3M/4 = 0.75meter.

The formula says that s = 7500/F = 7500/100 = 75cm, which is 0.75 meters.

In general, the wavelength(L), frequency(F), and speed (S) of propagation of ANY wave is L = S/F. Works for sound, too, if you sub in the speed of sound in whatever medium is conducting the sound. In air, it's about 1100 Ft/sec; in solid objects, it can be much faster. Speed of EM waves in a transmission line is lower than the speed of light in a vacuum, so you have to know which transmission line parameters you have. Notice that if we'd use 186,000 miles/Sec for the speed of light, we'd have had to do conversions of miles to cm  to get the answers to be numerically correct.

i'm gonna look up electrical degrees, so it isn't imperative to define it. anyone able to help me?

If a wave is 2meters long in a particular transmission line, that's 360 degrees. So a transmission line that's 1/4 wavelength long is 90 degrees "long".

also, with inductors, how do i find k? k is the coefficient of coupling, 0 is no coupling whereas 1 is maximum coupling.

Coefficient of coupling is computed based on the mechanical/physical outlines of the conductors and their field equations. Coupling is maximum when the inductors are wound so as to occupy the same physical space, as nearly as possible. This often works out to be to wind the inductors with each wire side by side, also called "bifilar". Since the wires can never be actually  in the same physical space, the coefficient of coupling can never be truly unity. Coupling decreases as the two inductors overlap less then as they are further apart. And since fields are directional, coupling also decreases as the field from one coil rotates to be 90 degrees/orthogonal to the other. You can also never get truly zero coupling, since EM fields are infinite in extent, but they decrease to negligible coupling quickly.

[R.G.]

7500 is 1/4 the speed of sound in something like kilometers per second. 

7500 is (1*10E6)/4 times the speed of *light* in cm/sec.

[frank_p]

Works for both acoustical and electromagnetic (and thus optical) waves.

7500 is 1/4 the speed of sound in something like kilometers per second. 

7500 is (1*10E6)/4 times the speed of *light* in cm/sec.

Speed of sound and speed of light are completely different, in magnitude, in nature and propagation theory.
I never understood completely what is the meaning of speed of light: it's quite complex.

[sethj]

speed of light in any medium is really the phase velocity, and its calculated as the inverse of the square root of permiablility (mu) and permittivity (epsilon). phase velocity is just the rate of the rise and fall of the wave... using sines for a model of a wave, the 90 degree point is the top of the first rise.

as for the line acting as an inductor, it can also be a capacitor!  to be an inductor, the line must provide a return path.  the line out couples with the line back, and you've got your inductor. to make it into a capacitor, just break the circuit: now the two lines (the line out to the break, and the line back from the break) form the two conducting plates of a capacitor.  surplus electrons will pool in one line, and an electric field is stored between them.

these ideas are used all the time in microwave circuit design, where we use the physical shape of conductors to tune bandwidth, and of course the concepts can totally help one isolate weird noise and filter problems in pedals!

[panterafanatic]

thanks for the help guys. would separating each inductor in its own metal housing reduce coupling?

[sethj]

yup.

[frank_p]

The problems I get with speed of light is how it can relate to itself.  "Supposedly" (Is this a french term: I've read somewhere ) when light travel to a certain speed, and an other photon can travel to a velocity relative from the first photon speed:  So light velocity speed is relative to itself: that is : (Where is the relation point to a photon speed to itself...)  Light speed is always going away from itslf at the same light-speed... )
How far is it going...  I think maybe this is relativity in "Mother's nature "quacquery" (in the sense of scientific meaning that I don't understand).

Is it a "relative" expression of speed ?  If it is so In wich book can I read to understand that ?

HFP

P.S.: Is this going out of the context of stompboxes...

[George Giblet]

What are you trying to understand?

The bottom line is don't try to understand inductance and coupling by reading about transmission lines.

While the theory transmission lines involves the ideas of inductance and capacitance there is a *lot* more going on and you will only get lost and confused, it will screw your brain,  and the core understanding will the totally lost!   Moreover the majority of the discussions, while correct from a physics point of view don't really apply directly to audio electronics.

From a practical point of view the world of transmission lines is different to the world of audio electronics.   In audio if you have a figure 8 wire with a load at the end, say a resistor, and you measure the resistance at the "other" end of the wire and you will end up with the same resistance.  For example you don't really care what effect multimeter leads have when you measure a 10k resistance.   The multi meter is DC ie. the lowest frequency.  If the multimeter used audio frequency AC to measure resistance you will still end-up with the same conclusions.  

