Tantalum capacitors provide high capacitance for a given size though they have higher ESL than ceramic and are, therefore, not the optimum choice for high frequency decoupling.  The common solution is to parallel tantalum capacitors for bulk capacitance and ceramic for high frequency decoupling.  A popular rule of thumb is to parallel ceramic capacitors of different values, such as 0.1 uF, 0.01 uF and 0.001 uF to provide wideband decoupling.  In theory, this sounds like an ideal solution but in practice, it can lead to disastrous results. 

Table 1 lists lists the four cases we will use to evaluate capacitor performance. The capacitors picked are arbitrary, but the math and general solution is independent of the specific capacitors.  The ESL and ESR of the 470 uF capacitor are measured using the OMICRON Lab Bode 100 in conjunction with the OMICRON Lab B-SMC impedance adapter.  These are low cost general purpose tools that perform gain-phase as well as impedance measurement. Fig. 1. shows the setup for the 470 µF capacitor impedance measurement.

Fig. 1. 470 µF tantalum capacitor is installed in the B-SMC impedance adapter for measurement.

Fig. 2. 470 µF tantalum capacitor impedance curves showing the ESR and ESL at 5MHz.

The 470 µF tantalum capacitor ESR and ESL at 5MHz are 41.9mΩ and 4.62nH respectively as seen in Fig. 2. Using the same setup, the ESR and ESL of the ceramic capacitor are measured to be 15.9mΩ and 1.29nH, respectively (Fig. 3).

Fig. 3. 0.1 µF Ceramic capacitor ESR and ESL measurement.  The ESL is determined from the 14MHz series resonance or from the impedance at 40 MHz.  Either calculation results in 1.29 nH.