Need a PSpice model for Belden-like 50 ohm Twinax

R

Robert Macy

Guest
What a lot of spam on this group!!!

Need a PSpice model for 50 ohm Twinax cable

To Jim Thompson: Even tables would help like you did for the 36 Awhg
wire.

Robert
 
On Tue, 24 Nov 2009 12:05:47 -0800 (PST), Robert Macy
<macy@california.com> wrote:

What a lot of spam on this group!!!
Goolge groups has a lot of spam. If you use a real newsreader (and of
course, server) you won't see the googlespam.

Need a PSpice model for 50 ohm Twinax cable

To Jim Thompson: Even tables would help like you did for the 36 Awhg
wire.

Robert
 
On Tue, 24 Nov 2009 12:05:47 -0800 (PST), Robert Macy
<macy@california.com> wrote:

What a lot of spam on this group!!!

Need a PSpice model for 50 ohm Twinax cable

To Jim Thompson: Even tables would help like you did for the 36 Awhg
wire.

Robert
If you're using PSpice, it has a part, "TLOSSY", which you should be
able to match closely to your cable.

Hint: For Twinax, use two "TLOSSY" in parallel, and read the reference
guide as regards "coupling" of transmission lines.

...Jim Thompson
--
| James E.Thompson, CTO | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona 85048 Skype: Contacts Only | |
| Voice:(480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |
 
On Nov 25, 6:53 am, Jim Thompson <To-Email-Use-The-Envelope-I...@My-
Web-Site.com> wrote:
On Tue, 24 Nov 2009 12:05:47 -0800 (PST), Robert Macy

m...@california.com> wrote:
What a lot of spam on this group!!!

Need a PSpice model for 50 ohm Twinax cable

To Jim Thompson: Even tables would help like you did for the 36 Awhg
wire.

Robert

If you're using PSpice, it has a part, "TLOSSY", which you should be
able to match closely to your cable.

Hint: For Twinax, use two "TLOSSY" in parallel, and read the reference
guide as regards "coupling" of transmission lines.

                                        ...Jim Thompson
--
| James E.Thompson, CTO                            |    mens     |
| Analog Innovations, Inc.                         |     et      |
| Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    |
| Phoenix, Arizona  85048    Skype: Contacts Only  |             |
| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  |
| E-mail Icon athttp://www.analog-innovations.com|    1962     |
Hi, Jim, been awhile,

Is there a way to include skin effect impedance changes?

From what I saw, TLOSSY won't work. Is not accurate. I need to
confirm that.

For example, in TLOSSY there is no term included for SHIELD impedance,
only the center conductor's impedance. And, you and I both know the
damage that SHIELD impedance does in the presence of an 'unbalanced'
load.

So try this, if your system has TLOSSY, drive with perfect 50 ohm
differential +-1V source into perfect 50 ohm 7ft long Twinax
simulation, into 100 ohm and 50 ohm load, over the range of 10MHz to
1GHz. In real life, there will be shield currents that generate
radiating EMI. Did PSpice predict them, or did it make them all below
-300dB? Compare to a 100 segment representation of a 'discrete'
representation for Twinax. You'll see the impact of the SHIELD
impedance gets totally lost using TLOSSY.

Help.
 
On Wed, 25 Nov 2009 08:30:04 -0800 (PST), Robert Macy
<macy@california.com> wrote:

On Nov 25, 6:53 am, Jim Thompson <To-Email-Use-The-Envelope-I...@My-
Web-Site.com> wrote:
On Tue, 24 Nov 2009 12:05:47 -0800 (PST), Robert Macy

m...@california.com> wrote:
What a lot of spam on this group!!!

Need a PSpice model for 50 ohm Twinax cable

To Jim Thompson: Even tables would help like you did for the 36 Awhg
wire.

Robert

If you're using PSpice, it has a part, "TLOSSY", which you should be
able to match closely to your cable.

Hint: For Twinax, use two "TLOSSY" in parallel, and read the reference
guide as regards "coupling" of transmission lines.

                                        ...Jim Thompson
--
| James E.Thompson, CTO                            |    mens     |
| Analog Innovations, Inc.                         |     et      |
| Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    |
| Phoenix, Arizona  85048    Skype: Contacts Only  |             |
| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  |
| E-mail Icon athttp://www.analog-innovations.com|    1962     |

Hi, Jim, been awhile,

Is there a way to include skin effect impedance changes?

