# [SOLVED]Why does the inductance reduce with increase in width of a transmission line?

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#### venn_ng

##### Member level 5
I was playing with this tool

I observe that the inductance drops with increase in width of the metal. Doesn't the total loop area remain the same regardless of increase in width? I am not sure why the inductance has to drop with increase in width.

#### vfone

Wider structures have less inductance and the answer is: inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it.
So, wider electrical conductor oppose less to the current flowing through it, so will have less inductance value.

#### mkrupi10

##### Newbie level 6
Wider structures have less inductance and the answer is: inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it.
So, wider electrical conductor oppose less to the current flowing through it, so will have less inductance value.
You just described resistence.
--- Updated ---

Inductance is measure of how much magnetic flux is created for unit of current.
In ideal case: Ideal wire conductor with zero diameter would have largest inductance, becouse it creates large magnetic flux wery close to wire surface, where loop for flux is small and B is largest.
Lets look similiar problem: Planet A and B have the same mass but planet B have smaller diameter. So planet B have stronger gravity on the surface of planet. It's becouse surface is closer to center of planet's mass, than on planet A.

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#### venn_ng

##### Member level 5
You just described resistence.
--- Updated ---

Inductance is measure of how much magnetic flux is created for unit of current.
In ideal case: Ideal wire conductor with zero diameter would have largest inductance, becouse it creates large magnetic flux wery close to wire surface, where loop for flux is small and B is largest.
Lets look similiar problem: Planet A and B have the same mass but planet B have smaller diameter. So planet B have stronger gravity on the surface of planet. It's becouse surface is closer to center of planet's mass, than on planet A.
Yes, precisely the measure of magnetic flux and not some tendency to oppose current, which is unfortunately a misnomer and people are taught that way in school.
My question is in the case of parallel traces, the distance between them is still the same ('H' in this tool https://www.eeweb.com/tools/broadside-trace-inductance), while I change the width 'W'. In that case, the magnetic flux between should be the same regardless of the width, isn't it?

-Venkat

#### volker@muehlhaus

In that case, the magnetic flux between should be the same regardless of the width, isn't it?
You miss self-inductance of each line (each of the conductors). That depends on line width, and decreases with width.

#### venn_ng

##### Member level 5
You miss self-inductance of each line (each of the conductors). That depends on line width, and decreases with width.
In the end, what matters is the total loop area, right? Isn't it the same in both the cases?

#### volker@muehlhaus

In the end, what matters is the total loop area, right?
No, your model idea is too simplistic. Total inductance is the two individual trace inductances minus mutual inductance.

And for each single traces self inductance, size matters. A very simple example: https://www.eeweb.com/tools/wire-inductance

### venn_ng

points: 2

#### venn_ng

##### Member level 5
Thanks for the reply. I appreciate it. Why does the self-inductance drop with increase in width? Can you explain me in terms of magnetic flux?

#### FvM

##### Super Moderator
Staff member
Consider a round conductor. You get an axisymmetric field, flux is ~1/r. A thin conductor is inducing more voltage next to the conductor. Respectively the self inductance of a coaxial conductor geometry is ~ ln(ra/ri).

venn_ng

### venn_ng

points: 2

#### vfone

- the electrical resistance of an object is a measure of its opposition to the flow of electric current.
- inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it.

The self inductance of a wire segment (or microstrip line) is the flux linkages with that wire per unit current flowing through that wire.
Inductance L(Henry) = v/(di/dt) where v is the voltage drop across the wire segment.
Can say that inductance L is a measure of an inductor “resistance” to the change of the current flowing through the circuit, and the lower will be the rate of current change, the larger is its value in Henries.
Thicker or shorter the wire segment (or the strip line) will be less voltage drop across the segment, so will have less inductance in Henries.

#### venn_ng

##### Member level 5
- the electrical resistance of an object is a measure of its opposition to the flow of electric current.
- inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it.

The self inductance of a wire segment (or microstrip line) is the flux linkages with that wire per unit current flowing through that wire.
Inductance L(Henry) = v/(di/dt) where v is the voltage drop across the wire segment.
Can say that inductance L is a measure of an inductor “resistance” to the change of the current flowing through the circuit, and the lower will be the rate of current change, the larger is its value in Henries.
Thicker or shorter the wire segment (or the strip line) will be less voltage drop across the segment, so will have less inductance in Henries.
Just don't call it resistance...Resistance dissipates energy in the form of heat, inductance stores energy..It's just a misnomer, can be misleading. People tend to think that inductance is bad, which is not sometimes.

#### venn_ng

##### Member level 5
Consider a round conductor. You get an axisymmetric field, flux is ~1/r. A thin conductor is inducing more voltage next to the conductor. Respectively the self inductance of a coaxial conductor geometry is ~ ln(ra/ri).
Ok that makes sense. So basically, you are saying that the surface area is increasing as the diameter is increasing and hence the current / Area drops as 1/r as 'r' is increased and this, in turn, drops the magnetic flux B. Is my interpretation correct?

#### barry

People tend to think that inductance is bad, which is not sometimes.
I dont think electrical parameters have virtues like 'bad' or 'good'.

#### venn_ng

##### Member level 5
I dont think electrical parameters have virtues like 'bad' or 'good'.
I meant, people tend to think that having parasitic inductance will screw up the performance, which is not the case. You can't look at it the same way as you look at a resistance.

#### biff44

when you make a narrow strip as a center conductor, you restrict the flow of electrons...which forms an inductance

#### venn_ng

##### Member level 5
when you make a narrow strip as a center conductor, you restrict the flow of electrons...which forms an inductance
Nope that's resistance

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