The ε_{r
}as recalculated and the results are shown below in Figure 4.

Figure 4

Figure 4 shows that the measured ε_{r
}still varies with both frequency and sample size, but the curves of the two larger samples now coincide at 10 to 100 MHz. The curve of the
smallest (1 cm^{2} ) sample has moved considerably from the other three and it is obvious that this sample is too
small for accurate results. A closer examination shows that the 4 cm^{2}
sample is also inadequate and it is not until the sample size reaches 16 cm^{2}
that a reasonably smooth curve is produced. If the smallest sample is ignored, the minimum spread is now 1.3% at 5 MHz.

The next problem was to find the actual ε_{r
}from the recalculated data. The text books tell us that the phase shift across a capacitor is 90^{0}, so the
measurements were repeated at ten degree phase intervals. The results were again calculated with Formula 4 and are shown below in Figure 5.

Figure 5.

If the smallest sample is again ignored, the minimum spread is now 0.85% at 90^{0}. We are now in the right ball
park area for measurement accuracy and a check is warranted.

PCB-D

This has one circular sample 16 cm^{2 }on the top, and a mirrored ground
plane on the bottom. The VNA was calibrated and the phase length of the semi rigid cable was removed from the test by performing a port extension. The
capacitance at 90^{0 }was measured at the capacitor centre and the ε_{r
}calculated at 4.254 using the circular capacitor method.

PCB-E

This PCB was manufactured from the same sheet as PCB-D in order to obtain a similar ε_{r}.
This has a calculated 50Ω microstrip transmission line and the PCB fits into a FLEXI-BOX for the measurement. The track width was calculated at 2.87
mm using the microstrip calculator. This calculator was later updated and
now indicates 2.861 mm for a 50Ω microstrip. However, the results for the 2.87 mm track are excellent and are shown below in Figures 6&7.

Figure 6

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