From what I saw, TLOSSY won't work. Is not accurate. I need to
confirm that.

For example, in TLOSSY there is no term included for SHIELD impedance,
only the center conductor's impedance. And, you and I both know the
damage that SHIELD impedance does in the presence of an 'unbalanced'
load.

So try this, if your system has TLOSSY, drive with perfect 50 ohm
differential +-1V source into perfect 50 ohm 7ft long Twinax
simulation, into 100 ohm and 50 ohm load, over the range of 10MHz to
1GHz. In real life, there will be shield currents that generate
radiating EMI. Did PSpice predict them, or did it make them all below
-300dB? Compare to a 100 segment representation of a 'discrete'
representation for Twinax. You'll see the impact of the SHIELD
impedance gets totally lost using TLOSSY.

Help.
The fundamental problem with PSpice coax models, in general, is the
assumption that the shield is an equipotential from end-to-end :-(

If you have the patience for it I guess you could build up your own
lumped model with coupling between inductors ;-)

...Jim Thompson
--
| James E.Thompson, CTO | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona 85048 Skype: Contacts Only | |
| Voice:(480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |
 
On Nov 26, 12:53 pm, Jim Thompson <To-Email-Use-The-Envelope-I...@My-
Web-Site.com> wrote:
On Wed, 25 Nov 2009 08:30:04 -0800 (PST), Robert Macy





m...@california.com> wrote:
On Nov 25, 6:53 am, Jim Thompson <To-Email-Use-The-Envelope-I...@My-
Web-Site.com> wrote:
On Tue, 24 Nov 2009 12:05:47 -0800 (PST), Robert Macy

m...@california.com> wrote:
What a lot of spam on this group!!!

Need a PSpice model for 50 ohm Twinax cable

To Jim Thompson: Even tables would help like you did for the 36 Awhg
wire.

Robert

If you're using PSpice, it has a part, "TLOSSY", which you should be
able to match closely to your cable.

Hint: For Twinax, use two "TLOSSY" in parallel, and read the reference
guide as regards "coupling" of transmission lines.

                                        ...Jim Thompson
--
| James E.Thompson, CTO                            |    mens     |
| Analog Innovations, Inc.                         |     et      |
| Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    |
| Phoenix, Arizona  85048    Skype: Contacts Only  |             |
| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  |
| E-mail Icon athttp://www.analog-innovations.com|   1962     |

Hi, Jim, been awhile,

Is there a way to include skin effect impedance changes?

From what I saw, TLOSSY won't work.  Is not accurate.  I need to
confirm that.

For example, in TLOSSY there is no term included for SHIELD impedance,
only the center conductor's impedance.  And, you and I both know the
damage that SHIELD impedance does in the presence of an 'unbalanced'
load.

So try this, if your system has TLOSSY, drive with perfect 50 ohm
differential +-1V source into perfect 50 ohm 7ft long Twinax
simulation, into 100 ohm and 50 ohm load, over the range of 10MHz to
1GHz.  In real life, there will be shield currents that generate
radiating EMI.  Did PSpice predict them, or did it make them all below
-300dB?  Compare to a 100 segment representation of a 'discrete'
representation for Twinax.  You'll see the impact of the SHIELD
impedance gets totally lost using TLOSSY.

Help.

The fundamental problem with PSpice coax models, in general, is the
assumption that the shield is an equipotential from end-to-end :-(

If you have the patience for it I guess you could build up your own
lumped model with coupling between inductors ;-)

                                        ...Jim Thompson
--
| James E.Thompson, CTO                            |    mens     |
| Analog Innovations, Inc.                         |     et      |
| Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    |
| Phoenix, Arizona  85048    Skype: Contacts Only  |             |
| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  |
| E-mail Icon athttp://www.analog-innovations.com|    1962     |
Thought I was 're-inventing' the wheel, so stopped to ask.

Thank you for confirming that my 24 section model of 2 inch pieces has
been worth it.

Very educational results!

Some conclusions so far: shield conductance MUST be kept low, center
conductors can be [almost] any size.

I'm trying to make the model so I can simulate adding beads to the
cable, but so far this has been tedious and testing my understanding
of the very basics.
 
