# The Role of a Decoupling, Inductance, and Resistance in a PDN

*You might want to add one of these components to your decoupling network*

In a previous article, we looked at the role of decoupling capacitors, as well as the difference between decoupling and bypassing. A decoupling capacitor provides the same functions as a bypass capacitor, but it also provides another important function in that it compensates changes in the ground potential as an IC switches.

There is another important point involved in designing your PDN to ensure power integrity. This is the role of inductance when designing your PDN. In high speed designs (which is every design nowadays), the decoupling network is generally purely capacitive, until you start looking at sufficiently high frequencies. Now there is inductance that can produce a large transient response in the PDN. This brings up two questions:

- Since power on a PDN can exhibit some transient response with inductance, can we make sure the response is critically damped?
- If the answer to #1 is "No," can we ensure the voltage disturbance due to current drawn into the PDN is minimized?

The answer to #1 is "Yes," but as we'll see, going the route of #2 is more practical and is standard practice in the industry. As we'll see, making an attempt at #1 gives us a chance to learn plenty about real capacitors, inductance in a PDN, and what is decoupling.

## The Goal of a PDN Decoupling Network

Designing a decoupling network is not a simple task. With lower frequency circuits, using a decoupling capacitor was sufficient for decoupling. The self-resonance frequency of many smaller capacitors was still somewhat higher than the knee frequency for many logic families, thus it would be difficult to drive a power bus to resonance during switching. Furthermore, decoupling capacitors would also act as a bypass capacitor to compensate potential changes as ICs switched.

With faster logic families, knee frequencies can now coincide with the self-resonance frequency of the equivalent circuit formed by the bypass/decoupling capacitor, the power supply bus, any nearby bypass/decoupling capacitors, conductors that connect components, and the components themselves. This creates the potential for ringing in the power bus with high speed circuits as logic gates switch. Under repeated switching, this would cause a driven resonant oscillation in the power bus with high amplitude. Just as was the case with ground bounce, a single switching output on an IC may not have much of an effect, but many components switching simultaneously can produce significant ringing in the power bus and large changes in the voltage level seen across an IC's power pins.

For this reason, inductance in a PDN is seen as a bad thing: it creates higher impedance throughout the PDN's impedance spectrum beyond a particular frequency limit. High broadband impedance is bad for broadband digital signals as these signals will transform the transient current into a larger voltage throughout the signal bandwidth. At high current draw, ringing in a power bus can exceed tolerances on core voltage levels near one of the resonance frequencies in the PDN. There are some guidelines that suggest adding an inductor, capacitor, and sometimes a resistor to bring ringing within limits. It's worth looking at exactly how inductance affects the power bus and ringing, and what a "critically damped" PDN might look like.

## Suppressing PDN Ringing With a Decoupling Network

As discussed in the previous article, the equivalent RLC model for the decoupling capacitor may be underdamped, and you can try to bring this circuit as close to the critically damped case as possible. However, you will need to consider the entire equivalent circuit for the decoupling capacitor and the rest of the system.

Ideally, you want to suppress ringing in a few ways:

- Critically damp or overdamp the response on the power bus. This is rather simple as it requires adding some passives (inductor, resistor, or both) to modify the conditions for resonance.
- Add components that shift the resonance frequency in any portion of the circuit to values that are outside the power spectrum for the switching signal. The savvy reader will probably notice that this is just a restatement of point #1
- Add more capacitors with different resonant frequencies in parallel to try and smooth out the entire PDN impedance spectrum. The overlapping low impedance portions should combine to give a sufficiently low impedance throughout the signal bandwidth.

#1 and #2 might be okay for an analog PDN as you should only care about what happens within a very narrow bandwidth. #3 is more important for digital components, which have broad bandwidth.

### The Damping Perspective

These three methods are somewhat mutually exclusive. Adding an inductor in series between the decoupling capacitor and an IC will increase the impedance seen by any high frequency signals (including a ringing signal) propagating towards the load, but it will also decrease the resonance frequency. Additionally, it will decrease the damping constant by a greater level since the resonance frequency is only inversely proportional to the square root of inductance. Therefore, if the response from the decoupling capacitor is already overdamped, adding a series inductor between the decoupling capacitor and the load can bring the response closer to critical damping.

If the response seen on the power rail is already underdamped, then you need to increase the damping constant and decrease the ringing amplitude. One simple way is to use a capacitor with larger equivalent series resistance (ESR). Note that electrolytic capacitors tend to have larger ESR values. The other option is to add a resistor and inductor before the relevant IC, as shown in the circuit below:

*Full decoupling network with a bypass capacitor*

Note that L in the above model is equal to the inductance of the conductor (e.g., power plane inductance) leading to the load plus the value of the decoupling inductor. The damping constant in the equivalent RLC network formed by the load, decoupling capacitor, L, and R is equal to the usual value for an RLC series circuit. Adding the inductor decreases the natural resonance frequency, while adding a small resistor R can increase damping in the circuit. When R is equal to the critical value shown above, then the transient response in this circuit will be critically damped.

Resistors are great for adding damping. Unfortunately, you lose power, so a resistor is only good when it has a low value so that it does not drop too much voltage. An alternative way to look at damping would take out the resistor and just consider the decoupling/bypass capacitance with any inductance between these and the load.

### An Alternative Decoupling Network

The network shown above will increase the DC voltage drop throughout the PDN, thus there is an alternative decoupling network that provides the critical damping:

*Alternative decoupling network with a bypass capacitor*

These equations tell you what the limits are on the bypass and decoupling capacitances for given ESR, ESL, and L values, which will give you critical damping. Note that L is not necessarily a real inductor; we could be looking at the inductance of the power rail.

In this network, the critical resistance is the same as that shown in the earlier network. However, there is also a restriction on the values of the decoupling and bypass capacitors (shown above). Increasing the damping resistance between the limits shown above will cause the response to move into the overdamped regime, thus slowing down the overall response from the decoupling capacitor.

## Final Thoughts on PDN Impedance

It's important to remember the role of inductance in any PDN, whether it's a parasitic element or it's intentionally placed. The circuit viewpoint states that a bypass capacitor placed between the power and ground pins on the load will provide a low impedance path to ground for high frequencies, basically lowering the overall PDN impedance below the capacitor's self-resonance frequency and making the PDN look like a low-pass filter. Inductance is counter productive and eventually turns the impedance purely inductive.

This should illustrate the point of placing decoupling capacitors on the PDN along with bypass capacitors near large ICs. The decoupling capacitors provide a set of low-impedance elements in parallel, with the goal of creating an overall low impedance in the PDN.

When designing a PDN for your PCB, you’ll need the layout and simulation tools in Altium Designer to ensure your board is free from power integrity and signal integrity problems. Using circuit simulations will help you qualify your component selection and layout, as well as allow you to visualize electrical behavior in the PDN during a transient event.

Contact us or download a free trial if you’re interested in learning more about Altium Designer. You’ll have access to the industry’s best routing, layout, and simulation tools. Talk to an Altium expert today to learn more.