Local filtering in a single integrated circuit

Every PCB needs quite a few bypass capacitors to offset the inductance of the power lines. But each PCB actually only needs one ideal bypass capacitor to completely solve the power distribution problem.

Unfortunately, there is no ideal capacitor. Every individual capacitor has a certain amount of series lead inductance, L, and at very high frequencies, its impedance will rise, rather than fall. Whether lead inductance becomes a problem depends on the digital corner frequency, F, as shown below, and the impedance, X, that must be achieved.

We can calculate the highest effective frequency for a given bypass capacitor:

A properly sized capacitor is effective at frequencies between FPSW and Fbypass. Fortunately, there is a large gap between the two frequencies.

Example: The maximum effective frequency of the bypass capacitor

According to Example 8.1, assume that a 10UF capacitor has a series inductor of LC2=5NH. The XMAX we want to achieve is 0.1 ohm. Calculate its maximum effective frequency:

This capacitor is effective from 159KHZ to 3.18MHZ, a range of about 16:1.

A large bypass capacitor allows us to reach the frequency Fbypass. To ensure low impedance above Fbypass, another capacitor with a lower impedance is needed in series. The best way to get very low inductance is to connect many small capacitors in parallel. A parallel array of bypass capacitors can be spread around the printed circuit board.

There are three factors that will determine the impedance between power and ground:

At low frequencies, it depends on the inductance of the power supply lines
. At medium frequencies, it depends on the impedance of the board-level bypass capacitors.
At high frequencies, it depends on the impedance of the distributed capacitor array.

The next step is the process of designing the bypass capacitor array. Although this process is mostly similar to the procedures in "Inductance of Power Distribution Lines", the difference is that "Inductance of Power Distribution Lines" determined the inductance of the power line, but here you need to design and determine the series inductance of the local bypass capacitors.

1. We want the system to reach a frequency of FKNEE. To calculate the plant inductance tolerance at such a high frequency, see formula () for the definition of the corner frequency.

2. Find the series inductance LC3 of the bypass capacitors you plan to use. A surface mounted capacitor, along with a very short, wide via, has a typical series inductance of 1NH. A typical series inductance value for a plug-in bypass capacitor is 5NH. Use these values ​​to calculate the number of bypass capacitors needed to achieve the total target inductance.

3. Below the frequency F bypass, the total impedance of the capacitor array must be less than XMAX, and the total array capacitance is calculated from this.

4. Calculate the capacitance of each element in the array.

Example: Capacitor Array

We use 10UF bypass capacitor and 5NH series inductor, and we hope to get XMAX=0.1 ohm.

We need an array of 32 capacitors, each 0.016uF, with a series inductor of 5nH or less.