It is not possible to remove fringing capacitance, but the resultant phase shift can be modeled as a function of frequency using C0 through C3 (C0 +Cl x f + C2 x f2 + C3 x f3,with units of F(Hz), C0(fF), C1(10-27F/Hz), C2(10-36F/Hz2) and C3(10-45F/Hz3), which are the coefficients for a cubic polynomial that best fits the actual capacitance of the “open.”
A number of methods can be used to determine the fringing capacitance of an “open.” Three tech- niques, described here, involve a calibrated reflec- tion coefficient measurement of an open standard and subsequent calculation of the effective capaci- tance. The value of fringing capacitance can be cal- culated from the measured phase or reactance as a function of frequency as follows.
Ceff = | tan( | ∆∅ | ) | = | 1 |
2 |
| | | 2πfX |
| 2πfZ0 |
Ceff – effective capacitance ∆∅ – measured phase shift f – measurement frequency F – farad
Z0 – characteristic impedance X – measured reactance
This equation assumes a zero-length open. When using an offset open the offset delay must be backed-out of the measured phase shift to obtain good C0 through C3 coefficients.
This capacitance can then be modeled by choosing coefficients to best fit the measured response when measured by either method 3 or 4 below.
1.Fully calibrated 1-Port–Establish a calibrated reference plane using three independent standards (that is, 2 sets of banded offset shorts and load). Measure the phase response of the open and solve for the capacitance function.
2.TRL 2-PORT–When transmission lines standards are available, this method can be used for a com- plete 2-port calibration. With error-correction applied the capacitance of the open can be meas- ured directly.
3.Gating–Use time domain gating to correct the measured response of the open by isolating the reflection due to the open from the source match reflection and signal path leakage (directivity). Figure 3 shows the time domain response of the open at the end of an airline. Measure the gated phase response of the open at the end of an airline and again solve for the capacitance function.