On Fri, 27 Nov 2009 08:19:22 -0800 (PST), Robert Macy
<macy@california.com> wrote:

On Nov 26, 12:53 pm, Jim Thompson <To-Email-Use-The-Envelope-I...@My-
Web-Site.com> wrote:
On Wed, 25 Nov 2009 08:30:04 -0800 (PST), Robert Macy





m...@california.com> wrote:
On Nov 25, 6:53 am, Jim Thompson <To-Email-Use-The-Envelope-I...@My-
Web-Site.com> wrote:
On Tue, 24 Nov 2009 12:05:47 -0800 (PST), Robert Macy

m...@california.com> wrote:
What a lot of spam on this group!!!

Need a PSpice model for 50 ohm Twinax cable

To Jim Thompson: Even tables would help like you did for the 36 Awhg
wire.

Robert

If you're using PSpice, it has a part, "TLOSSY", which you should be
able to match closely to your cable.

Hint: For Twinax, use two "TLOSSY" in parallel, and read the reference
guide as regards "coupling" of transmission lines.

                                        ...Jim Thompson
--
| James E.Thompson, CTO                            |    mens     |
| Analog Innovations, Inc.                         |     et      |
| Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    |
| Phoenix, Arizona  85048    Skype: Contacts Only  |             |
| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  |
| E-mail Icon athttp://www.analog-innovations.com|   1962     |

Hi, Jim, been awhile,

Is there a way to include skin effect impedance changes?

From what I saw, TLOSSY won't work.  Is not accurate.  I need to
confirm that.

For example, in TLOSSY there is no term included for SHIELD impedance,
only the center conductor's impedance.  And, you and I both know the
damage that SHIELD impedance does in the presence of an 'unbalanced'
load.

So try this, if your system has TLOSSY, drive with perfect 50 ohm
differential +-1V source into perfect 50 ohm 7ft long Twinax
simulation, into 100 ohm and 50 ohm load, over the range of 10MHz to
1GHz.  In real life, there will be shield currents that generate
radiating EMI.  Did PSpice predict them, or did it make them all below
-300dB?  Compare to a 100 segment representation of a 'discrete'
representation for Twinax.  You'll see the impact of the SHIELD
impedance gets totally lost using TLOSSY.

Help.

The fundamental problem with PSpice coax models, in general, is the
assumption that the shield is an equipotential from end-to-end :-(

If you have the patience for it I guess you could build up your own
lumped model with coupling between inductors ;-)

                                        ...Jim Thompson
--
| James E.Thompson, CTO                            |    mens     |
| Analog Innovations, Inc.                         |     et      |
| Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    |
| Phoenix, Arizona  85048    Skype: Contacts Only  |             |
| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  |
| E-mail Icon athttp://www.analog-innovations.com|    1962     |

Thought I was 're-inventing' the wheel, so stopped to ask.

Thank you for confirming that my 24 section model of 2 inch pieces has
been worth it.

Very educational results!

Some conclusions so far: shield conductance MUST be kept low, center
conductors can be [almost] any size.

I'm trying to make the model so I can simulate adding beads to the
cable, but so far this has been tedious and testing my understanding
of the very basics.
Some years ago I evaluated and modeled wirebonds for Intel... took me
about 6 months of tedious data fitting :-(

...Jim Thompson
--
| James E.Thompson, CTO | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona 85048 Skype: Contacts Only | |
| Voice:(480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |
 
On Nov 27, 12:20 pm, Jim Thompson <To-Email-Use-The-Envelope-I...@My-
Web-Site.com> wrote:
On Fri, 27 Nov 2009 08:19:22 -0800 (PST), Robert Macy
....snip...
Thank you for confirming that my 24 section model of 2 inch pieces has
been worth it.

Very educational results!

Some conclusions so far:  shield conductance MUST be kept low, center
conductors can be [almost] any size.

I'm trying to make the model so I can simulate adding beads to the
cable, but so far this has been tedious and testing my understanding
of the very basics.

Some years ago I evaluated and modeled wirebonds for Intel... took me
about 6 months of tedious data fitting :-(

                                        ...Jim Thompson
--
| James E.Thompson, CTO                            |    mens     |
| Analog Innovations, Inc.                         |     et      |
| Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    |
| Phoenix, Arizona  85048    Skype: Contacts Only  |             |
| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  |
| E-mail Icon athttp://www.analog-innovations.com|    1962     |
Help!! See questions at end.

