The following is an example of one application for OptEM Interconnect Designer (OptEM ID). A 100 Ohm dual stripline is to be constructed as shown in Figure 1. The challenge is to calculate the dimensions of the conductor width (width) and the thickness of the dielectric (th) using the following assumptions.

the impedance between conductors T1 and T2 is to be 100 Ohm

the dielectric is FR-4 with a dielectric constant of 4.6 and a tangent delta of 0.001

all conductors are 1 oz. Copper (Cu)

The following three steps are all that are needed to solve this problem using OptEM ID:

1. Define the Stackup

The geometry stackup is defined using the Fabrication Table dialog box. In this case, 7 layers are required to define the stackup:

• plane1 (bottom Cu reference plane with thickness=0.03556 mm)
• die1 (FR-4 dielectric with thickness defined as the variable th)
• T1 (deposited Cu with thickness=0.03556 mm)
• die2 (FR-4 dielectric with thickness defined as the variable th)
• T2 (deposited Cu with thickness=0.03556 mm)
• die3 (FR-4 dielectric with thickness defined as the variable th)
• plane2 (top Cu reference plane with thickness=0.03556 mm)

This stackup can be saved for future use and will save time for future analyses.

2. Create a Cross Section Using the Stackup

A cross section is created which references the above stackup. The following two conductor traces are placed in the cross section:

• trace T1 on layer T1 with width defined as the variable width
• trace T2 on layer T2 with width defined as the variable width

3. Perform Parametric Plotting

The analysis frequency is set to DC and a parametric analysis is performed on the cross section. The variable th is swept through the values of 0.10 mm, 0.15 mm, 0.20 mm and 0.25 mm. For each th value, width is swept through 13 values from 0.02 mm to 0.14 mm. While this analysis is running in the background, the analysis frequency is changed to 1GHz and another parametric analysis is submitted.

The two parametric analyses were performed nearly simultaneously on a Hewlett-Packard B160L computer running at 160MHz. This allowed the 104 (13x4x2) cross-section analyses to complete in under 2.5 minutes.

After each analysis completed, the value of Zdiff was plotted as a function of the variable width. This resulted in the two plots shown in Figure 2 and Figure 3.

By intersecting the 100 Ohm line through the curves plotted above it is determined that the values of width and th which generate a 100 Ohm line are as follows:

As a result of skin and proximity effects, an increase of frequency results in a reduction of inductance and an increase of resistance. However, in this example, changes of inductance dominate the frequency behavior of the impedance so the conductor width must be reduced to maintain a 100 Ohm characteristic impedance when the frequency is increased from DC to 1 GHz. Depending on the signal spectrum, a conductor width between 0.0403 mm and 0.0274 mm should be chosen if the dielectric thickness is 0.10 mm.

In general, differential impedance is increased when:

the separation between signal lines is increased,

the separation between signal lines and ground is increased, or

the dimensions of the conductors are reduced.

Having determined the values of width and th to obtain 100 Ohm at 1GHz, each of these cases can be investigated further. As an example, for each case, it is simple to determine how the differential characteristic impedance varies with frequency by sweeping the analysis frequency from 10MHz to 10GHz and plotting the value of Zdiff. The variation of Zdiff with frequency is plotted in Figure 4.

From the values plotted in Figure 4, the value of Zdiff at 100MHz, 300MHz, 1GHz and 3GHz are as follows:

The magnitude of the characteristic impedance is reduced with increases in frequency due to the skin effect. In the example above, the characteristic impedance is reduced by 2 to 4 Ohms when frequency (f) increases from 100 MHz to 3 GHz. This may not seem like much but most available tools will only provide the very high frequency limit (one value) and argue they have a 4-digit accuracy.

The reason for the reduction of characteristic impedance is simple. As the skin effect pushes current towards the conductor surface and the proximity effect accumulates return currents under the signal line, inductance is reduced and resistance is gradually increased (proportionally to sqrt(f)). Thus, the reduction in characteristic impedance can be determined by noticing the numerator of the characteristic impedance formula grows slower with frequency than the denominator. Both terms of the numerator (R and 2*pi*f*L) are growing slower than frequency whereas both terms of the denominator (G and 2*pi*f*C) are proportional to f (assuming a constant loss tangent).

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