Lamda equals to how many degrees on smith chart

[circuitking]

On a transmission line, if we take standing wave then the distance between two voltage maxima or minima is lamda/2, which is 360°. So lamda equal to 720° degree on smith chart. But if I have to calculate physical length of the line, I ll follow this.
Say electrical length BL =30 then

360°-->lamda,
30°--->30°*(lamda/360) so L=lamda/12. So here I am using 360° as lamda. Where am I making mistake?

 

[volker@muehlhaus]

360°-->lamda

Why do you switch back to 360°? You are correct that one turn on the Smith chart is lambda/2. That's also shown on the outermost scale, which ranges from 0 to 0.5
https://de.wikipedia.org/wiki/Smith-Diagramm#/media/Datei:Smith_chart_gen.svg

You mentioned physical length. When you convert from electrical length to physical length, you need to consider the effective propagation constant. In most cases that is: physical length = electrical length / sqrt(eps_effective).

 

[circuitking]

You are correct that one turn on the Smith chart is lambda/2. That's also shown on the outermost scale, which ranges from 0 to 0.5

https://de.wikipedia.org/wiki/Smith-Diagramm#/media/Datei:Smith_chart_gen.svg

Yes I know but by doing this (360°-->lamda, 30°--->30°*(lamda/360), so L=lamda/12) also gives us correct physical length of the line, isn't it? That's what I don't understand.

 

[volker@muehlhaus]

Yes I know but by doing this (360°-->lamda, 30°--->30°*(lamda/360), so L=lamda/12) also gives us correct physical length of the line, isn't it?

In the Smith chart, a line with 30° electrical length will turn 60° in the Smith chart. But in transmission, it has 30° phase, of course. And if the line is built from air dielectric, it has a physical length of lambda0*30°/360° where lambda0 is the wavelength in air.



Note the conversion from electrical length (lambda * 30/360) to physical length. Only for lines with eps_r=1, both are the same. For real lines, wavelength in the medium is smaller than wavelength in air, by factor sqrt(eps_effective). So the physical length of a teflon line (eps_r=2.1) must be smaller by that factor sqrt(2.1)

 

[circuitking]

Only for lines with eps_r=1, both are the same.

Thanks, I understand. So, as long as eps_r=1 I can use this.

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In the Smith chart, a line with 30° electrical length will turn 60° in the Smith chart.

Why is this?

 

[volker@muehlhaus]

Why is this?

Because the signal travels 30° thru the line, and the reflected portion another 30° on the way back.

That's what seemed unclear in your first question, if the 30° was for the electrical length parameter of the line (S21 angle) or for the rotation angle in the Smith chart (S11 angle)

 

[circuitking]

That's what seemed unclear in your first question, if the 30° was for the electrical length parameter of the line or for the rotation angle in the Smith chart.

That is the electrical length I got from smith chart utility, so I think it is the electrical length parameter of the line.

Because the signal travels 30° thru the line, and the reflected portion another 30° on the way back.

But If I have matched condition, then I will not have reflected portion. In that case, shouldn't it be 30° only?

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Note the conversion from electrical length (lambda * 30/360) to physical length.

I hope you meant "Note the conversion from electrical length (30°) to physical length (lambda * 30°/360°)"

 

[volker@muehlhaus]

I'll stop here, because you seem to misunderstand my posts and my use of the term "physical length".

 

[circuitking]

I'll stop here, because you seem to misunderstand my posts and my use of the term "physical length".

I didn't see that edited your 1st post. May be I misunderstood but I want to correct it now.

Anyway If you remember from other post
https://www.edaboard.com/showthread...ansmission-line-component-in-Virtuoso-and-ADS

I said that there are these parameters.

1.Electrical length (in terms of lambda)
2.Electrical length (in terms of angle)
3.Physical length

and I also mentioned that "So I always need to convert from electrical length (EL, found in smith chart utility) to physical length(EL*lambda/360) ".

1. I know electrical length (EL) is phase constant (B)* length of the line (l)(this is Physical length as per me, doesn't everybody considers like this, correct me if I am wrong)
2.You mentioned physical length = electrical length / sqrt(eps_effective), I am not sure about this, could you tell how this conversion works.
3.Finally, as I mentioned in the previous post, this is how I convert physical length = EL*lambda/360, which is the point of this thread discussion. Hope I clarified what I am looking for. If you think now I am in right direction then you can reply.

 

[volker@muehlhaus]

To avoid going in circles, let's do is on your specific example. Please specify
- frequency
- your electrical length in degree
- effective permittivity of your line

That last parameter is important for real world use because the phase delay varies with material, at the same physical length. I guess you don't build a line from air filld coax, so we need to agree on a material to calculate a physical length from a given phase delay.

 

[pancho_hideboo]

On a transmission line,
if we take standing wave then the distance between two voltage maxima or minima is lamda/2, which is 360°.

Wrong.
It is 180degree.

So lamda equal to 720° degree on smith chart.

Right. This is round-trip.

So here I am using 360° as lamda.
Where am I making mistake?

Simply you can not understand basic wave equation.
You can not understand oneway-trip and round-trip at all.

S11 and S22 undergo round-trip.
S21 and S12 undergo oneway-trip.

β=2*pi/λ

Oneway trip : exp(-j*β*L)
Round trip : exp(-j*2*β*L), This is a phase rotation in smith chart.
See https://www.edaboard.com/showthread...n-line-component-in-Virtuoso-and-ADS/page2#31

L=λ/4 <-> θ=90degree
L=λ/2 <-> θ=180degree
L=λ/1<-> θ=360degree

But If I have matched condition,
then I will not have reflected portion.
In that case, shouldn't it be 30° only?