Two free tools [femm 4.2 and LTSpice] have got me to here:

These simulated cables have center conductor and shield of solid
copper. Dimensions I guessed at after measuring some RG58 on the
bench. Results were Zo=74.3 ohms, so I left everything alone for
now. I assumed er was 2.26, just to match lengths a bit better, and
assumed no dielectric loss at high frequency. I now have 50 sections
of A and B lossy transmission lines, not coupled to each other, but
independent within a single shield. This is not strictly correct
representation, but most differential cables are dominantly separate.
For example most 100 ohm differential cables are approx. 75 ohm, 75
ohm to shield and only 300 ohm between the pair.

There are so many assumptions in this model, I abandoned rigorous
analyses and am opting for just obtaining an understanding of what's
going on. With that in mind, I found out that at even very low
frequenices where I expected the magnetic field to extend outside the
shield, it did not! Even with 1 amp flowing through the conductors,
the field dropped to nanoteslas within 1 thousand of an inch away from
the shield. To measure current in such a cable would require SQUIDs!

Next even at 100 MHz where skin depth is eating you alive, the shield
stays predominantly resistive loss, by 3 orders of magnitude. That
means each section of this transmission line can be modeled with four
components: center series inductor, center series resistor, center/
shield capacitor, and shield resistance. I then took Jim Thompson's
PSpice model for skin effect. His table of values at frequencies, by
extrapolation, I added a 2GHz term.

The idea is that unbalance of driver, cable, and load will cause
unbalanced currents to flow back along the outside of the cable and
this will form an excellent radiating antenna. The goal was given
manufacturing tolerances find how large the signal on the shield will
be? It was assumed the signal on the shield must stay below 100
microvolts, else the cable will be an efficient radiator, causing the
resulting system to fail FCC and CE EMC Class B limits.

Final model for the differential cable in free space, linked all 50
sections of A and B to create an approximately 12 foot cable.
That model was inserted into a perfect differential 1V drive through
matching impedance, driving the lossy cable, to matched resistive
loads.

Note: I discovered the impedance of the shield trying to radiate is so
low that trying to represent free space as a transmission line or as a
straight resistance of 377 ohms made very little difference in the
amount of signal appearing on the shield.

Given 5, 10, and 15% manufacturing variations the RESULTS were
interesting:
As expected, when the system is matched, there is "nothing" on the
shield.
Picture one of the cables is made with 'thin' center conductor:
however, resistance variation of the center conductor made little
difference
More important was the center inductance [and capacitance, given
variations in dielectric]
Any of those variations, kept the signals on the shield below 10-30
microvolts, so no problem, BUT! increase the shield impedance and the
numbers dramatically increased.

So the final conclusions were that the cable can be made pretty badly
[non uniformly], internally, but the shield had better be good.

Now my question: What range of frequencies will a 50 section of L, C,
and R be reasonable to use?

For example low frequency all 50 sections have now lumped together,
doesn't that make the model good from DC to ?? MHz?

At high frequencies, the single section has now dominated and the
model is not valid. What is that frequency?

Is it 1/(2 pi sqrt(LC)) ??

Or, do I use that 'less than 1/4 wavelength concept' and to be really
conservative 1/10 wavelength?
 
On Sun, 6 Dec 2009 10:30:18 -0800 (PST), Robert Macy
<macy@california.com> wrote:

On Nov 27, 12:20 pm, Jim Thompson <To-Email-Use-The-Envelope-I...@My-
Web-Site.com> wrote:
On Fri, 27 Nov 2009 08:19:22 -0800 (PST), Robert Macy
...snip...
Thank you for confirming that my 24 section model of 2 inch pieces has
been worth it.

Very educational results!

Some conclusions so far:  shield conductance MUST be kept low, center
conductors can be [almost] any size.

I'm trying to make the model so I can simulate adding beads to the
cable, but so far this has been tedious and testing my understanding
of the very basics.

Some years ago I evaluated and modeled wirebonds for Intel... took me
about 6 months of tedious data fitting :-(

                                        ...Jim Thompson
--
| James E.Thompson, CTO                            |    mens     |
| Analog Innovations, Inc.                         |     et      |
| Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    |
| Phoenix, Arizona  85048    Skype: Contacts Only  |             |
| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  |
| E-mail Icon athttp://www.analog-innovations.com|    1962     |

Help!! See questions at end.