Transmission lines is completely different when you place a load at one end the impedance you measure at the other is, in general, grossly different.    In fact the load at one end can be an open circuit and the load at the other end might look like a capacitor or resistor!!!  and if you change the length of the wire you will get a complete different behaviour!    Here's some examples,
- If the load end of a transmission line is open circuit the transmission line looks like a capacitor at low frequencies, when you reach the frequency for the quarter-wave-length it will look like a short circuit, when you exceed this frequency it starts to look like an inductor, when you reach the frequency for the half-wavelength is looks open circuit again.
- If the load end of a transmission line is short circuit the transmission line looks like a inductor at low frequencies, when you reach the frequency for the quarter-wave-length it will look like a open circuit, when you exceed this frequency it starts to look like a capacitor, when you reach the frequency for the half-wavelength is looks shorted circuit again.

Hopefully this convinces you that the world of transmission lines isn't the place to start!

You should be reading "AC circuit theory" which explain the impedance of an inductor and ho wit increases with frequency,
http://www.animations.physics.unsw.edu.au/jw/images/AC_files/AC5.gif

If you want to understand more about physical coupling of fields then there's two types of coupling: Self Coupling and Mutual Coupling.  The basic inductor has two connections of a single wire.   When a coil of wire carries a current the each coil produces a magnetic field, when you have a coil turns near each other the total field is the sum of all the individual fields.   This is self coupling or self inductance.  When the coil is *very* long the field from all the turns passes through, ie couples with, all the other turns,

http://plasma.kulgun.net/sol_page/B_solenoid.gif

In a more practical short coil the field from the coil at one end bends and does not *all* pass through that at the coil at the other end,

http://www.physics.upenn.edu/courses/gladney/phys151/lectures/images/solenoid_field.gif

The self coupling aspects isn't really of use, other than to understand coupling.  If there is high self coupling then an inductor will produce a higher inductance for the same amount of turns effectively allowing you to use less wire.

When you have magnetic material for a core the field tends to stay in the magnetic material and not the surrounding air, and this help to increase the coupling.

Mutual coupling is when you have two or more coils,   it relates to how much of the field from one of the coils passes through that of the other coil.  If you imaging two loops they have strong coupling (k=1) when they are close and weak coupling (k~0) when they are far apart.

For a transformer you want a high degree of mutual coupling so they why you will see transformer coils very close together or using magnetic materials for the cores.

You can have mutual coupling between arbitrary shaped objects this can be defined and calculated but it's complex.

[frank_p]

   

I am guessing this is not addressed to me.
OK' George:
First encouter on DIYstompboxees (Is it).
Cool reply:
Let I digest my Martini and I'll be toatallly in a receptive Mood :

I am drunk at this hour and (anyway) I will never argue with you (I'm in mech. eng.)  Just I'll read your typings and I'll be studying them.
It's a good option for me as I am not into figuring who is right.

HFP

[George Giblet]

I am guessing this is not addressed to me.

No, it was for the original poster.

It's a good option for me as I am not into figuring who is right.

I don't think what I have written contradicts what any of the previous posters said

There are many parallels between light and sound propagation, many of the differential equations follow similar forms.  The mode of propagation is of course different.  Even the equation for the speed of sound and light can be written is similar forms,
eg  speed of light  = 1/sqrt( ur*er),  speed of sound = 1/ sqrt( density * compressibility).

I don't know how much acoustics you have done but there are acoustic transmission lines, a common application is horns and instruments like trumpets.  There's also transfer of acoustics down pipes/tubes, you end up with exactly the same 1/4 wave behaviours and the transformations of  acoustic open and short circuits.   Just like the wire has two ends the pipe has two ends.  If you take a helmholtz resonator made from an enclosure and a pipe, the mass on an air-spring view is like the audio frequency inductance and capacitance view of a circuit.  It's called a lumped model where the mass in pipe bounces on the springy air in the enclosure.  Usually that's as far as you take the analysis however high frequencies can propagate in the pipe like a transmission line because the 1/4 wavelengths approach the dimensions of the pipe length.  If you want to see the behaviour at those frequencies you need to look at the transmission line view.

[George Giblet]

frankp, regarding the relativity stuff read this,

http://www.wbabin.net/physics/waterman8.pdf

Two things traveling towards each other is one of my favourites.

[Ripthorn]

7500 is 1/4 the speed of sound in something like kilometers per second. 

7500 is (1*10E6)/4 times the speed of *light* in cm/sec.

Yes, light.  I'm an acoustician, so whenever I think c, I think speed of sound.  I was responding while thinking in acoustics and translating into E&M.  Looks like I missed one.

[panterafanatic]

What are you trying to understand?

The bottom line is don't try to understand inductance and coupling by reading about transmission lines.

