At 04:57 PM 24/02/99 +0000, you wrote:
>Hi John,
> First I would like to confirm What Dan Brandler said about doing the
>back calculation using Imperical data. Almost always when we do this we get a
>lower DK than the supplier recommends. You must realize that the Laminate
>suppliers publish a "blanket" DK value that is supposed to be an average
of all
>their constructions. The DK value for a specific laminate is dependent on the
>resin to Glass ratio. So you see this can be quite variable depending on the
>specific laminate used. From the Board standpoint, the lamination Process is
>also a variable that depends on how much resin is retained in the cured
prepreg
>vs. the glass content. I caution all who do the Impedance modeling to be aware
>of this. The best thing you can do is do the back calculation of the model to
>see what the actual DK value is. Also remember this is also a function of the
>frequency at which the board is supposed to operate at. The values from most
>models provides the Characteristic Impedance at 1 Megahertz.
>
>I hope this is of some help,
>
>Regards,
>Les
Dear Les,
Your comments regarding core, pre-preg and glass/resin ratio are very apt.
For many controlled impedance designs the value of Er for the material at
a frequency of 1 GHz is more representative for modelling purposes. This
makes sense when you consider for example that a 50 MHz square wave
digital clock, with 1ns rise/fall times will have a signal bandwidth of around
350MHz. You can look at this from two points of view:
1. BW = 0.35 / tr
(simple equation that relates the time domain to the frequency domain,
where; BW = bandwidth and tr = risetime)
2. Fourier Series and Harmonic Analysis
A square wave can be synthesized by a series of single frequency sine
waves. A fundermental (50 MHz) plus a weighted sum of all the odd
harmonics, a third harmonic (150MHz), fifth harmonic (250MHz) and
a seventh harmonic (350MHz). Digital clocks are bandwidth limited,
and it is reasonable to ignore the odd harmonics above the seventh
(or ninth) in most cases.
A clock waveform is a wide bandwidth signal and it is the higher
frequency harmonics that contain the energy to produce the fast edge
transitions. (If a square wave is passed through a low pass filter the
HF energy is attenuated resulting in much slower edge transitions.)
From a Controlled Impedance point of view, a transmission line
will exhibit transmission line effects when the electrical length of
the line is greater than approximately a quarter of the electrical
length of the signal. This is the transition point when lumped circuit
theory needs to abandoned for distributed circuit theory.
For example, take a normal FR-4 board with a 6 inch physical length
stripline trace. The one way propagation delay time will be about 1ns.
So any digital signal with rise / fall times of less than 4ns propagating
along stripline traces in FR-4 longer than 6 inches will tend to exhibit
transmission line effects, such as reflections (if not terminated correctly).
A simple approximate way to calculate the electrical length of a
digital signal is to follow the following basic method:
c = velocity of light in a vacuum,
this is approximately 12 inches/ns in air,
FR-4 has a high frequency Er value of around 4,
signal velocity in a dielectric is inversely proportional to SQRT(Er),
so "in" FR-4 signals travel at 12 / SQRT (4) inches/ns = 6 inches/ns.
Therefore a 1ns edge on a stripline trace in FR-4 has an electrical
length of approximately 6 inches. This means that all stripline
traces longer than 1.5 inches in FR-4 boards with edge speeds
of 1ns or faster should be considered as transmission lines.
Microstrip traces propagate signals with field patterns mostly
distributed in the board substrate dielectric material, but some
field radiates in the surrounding air dielectric. Air has Er = 1, so
the effective relative permitivitty of the air/dielectric combination
will be lower than "pure" FR-4. This means that signals propagate
(approx 20% faster on surface traces (but also radiate more) than
on internal traces. However, application of solder mask can reduce
this somewhat. This means that all microstrip traces longer than
about 1.2 inches on FR-4 boards with edge speeds of 1ns or faster
should be also be considered as transmission lines.
Impedance can be controlled by micro adjusting trace width to
compensate for variations in laminate thickness and material Er.
The latter can be dangerous, as the secondary effect of a change
in material Er is a variation in signal propagation delay. This means
that impedance could be adjusted to be in spec, but the change in
signal propagation delay could result in circuit timing errors if say a
bus/clock system is not routed for matched electrical length conditions.
In the analog world this situation needs to be looked at from a slightly
different perspective. The signal propagation speeds will be similar to
those above, remember VELOCITY = FREQUENCY x WAVELENGTH,
and wavelength is dependant on the medium through which the wave
is travelling. However, some analog signals are narrow bandwidth and
the printed circuit layout is designed to include electrical lengths that
resonate (or couple, filter, etc... or have a known VSWR) at a given
impedance and frequency range. This is why it is important to find out
whether you are dealing with a mainly analog or digital design. If a
narrow frequency (sinusoidal) bandwidth is used then this will provide
a better indication of what frequency to use in your impedance modelling.
In a digital design, clock frequency can give you an indication of bandwidth,
but it's edge transition duration (rise / fall time) that defines the
electrical
length. This should be used to find out the highest frequency content in
the signal. This will then provide an indication of what frequency to use in
models for material relative permittivity (Er) and transmission line impedance.
I suggest that if you are not sure (or cannot confirm exact values) then
assuming a bandwidth of 1 GHz, 0.35 ns risetime and an Er of around
4.2 will be reasonable ball park figure to start with for modern designs.
These figure may need revising if you are working on leading edge
technology designs.
I hope my ramblings are helpful. Now I must do some real work.
Best regards
Andy Burkhardt
Product Manager
Email: [log in to unmask]
Tel: + 44 1481 253081
Fax: + 44 1481 252476
http://www.polar.co.uk
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