Corner frequency measurement

As expected, the corner frequency shifts from = 30 kHz (vertical) to = 300 kHz (coplanar). The effect of the stray capacitance is visible in the measured spectrum for the vertical configuration where a pole at 1 MHz is visible (corresponding to a Qj = 130 pF, due to large couplings through the silicon substrate and to the long metal tracks below the passivation, but still negligible with respect to = 6 nF). 

If the electrode size and material let the frequency range to cover the whole electrode details in the impedance spectrum, the measured impedance amplitude versus frequency would look like seen in Fig. 5.13. The values for Rs, Rpw and Chw can be read off and calculated from the saturation values and corner frequencies as marked in the figure. 

In Fig. 12.166 sphere and CDE calculations are compared with measurements on MgO cubes well dispersed in KBr neither is very satisfactory. The calculated position of peak absorption by spheres is fairly close to that measured but not coincident with it the CDE calculations show appreciable absorption over approximately the same frequency range as the measurements but no structure. If the optical constants we have used accurately place the Frohlich frequency, Fig. 12.166 suggests that neither spheres nor a broad distribution of shapes are good approximations for MgO particles. This is hardly surprising because electron micrographs reveal that MgO smoke is composed of cubes. These cubes are so nearly perfect that they have been used to quickly determine the resolution of electron microscopes degraded resolution results in apparently rounded corners. 

Noise and vibration measurements are made with microphones and accelerometers. Sometimes, sophisticated instruments like laser vibrometers are used for NVH work. Common noise fixes include cutting slots and/or chamfers on the brake pads and linings, the application of constrained layer damping noise insulators to the back of the brake pad shoe plates, and detuning the resonant frequency of mechanical brake corner components. 

The maximal deviation is 6 mO. (equals 9% at this frequency), whereas the largest relative deviation of the impedance magnitude is at 14%. The reason for the curves drastically different patterns is the vast acquisition range the impedance magnitude is measured in. On the graph in the bottom left corner of Fig. 7 you can see the simulative impedance/phase plot and the average value curves of the measured results for all measurement equipment. The smallest impedance is 1 mQ at 1 kHz and the maximal deviation of 14% refers to an absolute value of 140 pQ. 

We can determine these corners analytically if we assume a particular functional dependence and make measurements at two or more frequencies, and manipulate the measured values much like we did for the AC signal with Equations 10.11a and 10.11b. 

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