Two free tools [femm 4.2 and LTSpice] have got me to here:

These simulated cables have center conductor and shield of solid
copper. Dimensions I guessed at after measuring some RG58 on the
bench. Results were Zo=74.3 ohms, so I left everything alone for
now. I assumed er was 2.26, just to match lengths a bit better, and
assumed no dielectric loss at high frequency. I now have 50 sections
of A and B lossy transmission lines, not coupled to each other, but
independent within a single shield. This is not strictly correct
representation, but most differential cables are dominantly separate.
For example most 100 ohm differential cables are approx. 75 ohm, 75
ohm to shield and only 300 ohm between the pair.

There are so many assumptions in this model, I abandoned rigorous
analyses and am opting for just obtaining an understanding of what's
going on. With that in mind, I found out that at even very low
frequenices where I expected the magnetic field to extend outside the
shield, it did not! Even with 1 amp flowing through the conductors,
the field dropped to nanoteslas within 1 thousand of an inch away from
the shield. To measure current in such a cable would require SQUIDs!

Next even at 100 MHz where skin depth is eating you alive, the shield
stays predominantly resistive loss, by 3 orders of magnitude. That
means each section of this transmission line can be modeled with four
components: center series inductor, center series resistor, center/
shield capacitor, and shield resistance. I then took Jim Thompson's
PSpice model for skin effect. His table of values at frequencies, by
extrapolation, I added a 2GHz term.

The idea is that unbalance of driver, cable, and load will cause
unbalanced currents to flow back along the outside of the cable and
this will form an excellent radiating antenna. The goal was given
manufacturing tolerances find how large the signal on the shield will
be? It was assumed the signal on the shield must stay below 100
microvolts, else the cable will be an efficient radiator, causing the
resulting system to fail FCC and CE EMC Class B limits.

Final model for the differential cable in free space, linked all 50
sections of A and B to create an approximately 12 foot cable.
That model was inserted into a perfect differential 1V drive through
matching impedance, driving the lossy cable, to matched resistive
loads.

Note: I discovered the impedance of the shield trying to radiate is so
low that trying to represent free space as a transmission line or as a
straight resistance of 377 ohms made very little difference in the
amount of signal appearing on the shield.

Given 5, 10, and 15% manufacturing variations the RESULTS were
interesting:
As expected, when the system is matched, there is "nothing" on the
shield.
Picture one of the cables is made with 'thin' center conductor:
however, resistance variation of the center conductor made little
difference
More important was the center inductance [and capacitance, given
variations in dielectric]
Any of those variations, kept the signals on the shield below 10-30
microvolts, so no problem, BUT! increase the shield impedance and the
numbers dramatically increased.

So the final conclusions were that the cable can be made pretty badly
[non uniformly], internally, but the shield had better be good.

Now my question: What range of frequencies will a 50 section of L, C,
and R be reasonable to use?

For example low frequency all 50 sections have now lumped together,
doesn't that make the model good from DC to ?? MHz?

At high frequencies, the single section has now dominated and the
model is not valid. What is that frequency?

Is it 1/(2 pi sqrt(LC)) ??

Or, do I use that 'less than 1/4 wavelength concept' and to be really
conservative 1/10 wavelength?
Stumbled onto this...

"Time-Domain Skin-Effect Model for Transient Analysis of Lossy
Transmission Lines"

Chu-Sun Yen, Zvonko Fazarinc, & Richard L. Wheeler (all at hp)

Proceedings of the IEEE, VOL. 70, NO. 7, July 1982

I can't read the page numbers on the (crappy) copy I have, but there
is a numbering at the bottom of the first page...

0018-9219/82/0700-0750$00.75 Š 1982 IEEE

...Jim Thompson
--
| James E.Thompson, CTO | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona 85048 Skype: Contacts Only | |
| Voice:(480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

In wine there is wisdom,
In beer there is freedom,
In water there is bacteria
- Benjamin Franklin
 
On Dec 8, 12:10 pm, Jim Thompson <To-Email-Use-The-Envelope-I...@My-
Web-Site.com/Snicker> wrote:
On Sun, 6 Dec 2009 10:30:18 -0800 (PST), Robert Macy





m...@california.com> wrote:
On Nov 27, 12:20 pm, Jim Thompson <To-Email-Use-The-Envelope-I...@My-
Web-Site.com> wrote:
On Fri, 27 Nov 2009 08:19:22 -0800 (PST), Robert Macy
...snip...
Thank you for confirming that my 24 section model of 2 inch pieces has
been worth it.

Very educational results!

Some conclusions so far:  shield conductance MUST be kept low, center
conductors can be [almost] any size.

