Ralph,
As usual you've come through.
Although, I understand your points well and can't disagree with
you, I'm still not sure I can totally agree.
This "won't disagree but not really agree" stand comes from a
couple of observations:
1. That the telegraph equations get split up into "high
frequency" and "low frequency" equations depending upon
assumptions that retain or remove different parameters from
the complete equations, i.e. removing some of these parameters
from these equations allow one to study/predict results in
coax cables as I'm sure you're well aware. And, one can
"lump" parameters successfully for coax. But, I'm using the
same procedure for the case of a trace.
2. In my model, the units for resistance, inductance, and
capacitance are "per length". To extend the length of the
trace, I would not "cascade" the parameters as in adding more
sections of a filter network. (I don't know, but does Spice do
this in modeling?) The individual parameters only become
larger.
3. This is a 1 inch trace. Not feet of wire.
4. Finally, I can't believe that the trace DOES NOT act as a
low pass filter no matter what school or books have showed me
about transmission lines.
As stated by someone off line, frequency problems above 800 MHz
are well documented with FR-4. This forces me to believe I'm on
to "something". Yes, I agree with what you say about lumped
parameters versus distributed parameters, but even worst case
rough estimating tells me I'm near "something".
I guess if I were to be tacked against the wall, I'd have to say
OK. But, that still won't help me.
Doug McKean, ADC Video, [log in to unmask]
______________________________ Reply Separator
_________________________________ Subject: DES-PC Board Frequency
Limi
Author: [log in to unmask] at internet-mail Date: 5/9/96 2:33 PM
Subject: Time: 7:45 AM
OFFICE MEMO DES:PC Board Frequency Limits Date:
5/9/96
Doug:
The following your messages and are combined and reproduced here
to complete the query and information, my comments follow at the
end. Ralph
----------------- initial query ------
>I would like any responses to be off-line for the following
discussion.
>Please use the following email address: [log in to unmask]
>I made a simple mathematical model of a stripline, 1 inch trace,
on FR-4, nothing out of the ordinary as far as dimensions and
found to my surprise a resonant freq at about 800 MHz with a
20 to 40 dB roll-off above 800 MHz
>Could someone in the RF/Microwave world of nuts and bolts pc
board design tell me what I'm supposed to do at say 10 GHz
with regular pc board materials/construction/fabrication???
---end of initial query---
---start of second message with tech. info. follows ---- #004# >I
don't have any problem with going on the Net with this.
>This is more of a theoretical issue than anything else. Not
really related to IPC. With all the talk about too much
mail, I decided to throw the issue on the net with the option
to email direct.
>So without any further talk, here goes:
>I am trying to write a technical paper for my company on what I
have found.
>My basic model was based on a lumped parameter model of a one
inch copper trace with one end terminated with a signal
source, the trace lumped with trace resistance and trace
inductance in series, to a termination of a resistor (load)
and capacitor (dielectric) in parallel.
>I drop into the frequency domain with Laplace and write my
system response.
>Up to this point, I am still in line with any cross check of a
similar circuit in any circuit analysis book. If anyone is
into it, I'm following the basic derivation of
telegraph/telephone equations for transmission line signal
analysis. OK, so big deal.
>Now, I plug in "standard" values for the lumped parameters of
copper trace resistance per inch, copper trace inductance per
inch...
>I DERIVE the impedance of the trace using IPC impedance relation
for a stripline trace. From this, I derive capacitance per
inch. This is where I'm a little skittish about what I'm
doing.
>If I set the load resistance to infinity, I get a large resonant
spike at about 800 MHz. If I adjust the load resistance to below
150 ohms, the spike goes away. To anyone interested, I'm playing
around with the system damping factor from my second order system
response equation. Alright, so what???
>No matter what I do with the load resistance, there is a large
roll-off above 800 MHz. Like 40 dB!!!
>I'm using MathCad for printable output. I have Word,
Wordperfect, Excel, and MathCad software on an IBM compatible
486/66 MHz machine.
>So far, I have had two people say that they are interested, a
third has had no problem with boards (ECL based circuitry - I was
sort of expecting that), a fourth has seen designers wrestle with
running simulations - looking at results - do a little adjusting
- run simulation again and so on for a couple of weeks (Spice
based).
