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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