4 strip lines

8/8/2019 4 Strip Lines

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S-PARAMETERS OF STRIP LINES

STRIP LINE TUTORIAL

A strip line exhibits a TEM field, i.e. a transverse electromagnetic mode field, where the

dielectric field is perpendicular to the magnetic field, and both are perpendicular to the

direction of wave propagation.

W

H

From this sketch, we can conclude the following basic properties of a microstrip line,

depending on the geometry factor W/L:

Z0

W / H1 2 3 4

100Ω

20Ω

capacitive, most energyis in the dielectric material

inductive,mostly magnetic energy,half in the air, half in the dielectric material

εeff -> 1 εeff -> εr

The characteristic impedance, Z0, ranges from about 20Ω to about 100Ω. The limit of 100Ω

exists for a very simple reason: the width is much less than the hight, and such a structurecannot be manufactured (under-etching etc).



Strip Lines on Wafers -2-

characterization handbook 3LINES.doc | 18.03.02 Franz Sischka

This sketch allows to make some fundamental considerations:

As a matter of fact, a small microstrip line exhibits less capacitance than a wide one.

Inspecting the plot, this concludes that a lower capacitance in a microstrip line comes along

with a lower impedance Z0.

This is obvious, when recalling that

C

L~Z

Referring to crosstalk between lines, we can learn from the sketch above that a low

impedance microstrip line is capacitive. I.e. the energy is rather between the metal conductor

and the groud. I.e. two low impedance striplines side-by-side, will exhibit less cross-talsk than

two high impedance striplines. By the way, this is a key design rule for packages and

connectors.

As another important outcome, a shielding across a microstrip line will lead to the fact that the

impedance of the resulting strip line wil be lower, because more of the electro-magnetic field

will now be present in the enlarged electric field consisting of the previous field in the

dielectic layer plus the additional space between the active metal layer and the top cover.

Therefore, a cover across a microstrip line reduces the resulting impedance, and, thus, reduces

cross-talk between adjacent striplines.

To further reduce cross-talk of adjacent lines, i.e. to reduce the impedance of each line

(inclrease the electric field, i.e. make the lines more capacitive), reduce the height of the

dielectric material.

However, on the other hand, a cover 'kills' the performance of filters designed from strip lines

based on electric field coupling!

For more info, see

Steven Hamilton, 'RF Circuit and Component Modeling', International Courses for Telecom

Professionals, CEI-Europe, Internet address: www.cei.com





Modeling a lossy strip line from S-parameters

Tutorial:

The S-parameters of a strip line of length L and a characteristic impedance Z0, measured with

a network analyzer, can be considered like a transition of a 50Ω system into a Z0 system with

a long delay.

Therefore, the Sxx parameters in a Smith chart start in the center, i.e. at 50Ω, and turn then to

a curve around the value of Z0 of the strip line. For a lossless line, this curve is represented by

circles around the line's Z0. For a lossy line, this looks like a looping towards Z0. Like with

all S-parameters, this turning is always clock-wise.

- For a Z0 < 50Ω, the curve starts at 50Ω, and turns with -90° clockwise, i.e. downwards. If

the line is lossless, we have a circling curve centered around Z0, and touching again and

again the center of the Smith chart, i.e. 50Ω.For a lossy line, we have a looping around Z0

with the end point at Z0.

- For the special case of a line with a characteristic impedance of Z0=50Ω, lossless or lossy,we have all S11 and S22 parameters in the center of the Smith chart: at 50Ω.

- For a Z0 > 50Ω, the curve starts at 50Ω, and turns with +90° straight upwards. If the line is

lossless, we have again a circling curve centered around the line's Z0, and touching the

center of the Smith chart, i.e. 50Ω again and again (if it is long enough!). If the curve is

lossy, we will again have a looping towards the end point Z0.

The Sxy parameters in the polar plot start at '+1', and also turn clock-wise.

- For a lossless line of Z0=50Ω, we have circles with magnitude '1' . For a lossy 50Ω line, the

circles are replaced by a looping towards '0', because for a long, lossy line, there is no

signal reflected back any more.

