# The Role of a Decoupling Inductor and Resistor 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 for analog supplies. 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, but it can include some inductance for an analog design in order to damp the transient response in the analog PDN.

## The Goal of a Decoupling Network

Designing a decoupling network is not a simple task. With lower frequency circuits (i.e., analog signals with frequencies of less than ~50 MHz), 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 outputs switching simultaneously can produce significant ringing in the power bus and large changes in the potential seen by an IC.

For this reason, inductance in the digital section of a PDN is seen as a bad thing: it leads to higher inductance 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. Ringing in a power bus can reach ~1 V levels near one of the resonance frequencies in the circuit when high current is being drawn into the PDN. For analog decoupling networks, a decoupling inductor, capacitor, and sometimes a resistor can be used together if ringing in the power bus is severe.

## Suppressing Analog 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 should 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 this ringing in one of two ways. First, you can critically damp the response at the power bus. This is rather simple as it requires adding a decoupling inductor, resistor, or both to your PDN. Second, you can try to add components that shift the resonance frequency in any portion of the circuit to values that are much higher than the knee frequency for the switching signal.

Both 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.

## 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*

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

It's important to remember the role of inductance in any PDN, whether it's a parasitic element or it's intentionally placed. 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 turning the analog PDN into a low-pass filter below the capacitor's self-resonance frequency. Inductance combats this and eventually turns the impedance purely inductive.

You should also not use a decoupling capacitor with a series inductor/resistor for every single IC on your PCB. Instead, you should worry about placing the capacitor on the supply output for your analog supplies, which will then feed multiple ICs in your design.

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.