Maxwell's Dream Help: Tell me about the accuracy! Back to Overview

Approximations

If you want to calculate the result of a physical experiment, it is impossible to take all effects into acount. You don't believe that? Then try to calculate the trajectory of stone, which is thrown by a child. Of course you will take the gravitation into account. Maybe you even consider the air friction. But what about the Coriolis effect, which results from the rotation of the earth? Did you consider the loss of mass due to natural radio activity? What about relativistic effects? Any side effect from quantum mechanics?

You got the idea. It is impossible to take all effects into account. All we can do is to consider the relevant physical effects (gravitation, air friction) and we have to disregard the not so important ones (e.g. relativistic effects in our example).

Maxwell's Dream does some approximations also, which are discussed in the following section.

The endless triplate

We assume, that the triplate starts somewhere at -∞ and leads to +∞ and that the Triplate has no curve or bend. Of course, a real triplate in a real PCB has a limited length and may have many curves or sharp bends. As long as the straight segments of the triplate will be longer than 10 times the width of the signal trace, this is a good approximation.

The quasi-static approach

We assume, that the electrical field of the high-frequency signal has the same properties like the static field of a DC voltage. For typical triplate geometries of todays PCBs this approximation is good for frequency up to the GHz range. For frequencies larger than 5...10GHz you will see higher modes propagating along the triplate, which are not considered by Maxwell's Dream.

The loss-less approach

We assume, that the dielectric material has no losses and the resistance of the signal and ground planes is zero.

Electric borders left and right of the signal trace

To speed up the calculation, an electrical border is introduced both at the right and left side of the calculated cross area of the triplate.

These artificial ground planes at the right and left side increase the capacitance of the calculated triplate, compared to the real one. At the beginning of the calculation, the position of these electrical borders is chosen automatically for you. If you are sceptical about this automatism, you can look at the calculation monitor:

The parameter Qb / Qm tells you, how large the influence of the artificial electrical borders is. Qb is the induced charge at these borders, and Qm is the induced charge at the real ground planes (top and bottom). If there is no calculation error introduced by these borders at the left and right, the ratio Qb / Qm would be zero. If the ratio is a non-zero value, an error is introduced by the artificial borders. But the error by the artificial borders is much smaller than the value of Qb / Qm. Therefore the value of 0.01 given in this example is a very good value, because the error introduced by the artificial borders will be much lower than 1%.

The grid

The finite elements analysis divides the space between the signal trace and the ground planes into an array of elements. If this grid is too coarse, fine details of the electrical field can no longer be modelled. If the grid is too fine, calculation time is increased dramatically. Maxwell's Dream takes automatically care to choose a proper grid. If you have some doubts, you can increase the number of elements by selecting Fine Accuracy instead of Normal Accuracy.

A Reference

To verify the accuracy of Maxwell's Dream, it is good to compare Maxwell's Dream to a well known reference [1]. In this reference from IBM the capacity of Triplates with different geometries was measured with high accuracy. These results are compared with the results from Maxwell's Dream in the following table.

Geometry Reference result Maxwell's Dream
Coarse Accuracy
Maxwell's Dream
Normal Accuracy
Maxwell's Dream
Fine Accuracy
width=0.4
thickness=0.08
Sig2GND=0.23
GND2GND=0.611
49.803 pF/m 51.07 pF/m
+2.54%
50.11 pF/m
+0.61%
49.18 pF/m
-1.25%
width=0.4
thickness=0.08
Sig2GND=0.45
GND2GND=1.343
31.141 pF/m 33.17 pF/m
+6.51%
31.65 pF/m
+1.63%
31.38 pF/m
+0.76%
width=0.4
thickness=0.08
Sig2GND=0.83
GND2GND=1.800
25.827 pF/m 27.30 pF/m
+5.70%
26.58 pF/m
+2.91%
26.03 pF/m
+0.78%
Maximum Error -- 6.51% 2.91% 1.25%

As you can see, Coarse Accuracy is good for a quick overview, but should not be used for the final result. On the other hand, the Normal Accuracy and the Fine Accuracy are precise enough for the dimensioning of PCBs and multilayer ceramics. For such applications the dominating factor for error will be the tolerance in manufacturing, not the finite elements tool.


Literature

[1] Y.M.Hill, N.O.Reckord, D.R.Winner, A General Method for Obtaining Impedance and Coupong Characteristics of Practical Microstrip and Triplate Transmission Line Configurations, IBM J. RES. DEVELOP., May 1969


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