While the theory transmission lines involves the ideas of inductance and capacitance there is a *lot* more going on and you will only get lost and confused, it will screw your brain,  and the core understanding will the totally lost!   Moreover the majority of the discussions, while correct from a physics point of view don't really apply directly to audio electronics.

From a practical point of view the world of transmission lines is different to the world of audio electronics.   In audio if you have a figure 8 wire with a load at the end, say a resistor, and you measure the resistance at the "other" end of the wire and you will end up with the same resistance.  For example you don't really care what effect multimeter leads have when you measure a 10k resistance.   The multi meter is DC ie. the lowest frequency.  If the multimeter used audio frequency AC to measure resistance you will still end-up with the same conclusions.  

Transmission lines is completely different when you place a load at one end the impedance you measure at the other is, in general, grossly different.    In fact the load at one end can be an open circuit and the load at the other end might look like a capacitor or resistor!!!  and if you change the length of the wire you will get a complete different behaviour!    Here's some examples,
- If the load end of a transmission line is open circuit the transmission line looks like a capacitor at low frequencies, when you reach the frequency for the quarter-wave-length it will look like a short circuit, when you exceed this frequency it starts to look like an inductor, when you reach the frequency for the half-wavelength is looks open circuit again.
- If the load end of a transmission line is short circuit the transmission line looks like a inductor at low frequencies, when you reach the frequency for the quarter-wave-length it will look like a open circuit, when you exceed this frequency it starts to look like a capacitor, when you reach the frequency for the half-wavelength is looks shorted circuit again.

Hopefully this convinces you that the world of transmission lines isn't the place to start!

You should be reading "AC circuit theory" which explain the impedance of an inductor and ho wit increases with frequency,
http://www.animations.physics.unsw.edu.au/jw/images/AC_files/AC5.gif

If you want to understand more about physical coupling of fields then there's two types of coupling: Self Coupling and Mutual Coupling.  The basic inductor has two connections of a single wire.   When a coil of wire carries a current the each coil produces a magnetic field, when you have a coil turns near each other the total field is the sum of all the individual fields.   This is self coupling or self inductance.  When the coil is *very* long the field from all the turns passes through, ie couples with, all the other turns,

http://plasma.kulgun.net/sol_page/B_solenoid.gif

In a more practical short coil the field from the coil at one end bends and does not *all* pass through that at the coil at the other end,

http://www.physics.upenn.edu/courses/gladney/phys151/lectures/images/solenoid_field.gif

The self coupling aspects isn't really of use, other than to understand coupling.  If there is high self coupling then an inductor will produce a higher inductance for the same amount of turns effectively allowing you to use less wire.

When you have magnetic material for a core the field tends to stay in the magnetic material and not the surrounding air, and this help to increase the coupling.

Mutual coupling is when you have two or more coils,   it relates to how much of the field from one of the coils passes through that of the other coil.  If you imaging two loops they have strong coupling (k=1) when they are close and weak coupling (k~0) when they are far apart.

For a transformer you want a high degree of mutual coupling so they why you will see transformer coils very close together or using magnetic materials for the cores.

You can have mutual coupling between arbitrary shaped objects this can be defined and calculated but it's complex.

about the underlined, i'm not trying to learn one to use the other they are just two separate questions i had that i didn't understand at the time. also, R.G was it you that said the old inductors were slightly polar? if so, can i use a tiny weak bar magnet to somewhat polarize wah inductors? if so here should i place the bit of magnet.

also, thanks for the info on the line inductors and everything guys, i actually get it now.

[frank_p]

I don't know how much acoustics you have done but there are acoustic transmission lines, a common application is horns and instruments like trumpets.  There's also transfer of acoustics down pipes/tubes, you end up with exactly the same 1/4 wave behaviours and the transformations of  acoustic open and short circuits.   Just like the wire has two ends the pipe has two ends.  If you take a helmholtz resonator made from an enclosure and a pipe, the mass on an air-spring view is like the audio frequency inductance and capacitance view of a circuit.  It's called a lumped model where the mass in pipe bounces on the springy air in the enclosure.  Usually that's as far as you take the analysis however high frequencies can propagate in the pipe like a transmission line because the 1/4 wavelengths approach the dimensions of the pipe length.  If you want to see the behaviour at those frequencies you need to look at the transmission line view.

I've done a post graduate class (not the complete master, but only one class) in acoustics in 2000 and now that you cite those examples, it is slowly coming back to consciousness.   I found this class to be the most difficult one with the advanced thermodynamics one.  The past is slowly coming back to mind and I still have my binders somewhere...

frankp, regarding the relativity stuff read this,
http://www.wbabin.net/physics/waterman8.pdf
Two things traveling towards each other is one of my favourites.

I've read it two times and it's becoming a bit more comprehensible to me.  Thanks George.
I'll read it a couple of times more.