In Part I (see [1]) we investigated two four-layer PCBs with the power- and ground-plane pairs spaced 3 mils (Case A), and 30 mils (Case B) apart, respectively. The boards were populated with decoupling capacitors of the *sam*e value (1nF), placed at three different distances from the measurement point, as shown in Figure 1.

The conclusion of the Part I study was that the location of the capacitors was more critical on a 30-mil board than it was on a 3-mil board, leading to the choice of 30-mil boards for the part II study, as described next.

**Part II Study**

In Part II we use the 30-mil boards and populate them with multiple capacitors of the same value (Cases 1C, 2C, 3C) as well as with the capacitors of *different* values, decades apart (Cases 4C, 5C, 6C). The location of the capacitors for all cases in this study is 1 inch away from the measurement point, as shown in Figure 2.

The cases shown in Figure 2 are summarized in Table 1.

**Measurement Results**

Figure 3 shows the measurement setup used in this study, (this is the same setup we used in Part I [1], the only difference being the capacitor values).

Case 1B vs Case 1C – no decoupling capacitors vs. one 1nF capacitor

Figure 4 shows the impedance measurement for Case 1B & Case 1C.

*
Observations:* In Region 1 (1 MHz – 136 MHz) Case 1C-PCB has a lower impedance (7.6 dB difference at 90 MHz). In Region 2 (136 MHz – 291 MHz) Case 1B-PCB has a lower impedance. In Region 3 (291 MHz – 445 MHz) Case 1C-PCB has a lower impedance again. Beyond the frequency of 445 MHz the capacitor has no impact on the impedance.

*Case 1C vs Case 2C – 1 nF cap vs. two 1nF caps*

Figure 5 shows the impedance measurements for Case 1C & Case 2C.

*
Observations:* The addition of the second 1 nF capacitor extends the Region 1 in frequency from 136 MHz (see Figure 4) to 173 MHz. It also lowers the impedance curve in that region – at 90 MHz the impedance is lowered from -30.5 dB to -35 dB. This is a very desirable result.

Region 2 (where the Case 1C PCB outperforms the Case 2C PCB) is shifted to the right and extends from 173 MHz to 317 MHz. Region 3 is also affected and extends now from 317 MHz to 409 MHz. Beyond the frequency of 409 MHz the capacitors have no impact on the impedance.

*Case 2C vs Case 3C – two 1 nF caps vs. four 1nF caps*

Figure 6 shows the impedance measurements for Case 2C & Case 3C.

*
Observations:* Increasing the number of 1 nF capacitor from two to four extends the Region 1 further in frequency from 173 MHz (see Figure 5) to 215 MHz. It also lowers the impedance curve in that region – at 90 MHz the impedance is lowered from -35 dB to -40.9 dB. Again, this is a very desirable result.

Region 2 (where the Case 2C PCB outperforms the Case 3C PCB) is shifted to the right and extends from 215 MHz to 339 MHz. Region 3 is also affected and extends now from 339 MHz to 457 MHz. Beyond the frequency of 457 MHz the capacitors have no impact on the impedance.

The major conclusion of this part of the study is that, in Region 1, increasing the number of capacitors of the same value lowers the impedance curve and extends its frequency range.

Next, let’s investigate the cases when we use multiple capacitors spaced decades apart in values.

*Case 2C vs Case 4C – two 1 nF caps vs. one 1nF cap & one 10 nF cap*

Figure 7 shows the impedance measurements for Case 2C & Case 4C.

*
Observations:* The impact of the two capacitors one decade apart (1 nF & 10 nF) on the impedance curve is quite profound. Region 1 (where the Case 4C PCB has lower impedance) is reduced in frequency and extends from 1MHz to 58 MHz. Region 2 (where the Case 2C PCB has lower impedance) increases in its span and extends from 58 MHz to 208 MHz.

*Case 2C vs Case 5C – two 1 nF caps vs. one 1nF cap & one 100 nF cap*

Figure 8 shows the impedance measurements for Case 2C & Case 5C.

*
Observations:* Using two capacitors two decades apart (1 nF & 100 nF) shifts the Region 1 upper frequency to the left, from 58 MHz (see Figure 7) to 49 MHz. Region 2 increases in its span and extends from 49 MHz (vs. 58 MHz) to 224 MHz (vs. 208 MHz).

Next, let’s compare the Cases 4C (1 nF & 10 nF) and 5C (1 nF and 100 nF) directly.

*Case 4C vs Case 5C – one 1nF cap & one 10 nF cap vs. one 1nF cap & one 100 nF cap*

Figure 9 shows the impedance measurements for Case 4C & Case 5C.

*
Observations:* Using two capacitors two decades apart (Case 5C) vs. two capacitors one decade apart (Case 4C) decreases the impedance in the low frequency range, i.e., Region 1 (1 MHz – 24 MHz). In Region 2 (24 MHz – 87 MHz), Case 4C PCB has lower impedance. Beyond the frequency of 87 MHz the impedance of both boards is virtually the same.

Finally, let’s compare a board with four capacitors of the same value (Case 3C: 4 x 1 nF) with the board with 3 capacitors decades apart in values (Case 6C: 1 nF, 10 nF, 100 nF).

*Case 3C vs Case 6C – four 1 nF caps vs. one 1nF cap & one 10 nF cap & one 100 nF cap*

Figure 10 shows the impedance measurements for Case 3C & Case 6C.

*Observations:* Using three capacitors decades apart (Case 6C) vs. four capacitors of the same value (Case 3C) decreases the impedance in the low frequency range, i.e., Region 1 (1 MHz – 57 MHz). In Region 2 (57 MHz – 215 MHz), Case 3C PCB has lower impedance. In Region 3 (215 MHz – 347 MHz) the Case 3C PCB has lower impedance. Beyond the frequency of 347 MHz the capacitors have no impact on the impedance.

**References**

- Bogdan Adamczyk and Jim Teune, “Impact of Decoupling Capacitors and Embedded Capacitance on Impedance of Power and Ground Planes – Part I”,
*In Compliance Magazine*, March 2020.