- If the Z0 of the line is <>50Ω, we have a change in magnitude (see further below in the nextchapter), which is represented in the Sxy plot as ellipses for a lossless line, or as an elliptic

looping towards '0' for a lossy line.

For the modeling,

we commence with setting all line parameters to default, and the length to infinite.

The loss parameter is set to '0'.

In this case, we can determine Z0 from fitting the magnitude of the simulated curve to the

trace of the measured data in the Smith chart. We ignore the phase.

For Z0 = 50Ω

we have this situation:





CONDITIONS:L = infinite

Z0 = 50 Ω

loss (alpha) = 0delay (Beta) = default

RS = 0 Ω

Step 1: set length to infinite and adjust Z0 in Smith Chart

Sxx Sxy

And for Z0 less or bigger than 50Ω

we have:

Z0 = 25 Ω Z0 = 100 Ω

NOTE: For Sxx,all curvesstart for freq=0 in thecenter of the Smith chart

i.e. at 50 Ω.

Their end point at infinite length is their Z0 !

Z0 = 25 Ω

Z0 = 100 Ω

SxxSxy

After having determined Z0, we set the physical length of the strip line to its real, physical

value and adjust the strip line's delay by fitting Sxy:





REMAINING PARAMETERS:loss (alpha) = 0

RS = 0 Ω

Step 2: set length to its physical value and adjust delay (Beta) in Sxy

Sxx

Sxy

Then, we adjust the loss, again by fitting Sxy:

Sxy

Step 3: adjust loss (alpha) in Sxy

Sxx

REMAINING PARAMETER:

RS = 0 Ω

If the starting point of Sxx is not at 50Ω, and the starting point of the Sxy is not at '1', we need

to consider a series resistor (contact resistance) in series with the delay line model.

This is, last not least, the last remaining parameter of typical strip lines on the wafer:





Sxy

Step 4: adjust series resistor RS

Sxx

NOTE: if a shift to the left is required in Sxx,split the delay line into 2 and insert a resistorto ground between them !





S-PARAMETERS OF SERIAL LOSSLESS DELAY LINESWITH DIFFERENT IMPEDANCES

IC_CAP file: 2_S_plots_striplines.mdl

Delay lines show up in S-parameter plots with big phase shift. If they have no loss, -like the

SPICE models- they keep the magnitude. This is depicted below.

Z0=50 Ohm

50 Ohm~

f

phase turns 830 degrees!

corrected h omogenuous phase shift

of a 50 Ohm line

uncorrected

phase/rad

Note: See chapter 'Utilites' for the phase correction.

Yet, if there is a mismatch in the impedances, the phase is affected. The following plots give

an idea. Both lines have a delay of 30ps. The frequency is swept from 45MHz to 20GHz.





Case 1: impedance steps to lower value:

Z0=50 Ohm

50 Ohm~

30 Ohm

homogenuous phase shift

of two 50 Ohm lines

phase shift of a 50 Ohm system

followed by a 30 Ohm and 50 Ohm de lay line

phase/rad

___________________________________________________________________________

Z0=50 Ohm

30 Ohm~ 50 Ohm

phase/rad


of two 50 Ohm lines


followed by a 50 Ohm an d 30 Ohm delay line

NOTE: a step to lower impedance: -> more phase shift at low frequencies!





Case 2: impedance steps to higher value:

Z0=50 Ohm

70 Ohm~

50 Ohm

phase/rad




of two 50 Ohm lines

___________________________________________________________________________

Z0=50 Ohm

50 Ohm~ 70 Ohm

phase/rad




of two 50 Ohm lines

NOTE: a step to higher impedance: -> less phase shift at low frequencies!

As a final note, we can conclude that for lossless lines, there is no phase ripple, provided there

are no multiple reflections (connector mismatch, impedance mismatch). If we encounter phase

ripple, we have to take multiple reflections into consideration.

4 strip lines

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