Since an exact theoretical solution for microstrip does not exist, we must attack the problem indirectly. Since we cannot simply compare an exact theoretical answer to the answer calculated by the analysis, we must look for some effect that Z₀ has on a known component. This component then becomes our impedance standard.

Assume we have a lumped (small with respect to wavelength) element that we can place in a microstrip line. Assume also that we know the impedance of that lumped element exactly. Then we measure the element using a calibration algorithm which requires a transmission line of known characteristic impedance. If the characteristic impedance of that line is in error by, say, 10%, then the measured value of that lumped element is also in error by 10%. Thus the error in Z₀ is equal to the error in the measured value of the lumped element.

The fundamental problem is that no matter what component we choose, there are fringing fields associated with that component. The fringing fields store inductive and capacitive energy, thus changing the apparent impedance of the impedance standard. If the fringing fields are uncontrolled, the so-called impedance standard is no longer a standard.

The key to creating an accurate microstrip impedance standard is to control the lumped element fringing field stray discontinuities, as shall be described in this section.

Note that this standard is focused on quantitative determination of only the error due to dispersion. Although it could easily be changed, this standard is intentionally insensitive to subsectioning error. Subsectioning error is treated in detail in previous chapters.

For the lumped "standard impedance" element, we select a capacitor connected in series in the center of a microstrip through line, see Figure 7. The capacitor dielectric extends across the entire substrate surface. Otherwise, this benchmark would be appropriate only for 3-D arbitrary analysis tools. The problem geometry, as given, is suitable for any 3-D planar tool which can handle two layers.

Figure 7. Side view of the Microstrip Standard, a series (DC blocking) capacitor. See text on control of fringing discontinuities.

Before we can use a series capacitor as a microstrip standard, we must first understand and control the fringing field discontinuities. There are two such discontinuities, shunt capacitance to ground and series inductance. The shunt capacitance to ground is almost entirely from the bottom plate of the capacitor. The top plate of the capacitor is shielded from ground by the bottom plate. Thus port 2, in Figure 7, has no capacitance to ground.

The series inductance is not so easily handled. That there is series inductance is easily understood. The current distribution across the width of the microstrip line is different from the current distribution across the width of the capacitor plate. When current flows from the line to the capacitor plate, transverse currents must flow in order to transition the current from that on the microstrip line to that on the capacitor plate. This transverse current is the series inductance, Figure 8.

Figure 8. Top view of the series capacitor showing conceptual current flow. As the current distribution transitions from that on the microstrip line to that on the capacitor, a transverse current must flow. This causes a series inductance.

With this understanding, we can do two things to counter the undesired effect of the series inductance. First, we can simply make the line width narrower. This makes the distance that the transverse currents flow shorter and the corresponding inductance smaller.

Second, we can make the capacitance smaller so that the capacitive reactance is much much larger than the inductive reactance. Effectively, both of these measures may be used to move the series LC resonant frequency up far above the desired measurement range leaving the frequency independent capacitor unchanged.

Note that whatever small effect is left from the series fringing inductance, it increases the apparent error by making the "frequency independent capacitor" appear to vary with frequency. Thus, the results of this benchmark should be treated as upper limits to the error of an analysis. The analysis could actually be better than results of this benchmark indicate to the degree that the series fringing inductance influences the capacitor.

Now we have one last assumption: The capacitor is frequency independent. This will be true if all the displacement current of the capacitor (i.e., electric field lines going from one plate to the other) all pass through material of the same dielectric constant and that dielectric constant is independent of frequency.

There is one more aspect of the geometry we can control to realize a good standard, substrate thickness. While we can move the series resonant frequency as high as possible, as described above, we can also move the dispersive frequencies as low as possible. This is done by making the substrate thick, effectively moving the dispersive frequencies much lower. While expensive to do in experimental work, it is just a few keystrokes on a computer.