Coaxial cable simulation data
maurizio stefani
I am searching the coaxial cable simulation data to be used in circuit
simulation as SPICE or other.
I woud like to have the equation or models starting from coaxial data
like pF/km, attenuation, characteristic impedance .....
Is there some one able to help me?
Thank you in advance
--
Best Regards
m.stefani email-m...@aleniasystems.finmeccanica.it
tel. 0039-06-41973579
fax 0039-06-41973617
Allan Herriman
<mste...@aleniasystems.finmeccanica.it> wrote:
>I am searching the coaxial cable simulation data to be used in circuit
>simulation as SPICE or other.
>I woud like to have the equation or models starting from coaxial data
>like pF/km, attenuation, characteristic impedance .....
Hi Maurizio,
I've done quite a bit of spice modelling of twisted pair cables, so I
might be able to help.
I should warn you that *accurate* models for many km of cable at many
MHz aren't really feasible. YMMV.
1. The usual simple finite element model for a lossy transmission
line has RLGC parameters.
R is the series resistance (all parameters are per unit length)
L is the series inductance
G is the shunt conductance
C is the shunt capacitance
This means that you can simulate the cable with a bunch of "unit
length" sections that look like:
in----R---L--+---+--out
| |
1/G C
| |
0------------+---+---
Note: 1/G is a resistor with resistance 1/G.
To model the cable, just string several of these sections together.
One usually puts "half" sections at the ends. These look like:
| several |
in----R/2-L/2+---+--| full |----R/2-L/2----out
| | |sections |
1/G C |(from |
| | | above) |
0------------+---+--| |---------------0
| |
Note that I've assumed that the shield is grounded at both ends. A
more detailed model would also have series elements in the shield.
(This wasn't a problem for my balanced line models; I could just split
it straight down the middle and simulate exactly half of it, as I
didn't have a need to model common mode signals.)
A string of N sections actually makes a 2N pole low pass filter. Thus
the simulation will only work up to a particular frequency, and above
that frequency it will attenuate strongly, and the impedance will drop
to a low value.
This "brickwall" frequency is approximately 2 * (1/ (2 pi sqrt(LC)))
(where L and C are the values used in each section).
The simulation will be accurate enough up to some frequency less than
this. I suggest about half the brickwall frequency, but it depends on
your accuracy requirements.
If you need more bandwidth, then you need to make the "unit length"
smaller, so that you have more sections and each section models a
shorter length of cable. For a particular set of cable parameters,
the number of sections needed is roughly proportional to the product
of the length of the cable and the bandwidth you require.
(The largest simulation I've done used 120 sections. It modelled
3.7kM of 0.4mm twisted pair, and was good to about 500kHz.
(BTW, you can forget about using the (node limited) free evaluation
copies of spice.))
1b. In practical cables, *all* of these (RLGC) parameters vary with
frequency. R varies due to the skin effect (which may be significant
above only a few of kHz). L will vary due to the skin effect (as the
current distribution in the wire changes - but the effect in coax
would be different to the effect in twisted pair). G models the
dielectric loss, and this is a function of frequency. G at 0Hz (DC)
is determined by the leakage current, and is often assumed to be zero.
C doesn't seem to vary much with frequency.
I guess you could try to model this with frequency dependent
behavioural modelling of the above components, but it might take
forever to run.
I've had some sucess modelling the frequency dependence of R and L by
replacing the above L and R with:
----L1--R1--+--L2--+----
| |
+--R2--+
For most of the cables I've worked with I've been able to ignore G
completely, as R dominated the loss.
I built one simulator which had a small value resistor in series with
the capacitor to attempt to capture some of the frequency dependence
of G. (Remember G is usually ~0 at DC.)
1st method:
---+-
|
C
|
---+-
2nd method:
---+-
|
C
|
R'
|
---+-
3rd method:
---+---+-
| |
C' C
| |
R' |
| |
---+---+-
(If you're actually building these things in hardware, it's easiest to
use a capacitor with the same dielectric as the cable, but this
doesn't work in simulations. (I'd hate to have to model pulp
insulation that way.))
2. Most modern spices have lossy transmission line models ('T') built
in. These usually have fixed values of RLGC (i.e. RLGC are not
functions of frequency), so they don't model the skin effect or the
frequency dependence of dielectric loss, which will severely limit
their ability to model real cables.
However, the built in models will be faster to simulate than the
lumped model (above), and they are much easier to type in!
3. How do you work out the values of RLGC?
3a. Easy - they are specified. Sometimes the cable manufacturer may
have them. Sometimes Bellcore (or similarly oriented organisations
such as ETSI) will characterise cables and publish the results.
That's how I got the parameters for my simulations.