I'm trying to make the model so I can simulate adding beads to the
cable, but so far this has been tedious and testing my understanding
of the very basics.

Some years ago I evaluated and modeled wirebonds for Intel... took me
about 6 months of tedious data fitting :-(

                                        ...Jim Thompson
--
| James E.Thompson, CTO                            |    mens     |
| Analog Innovations, Inc.                         |     et      |
| Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    |
| Phoenix, Arizona  85048    Skype: Contacts Only  |             |
| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  |
| E-mail Icon athttp://www.analog-innovations.com|   1962     |

Help!!  See questions at end.

Two free tools [femm 4.2 and LTSpice] have got me to here:

These simulated cables have center conductor and shield of solid
copper.  Dimensions I guessed at after measuring some RG58 on the
bench.  Results were Zo=74.3 ohms, so I left everything alone for
now.  I assumed er was 2.26, just to match lengths a bit better, and
assumed no dielectric loss at high frequency.  I now have 50 sections
of A and B lossy transmission lines, not coupled to each other, but
independent within a single shield.  This is not strictly correct
representation, but most differential cables are dominantly separate.
For example most 100 ohm differential cables are approx. 75 ohm, 75
ohm to shield and only 300 ohm between the pair.

There are so many assumptions in this model, I abandoned rigorous
analyses and am opting for just obtaining an understanding of what's
going on.  With that in mind, I found out that at even very low
frequenices where I expected the magnetic field to extend outside the
shield, it did not!   Even with 1 amp flowing through the conductors,
the field dropped to nanoteslas within 1 thousand of an inch away from
the shield.  To measure current in such a cable would require SQUIDs!

Next even at 100 MHz where skin depth is eating you alive, the shield
stays predominantly resistive loss, by 3 orders of magnitude.  That
means each section of this transmission line can be modeled with four
components: center series inductor, center series resistor, center/
shield capacitor, and shield resistance.  I then took Jim Thompson's
PSpice model for skin effect.  His table of values at frequencies, by
extrapolation, I added a 2GHz term.

The idea is that unbalance of driver, cable, and load will cause
unbalanced currents to flow back along the outside of the cable and
this will form an excellent radiating antenna.  The goal was given
manufacturing tolerances find how large the signal on the shield will
be?  It was assumed the signal on the shield must stay below 100
microvolts, else the cable will be an efficient radiator, causing the
resulting system to fail FCC and CE EMC Class B limits.

Final model for the differential cable in free space, linked all 50
sections of A and B to create an approximately 12 foot cable.
That model was inserted into a perfect differential 1V drive through
matching impedance, driving the lossy cable, to matched resistive
loads.

Note: I discovered the impedance of the shield trying to radiate is so
low that trying to represent free space as a transmission line or as a
straight resistance of 377 ohms made very little difference in the
amount of signal appearing on the shield.

Given 5, 10, and 15% manufacturing variations the RESULTS were
interesting:
As expected, when the system is matched, there is "nothing" on the
shield.
Picture one of the cables is made with 'thin' center conductor:
however, resistance variation of the center conductor made little
difference
More important was the center inductance [and capacitance, given
variations in dielectric]
Any of those variations, kept the signals on the shield below 10-30
microvolts, so no problem, BUT! increase the shield impedance and the
numbers dramatically increased.

So the final conclusions were that the cable can be made pretty badly
[non uniformly], internally, but the shield had better be good.

Now my question: What range of frequencies will a 50 section of L, C,
and R be reasonable to use?

For example low frequency all 50 sections have now lumped together,
doesn't that make the model good from DC to ?? MHz?

At high frequencies, the single section has now dominated and the
model is not valid.  What is that frequency?

Is it 1/(2 pi sqrt(LC)) ??

Or, do I use that 'less than 1/4 wavelength concept' and to be really
conservative 1/10 wavelength?

Stumbled onto this...

"Time-Domain Skin-Effect Model for Transient Analysis of Lossy
Transmission Lines"

Chu-Sun Yen, Zvonko Fazarinc, & Richard L. Wheeler (all at hp)

Proceedings of the IEEE, VOL. 70, NO. 7, July 1982

I can't read the page numbers on the (crappy) copy I have, but there
is a numbering at the bottom of the first page...

0018-9219/82/0700-0750$00.75 Š 1982 IEEE

                                        ...Jim Thompson
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Thanks, the culmination seems to be to add a 'step' network structure,
so I'll try that.
 

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