No.
However there is no phase rotation actually since Γ=0.

 

[circuitking]

- frequency
- your electrical length in degree
- effective permittivity of your line

frequency-1 GHz
your electrical length in degree=41 degree
effective permittivity of your line=4.1 F/m

 

[volker@muehlhaus]

effective permittivity of your line=4.1 F/m

Maybe you misunderstood the question, I asked for permittivity (epsilon_r), not capacitance.

As mentioned above, the dielectric material used in the line will change the propagation speed (c_medium = c₀ / sqrt (εr*µr), so it changes the phase delay for a given geometric length! You cannot calculate the physical (geometrical) line length for a given phase delay if that value is missing!






To be precise, I asked for effective permittivity. For lines where all the electric field is in that dielectric (e.g. coax) that's simply the permittivity of the dielelectric materials. For lines where parts of the field is in air and other parts in dielectric, it's a bit more complicated and you want to use a tool like this: https://www.awr.com/software/options/tx-line

 

[circuitking]

Maybe you misunderstood the question, I asked for permittivity (epsilon_r), not capacitance.

I know what you meant from beginning related to epsilon_r. It is my mistake I wrote for epsilon_r= 4.1 F/m in my old report also. So I copied from there directly. I think I can work this out. Thanks.

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Useful for people who read it in future. There is a worked out example here https://www.rfwireless-world.com/Terminology/electrical-length-vs-physical-length.html.

 

[volker@muehlhaus]

I know what you meant from beginning related to epsilon_r.

Ok, great!

It seems that some confusion was the use of terms "physical length" vs. "electrical length".
Where I work, we use "electrical length" as described here in "use of term" section 2.: the length of an equivalent line with air dielectric. ("This line has a phyiscal length of 2m and an electrical length of 3m.")

Another source of confusion was your title "how many degrees on Smith chart" which indicates S11 phase, but you where looking for S21 phase.

frequency-1 GHz
your electrical length in degree=41 degree
effective permittivity =4.1 F/m

Lambda in air is 3e8 m/s / 1e9 Hz = 300mm
length of line assuming air dielectric: 300mm * 41/360 = 34.17mm
length of line assuming er=4.1: line length 34.17mm* sqrt(4.1) = 16.88mm

 

[circuitking]

360°-->lamda,
30°--->30°*(lamda/360) so L=lamda/12. So here I am using 360° as lamda. Where am I making mistake?

The image is taken from MICROWAVE AND RF DESIGN: A SYSTEMS APPROACH by Michael Steer. He uses the same way what I used. Say Figure 1.

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Wrong.
It is 180degree.

*Taken from https://nptel.ac.in/courses/117101057/slides 2/5.3.html. Say Figure 2.

Indeed, the rotation on smith chart is 360°, when the length of the line is lamda/2.

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In the Smith chart, a line with 30° electrical length will turn 60° in the Smith chart. But in transmission, it has 30° phase, of course.

Makes sense to me now. As in the attached figure2, 2Beta*l=2*pi, which is two times electrical length.



I moved 90° on smith chart and it added line with 45° EL. This is what I missed earlier.

I don't know whether I can say this here or not. This is off the topic, @ volker@muehlhaus. This is one of the documents I read on Transmission line https://muehlhaus.com/wp-content/uploads/2011/08/Analysis-of-RFIC-Transmission-Lines.pdf. Because of this document and from your user name, I realized that you work there.

 

[pancho_hideboo]

Surely learn Oneway-Trip and Round-Trip.

Simply you can not understand basic wave equation.
You can not understand oneway-trip and round-trip at all.

S11 and S22 undergo round-trip.
S21 and S12 undergo oneway-trip.

β=2*pi/λ

Oneway trip : exp(-j*β*L)
Round trip : exp(-j*2*β*L), This is a phase rotation in smith chart.

 

[ktr]

1 Ghz - 30 cm wavelength in air Epsilon = 1 -- 15cm wavelength in FR4 Epsilon= 4

1/sqrt(4) = 1/2 will be the velocity of wave in FR4 when compared to Air.

Electrical length in terms of S11,S22 ( Insertion loss, Return Loss) : A wave goes to the input matching, or output match of an active device and "reflects", in that reflection the wave traverses the distance twice; hence round-trip, hence double the length of the trace.

In terms of S21, S12 ( Forward gain, reverse gain). A wave goes through the active device, while gaining power or being attenuated in power, no reflection, just pass through; hence normal length of the trace.

 

[pancho_hideboo]

*Taken from https://nptel.ac.in/courses/117101057/slides 2/5.3.html. Say Figure 2.
Indeed, the rotation on smith chart is 360°, when the length of the line is lamda/2.

You can not understand very basic things at all.

Consider V and I which are located at L=λ/2 separation.

V(x=λ/2) = -V(x=0)
I(x=λ/2) = -I(x=0)

Phase differece for L=λ/2 is 180degree not 360degree.

On the other hand, Zin=V(x=λ/2)/I(x=λ/2)=V(x=0)/I(x=0)
So Zin and Γin are same as values at x=0.

That's all.

 

[volker@muehlhaus]

Phase differece for L=λ/2 is 180degree not 360degree.

He wrote "rotation on Smith chart" which is correct, as it refers to S11.