3b. The C value is usually specified (because it's easy to measure).
The characteristic impedance Z is always specified, often as a
function of frequency. You can find L by using the formula:
Z = sqrt(L/C)
Note that Z is in ohms. If C is in farads per unit length, then L is
in henrys (henries? :) per unit length.
(This formula is only accurate for lossless lines (no R or G), but it
is pretty good for practical cables.)
Sometimes Z may be specified as an S parameter.
3c. The DC value of R can be determined from the DC resistance of the
cable, which is (almost) always specified.
3d. G is rather hard to calculate, as this involves working out
whether loss is due to R or G. Both types of losses will increase
with frequency. I have no simple answer for this problem.
4. Further notes on lossy transmission lines:
4a. The attenuation at (really) low frequencies will be flat (i.e.
not a function of frequency). The attenuation is just determined by
the DC resistance of the cable (and possibly a small leakage term for
G).
4b. At some frequency, the attenuation will begin to increase. This
is due to the R and C parameters. The attenuation increases at
(roughly) 3dB/octave.
4c. At some higher frequency, the attenuation will flatten out, as
the impedance of L starts to dominate the series impedance.
4d. At still higher frequencies, the attenuation starts to increase
with frequency again. This is due to R increasing from the skin
effect. Again, the attenuation increases at (very roughly)
3dB/octave.
5. Some of the models I've done have been purely for simulation,
mostly for developing line hybrids for DSL applications.
The rest of the models I've done have been for the design of cable
(i.e. subscriber loop) simulators, which are used for testing DSL
hardware. It's a lot easier to use a board that you can hold in one
hand instead of lugging around a huge cable drum! This is
particularly important when you need to test a multiport DSL card.
(The last DSL board I designed had 12 ports. I think a square law
applies to lugging, so this would be 144 times worse if we had to use
cable drums instead of line simulator cards.)
5b. You can buy subscriber loop cable simulators. They use exactly
the same models that I've just described, but they will cost some tens
of thousands of dollars. They include fancy user interfaces to help
control a bank of relays which are used to switch in different numbers
of sections.
5c. I believe there is at least one company that produced a digital
line simulator (which didn't use a finite element model). They were
bought out by Wandel & Goltermann, but I don't know what happened to
their product (it's not listed on the W&G web site).
Regards,
Allan.
K7ITM
>Hi,
>I am searching the coaxial cable simulation data to be used in circuit
>simulation as SPICE or other.
>I woud like to have the equation or models starting from coaxial data
>like pF/km, attenuation, characteristic impedance .....
>
OK, the SPICE I use is Berkeley Spice 3f5. The transmission line model just
takes R, (series) resistance/unit length, L, (series) inductance/unit length,
G, (shunt) conductance/unit length, C, (shunt) capacitance/unit length, and the
length LEN in the same units as the other parameters. There are also some
simulation control parameters. That is all detailed in the Berkeley SPICE
manual.
You can get L and C rather easily from the line impedance and velocity factor,
which are usually given by the manufacturer. Just use the relationships:
time=length*c*velocity factor = sqrt(L*C), and characteristic impedance Z0 =
sqrt(L/C). c, of course, is the speed of light. You should be able to solve
those two for L and C. Generally for good cable up to about 1GHz, G may be
approximated as zero; almost all the loss is in the resistance of the
conductors. Unfortunately, that loss resistance, R, depends on frequency, and
SPICE isn't set up to model that very well. Rather than try to reproduce all
the possible equations that might help, I'd suggest you look at a transmission
lines reference. The "transmission lines" chapter of "Reference Data for
Engineers" published by Howard Sams has enough info in it. In particular, you
might want to use R(per 100 feet) = 0.434*(1/d + 1/D)*sqrt(f), where D is the
inside diameter of the outer conductor in inches, d is the diameter of the
inner conductor in inches, and f is the frequency of interest, in MHz. This
simple equation is pretty accurate for smooth copper conductors which are at
least a few skin-depths thick.
If I've answered the wrong side of the question for you...well, then I'd refer
you to a transmission lines book. One I like, but it's out of print, is King,
Mimno and Wing, "Transmission Lines, Antennas and Wave Guides." It's
relatively non-mathematical, but quite reasonably complete, IMHO.
Cheers,
Tom
Cheers,
Tom
Bill sloman
K7ITM wrote:
>
> m.stefani wrote:
>
> >Hi,
> >I am searching the coaxial cable simulation data to be used in circuit
> >simulation as SPICE or other.
> >I woud like to have the equation or models starting from coaxial data
> >like pF/km, attenuation, characteristic impedance .....