------- then then the third provided the details ------
I used the wrong word!
I apologize MICROSRIP is the correct word. NOT stripline.
I am doing Microstrip calculations on a Microstrip construction
Sorry about that.
Here's some specifics:
Dielectric Constant = 4.5
Dielectric Height = 0.029 inches
Trace Width = 0.008 inches
Trace Thickness = 0.0024 inches
Trace Length = 1.00 inch
Inductance per inch (assumed value) = 20 nH per inch
Calculated Impedance Value for Trace = 107 ohms
Derived Capacitance from Impedance = 2pF per inch
Signal Delay along trace = 187 psec
Resonant Frequency of trace without a load = 850 MHz
Thanks in advance, Doug McKean
From: [log in to unmask]
------------------------------------------------------
Doug-
You got different results because of different design and
modeling techniques/metholologies. Transmission lines are
modeled differently than a lumped parameter spice-like network
analysis model. What you analyzed using you lumped parameter
model is called a "series resonant circuit".
First, the transmission line (in theory) are frequency
independant, and therefore, the formulas do not take frequency
into account. Most of the transmission line modeling formulas
are based on the variables of dielectric constant and
capacitance. They extract these out of the more complex
transmission line formulas. The general formula for transmission
line impedance is:
Z(o) = sqrt ((R length + i omega (L length)) / (G length + i
omega (C length)))
where Z(o) is the impedance of the transmission line
R is the (series) resistance per unit length (including skin
effects) of the conductors
G is the (shunt) conductance per unit length between conductors L
is the inductance per unit length of the conductors
C is the capacitance per unit length between conductors i omega
are the complex quadratic operators.
----
Frequency domain network analysis is different because you are
now performing an electrical characterization of a resonant
circuit and low-pass filter.
When you do a "network analysis" using lumped parameter models,
the electrical characteristics of the network is very sensitive
to frequency and you are therefore performing an frequency domain
analysis.
In using a simple lumped parameter model, the output of your
source is connected to your lumped parameter model, which
consists of a series inductor in series with the distributed
capacitance to ground.
The resonant frequency of a series resonant circuit is when the
inductive and capacitive reactances are equal, and when solved
for frequency is equal to:
f(o) = 1 / (2 * pi * sqrt ( LC))
Which using your provided values of L (20 nanoH) and C (2
picoF)
Plug the numbers in and solve, your resonant frequency f(o) is
795.+ MHz.
In theory, at resonance, the impedance of a series resonant goes
to 0 (zero) and current is liminted only by the source impedance
and series resistances. The current waveform through the series
components is common to both the inductor and capacitor. The
derrived voltages across the capacitor and inductor are 90
degrees (lead/lag in quadature) out of phase with the current.
Because resonance, the series current is infinite, you will
develop very high
voltages (180 degrees out of phase) across the capacitor and
inductance (due to low intrinsic impedances). And because the
induced voltages are in quadrature and 180 degrees out of phase
they essentially cancel each other across the lumped parameter
network. This is why at resonance, you obtain the very high
voltage across the output capacitance of you lumped parameter
model.
Then as you load the capacitor with resistance you will change
the phase
relationships of the electrical network and the two voltages
across the inductance and capacitance are no longer 180 degrees
out of phase, rather some vector quantity.
As I mentioned in my previous post, the simple series inductace
an capacitance is a low-pass filter. In the frequency domain, as
the frequency increases the low-pass filter will do just that,
pass low frequencies based on the electrical characteristics at
that frequency(s). At resonance, you get what you observed, a
peak. Then depending on the number of lumped parameter models
you have in you model, the higher frequencies will be attenuated,
and using a multi-stage model, you will obtain the roll-off or
attenuation you observed (calculated).
And yes Doug -- as the more traditional printed board designs
make the transition into the world high frequency/speed we get
into the world of "serious" printed circuit design,
manufacturing, assembly and test.
And yes also to "Groovy" Dave Hoover, those individuals/companies
who are currently successfully working in this area have spent a
lot of resources to develop their CAE modeling tools in order to
obtain correlaton between their CAE tools and reality (what they
get as an end product).
Ralph Hersey
e-mail: [log in to unmask]
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