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32 DESIGN007 MAGAZINE I FEBRUARY 2020 equivalent series capacitance, or Cs (low- er left); and equivalent series inductance, or Ls (lower right). The logarithmic horizontal scale starts at 300 Hz and ends at 30 MHz. For this DUT, the 70-Hz IFBW setting provides a good compromise between fast sweep and low noise floor. The measurement result shows several fa- miliar details. From 300 Hz to almost 1 MHz, the impedance magnitude slopes downward, indicating capacitive impedance. The trace bottoms out at 850 kHz with a 2-mOhm value at the series resonance frequency. Beyond 850 kHz, the impedance magnitude slopes upward, indicating that we are in the inductive region. There are smaller secondary resonances and inflection points between 1.5 and 3 MHz, be- yond which the impedance stays clearly induc- tive. The effective series resistance plot, which is simply the real part of the measured com- plex impedance, on the upper right follows a similar pattern. At low frequencies, it runs par- allel to the impedance magnitude curve, and their ratio is the dielectric loss tangent [9] . Af- ter a broad minimum near the series resonance frequency, the effective resistance also trends upward with a few secondary resonances. On the lower left and right plots, you see the ca- pacitance and inductance extracted from the imaginary part of the measured complex im- pedance. With the data shown in Figure 6, we get pos- itive extracted capacitance and negative in- ductance (that we just ignore) below 850 kHz. Above 850 kHz, we get positive inductance and negative capacitance (which, again, you just ignore). Finally, if we look at the extract- ed capacitance and inductance curves, we no- tice that both are sloping downward slightly. The capacitance curve slopes downward due Figure 6: Measurement data of the 47-µF 1210 size ceramic multilayer capacitor taken in the co-planar fixture.