> >
>
> OK, the SPICE I use is Berkeley Spice 3f5. The transmission line model just
> takes R, (series) resistance/unit length, L, (series) inductance/unit length,
> G, (shunt) conductance/unit length, C, (shunt) capacitance/unit length, and the
> length LEN in the same units as the other parameters. There are also some
> simulation control parameters. That is all detailed in the Berkeley SPICE
> manual.
>
> You can get L and C rather easily from the line impedance and velocity factor,
> which are usually given by the manufacturer. Just use the relationships:
> time=length*c*velocity factor = sqrt(L*C), and characteristic impedance Z0 =
> sqrt(L/C). c, of course, is the speed of light.
Are you sure? IIRR it is the speed of light in the cable dielectric,
which is
typically around 2/3 of the speed of light in vacuum.
Bill Sloman, Nijmegen
James Meyer
>K7ITM wrote:
>>
>> You can get L and C rather easily from the line impedance and velocity factor,
>> which are usually given by the manufacturer. Just use the relationships:
>> time=length*c*velocity factor = sqrt(L*C), and characteristic impedance Z0 =
>> sqrt(L/C). c, of course, is the speed of light.
>
>Are you sure? IIRR it is the speed of light in the cable dielectric,
>which is
>typically around 2/3 of the speed of light in vacuum.
>
> Bill Sloman, Nijmegen
Looks OK to me, Bill. Perhaps it was late at night or early in the
morning when you read it the first time.
Jim
Roy McCammon
< lots of good info >
Instead of the primary parameters (R,G,L and C), you can usually
get (and are more likely to get) the secondary parameters (propagation
velocity, attenuation, and characteristic impedance), all vs frequency.
In fact, I suspect they measure the secondary parameters and calculate
the primary parameters from that. Velocity may be given as radians
of phase shift per unit length.
I usually put those in a lookup table (vs log of frequency),
do a spline fit on that, and use those parameters directly
to compute frequency domain transmission and reflection. FFT
for time domain.
Tom Bruhns
Well, there's just one problem. Although c*velocity factor is the speed
in cable, length * (c*v.f.) is NOT time! heh, heh. oops. How about I
try this again?? time = length/(c*v.f.) = sqrt(L*C). Sorry about that
first posting, and thanks to Bill for picking it up.
There. Now if you combine that and the Z0 = sqrt(L/C), you get C/length
= 1.0/(Z0*c*v.f.), which passes a two or three of my sanity checks: C
increases for decreasing Z0 and decreasing v.f., and the units on the
left match the units on the right: amp-seconds/volt-meter. In fact, it
leads to what I think is a useful result to carry around with me: 50
ohm solid polyethylene cable will be 100pF/meter (or 30pF/foot), pretty
close. 75 ohm coax will be about 2/3 of that. L=C*Z0^2, but I don't
need that as often as I want to know the capacitance so I leave that to
the calculator (either the one in my hand or the one in my head).
Cheers,
Tom
(same Tom, posting from my work address.)
John Woodgate
inimitably wrote:
>In fact, I suspect they measure the secondary parameters and calculate
>the primary parameters from that.
--
Regards, John Woodgate, OOO - Own Opinions Only.
Phone +44 (0)1268 747839 Fax +44 (0)1268 777124.
Did you hear about the hungry genetic engineer who made a pig of himself?
PLEASE DO ****NOT**** MAIL COPIES OF NEWSGROUP POSTS TO ME!!!!
Tom Bruhns
John Woodgate wrote:
>
> <37CA93CB...@mmm.com>, Roy McCammon <rbmcc...@mmm.com>
> inimitably wrote:
> >In fact, I suspect they measure the secondary parameters and calculate
> >the primary parameters from that.
> There is no other practicable way, AIUI.
It's not difficult to get a pretty accurate direct measurement of
capacitance in a known length, and I've had some modest success
measuring the inductance directly (though with poorer accuracy than the
capacitance), but since the resistance (and conductance) are rather
strong functions of frequency, and since the frequency of interest is
generally where the distributed nature of the line must be accounted
for, it's not very practical to measure them directly. Even capacitance
and inductance measurements at a frequency other than the operating
frequency are subject to some error because of frequency
dependencies--inductance usually more so than capacitance.
On the other hand, there are other measurements which can be made: for
example, knowing the capacitance and the conductor diameters (and being
assured that the conductors are reasonably close to co-axial), I can
calculate impedance. Knowing the dissipation factor of the dielectric,
I can calculate the conductance (and probably get a more accurate
estimate of it than I could trying to measure the line's electrical
parameters, at least through VHF for good dielectrics). There are quite
a number of measurements that can be taken which allow a degree of
cross-checking, which can be especially useful if one doesn't have
access to laboratory grade impedance and loss measurement
equipment/techniques.
Cheers,
Tom