**Design**

As a result, the importance and mechanisms of impedance (herein the meaning of PCB trace impedance – typically referred to as “characteristic impedance”) for signal integrity have been widely discussed and seem to be generally understood by PCB designers.

Simply put, PCB trace impedance is a measure of the resistance that a circuit opposes to a current once a voltage is applied. So far so good. But the concept of impedance is also used in PCB design to describe the behavior of power distribution systems/power distribution networks (PDS/PDN). And this PDN impedance is becoming more of a headache for PCB designers as IC vendors define increasingly tight so-called “target impedance limits” that a design must meet (a few milliohms over a broad frequency range).

Are you sure what the term PDN impedance means for you and what to pay attention to when designing a PDN? Let’s look at what PDN impedance and target impedance are and take a stab at explaining their importance for the design of modern high-speed digital boards.

The theory of electronics plays an elementary role in analyzing impedance issues, just to mention here Ohm’s law, Kirchhoff’s laws, and for inductance, Faraday’s laws. But even without diving in deeply, design engineers know that for board traces the characteristic impedance “Z0” is directly related (lossless case here, for simplicity) to the trace inductance (L) and the trace capacitance (C), or in formula definition:

For closely coupled traces and trace geometries with etching and copper roughness impact, however, such a prediction can become complicated. Design engineers should always keep in mind the relationship between capacitance and impedance is somehow inverse, which means if “C” increases, “Z0” decreases and vice versa. But how does this apply to power distribution systems?

Power distribution systems typically comprise a combination of larger (and/or smaller) copper areas together with power traces, PDN vias, and many small connection stubs to carry energy from the power sources (bucket converters, VRMs, or PMICs) to the active circuits (ICs) – with some discrete components (capacitors, resistors, inductors) in between. How and where does impedance come into play?

As clock and data frequencies increase and high-speed boards become densely populated with increasingly power-demanding integrated circuits (pin counts rising to over 1,000), ensuring a noise-free power distribution from the source to the sinks becomes a major challenge for the design engineer.

Typically, many IC buffers on a board simultaneously change their state. These fast-switching devices cause ripple voltages that propagate through the entire power distribution network and create noise peaks. These vary in frequency and location on the board. As we learned in school, energy will never just disappear. Therefore, the noise (= energy) can easily disturb any surrounding high-speed devices and circuits. Ripple voltages can also be strong EMI sources, creating high-impact parasitic EMI antennas through conductive coupling.

In switching mode, where there are voltages and current flows, the ratio between these two values forms the impedance of a PDN, like the simplified one in FIGURE 1. For the sake of simplification, only the plate capacitance of the planes is shown, just as not all different inductances are included in the figure either.

One approach to ensuring the proper operation of high-speed systems while maintaining the required performance is to control the power delivery network impedance over a certain frequency range (FDTIM = frequency domain target impedance method). This can be achieved by carefully designing the structure of the power distribution network and accounting for the total PDN capacitance and all various inductances. The overall capacitance number goes beyond the plate capacitance of the power-ground overlap areas and includes bulk capacitance of the large capacitors, all the decoupling capacitance and, at the end, the embedded capacitance within the IC packages and IC die itself.

The most straightforward approach to explain the impedance of a PDN is:

The impedance is affected by the physical separation within the power rail in the board stackup. As frequencies increase, the mutual inductance between the different circuits on the board cause the impedance of the power distribution network to increase. Due to various effects, the impedance of such a structure shows many peaks (resonances and anti-resonances). At higher frequencies, the impedance often negatively influences the input behavior of the ICs, which is highly undesirable, especially in the frequency range in which the ICs are supposed to operate.

Figure 1. Simplified schematic structure of a PDNX.

The knowledge and control of the target impedance have become a standard approach for proper PDN design, especially when designers must meet the given IC vendor or application specs. A target impedance, by definition, sets a limit on the highest impedance the power rail on the die may be exposed to in its connection to the PDN.

Different formula approaches, all based on Ohm’s law, state that the ratio of voltage to current results in the resistance (= impedance). For a PDN, the voltage in these formulas is the supply voltage in relation to the maximum ripple ([D]V) on the power supply, which ICs are allowed to accept. (IC vendors have this information.) In its simplest form, the target impedance can be described as:

The impedance waveform of a power delivery network should ideally be without larger peaks within the frequency band in which the ICs operate. This is the fundamental guiding principle in the target-impedance-based design approach of PDNs. Another matter of concern is the relevant bandwidth. For digital signals, the bandwidth comprises all frequencies between the clock and the knee point on a frequency curve, which can in a rule-of-thumb approach be defined as 0.35 divided by the fastest signal transient rise/fall time.

If all the harmonics of digital signal resonate at the same frequency, the transfer function for the return signal in a ground plane is rather flat, which is what we are looking for. For a really complex PDN, every occurring impedance peak is created by a parallel RLC circuit. The characterizing terms for such impedance peaks are:

- Parallel resonant frequency
- Characteristic impedance (and the q-factor, not discussed here)
- Peak impedance.

The parallel resonant frequency defines the frequency at which the inductive reactance equals the capacitive reactance. This frequency point can be calculated from:

When a transient voltage occurs at the resonant frequency of the peak, the amplitude of the resulting voltage swing may exceed the nominal voltage given by the target impedance equation. To further complicate the matter, often there are further impedance peaks (multiple resonances and anti-resonances) over a wider frequency range to deal with.

Not every peak that exceeds the target value means the system is not working. However, the peaks could lead to non-deterministic IC power failures during system operation. This opens a Pandora’s box for debugging such hardware failures. But even if the peak stays below the impedance limits, the circuit may not be perfectly safe, so countermeasures may be required to lower the impedance or shift occurring peaks in frequency.

To lower the impedance of the PDN, engineers can tweak two general things: reducing the inductance and/or increasing the capacitance of the PDN. The placement and value of decoupling capacitors play an important role in such an optimization, as this will affect both the capacitance and the inductance of the PDN. Placing the capacitors on the same layer as the IC supply pins, for example, minimizes the inductance. Unfortunately, this is often not possible for space or manufacturing reasons. Nevertheless, if resonance peaks are revealed in a PI analysis, the copper shapes of the PDN most likely must be modified to eliminate these peaks efficiently.

Unfortunately, given the complexity of today’s PDNs and all the parasitic effects, analyzing a circuit layout for PDN impedance can hardly be done with a good old pen and a sheet of paper. Furthermore, PCB CAD tools cannot handle target impedance issues simply by defining a design rule or adding an attribute to a power supply network, even if this is desirable for the design engineer.

If such an analysis reveals resonance peaks in a PDN exceeding the target impedance, corrections can be engineered in a virtual sandbox through the parametric study capabilities of some ECAD tools. Such corrections, for instance, include adding virtual decaps, changing values and ESL of the capacitors, or even turning them off without the need for physical design changes in the tool.

As a final reminder, digital engineers should always keep in mind the situation is often worse than initially thought (Murphy’s law). Power integrity issues such as impedance resonance peaks negatively influence the signal integrity behavior of boards, and in their nature as a (rather very large from the physical size of the structure) LC-resonator, a noisy PDN can easily become a strong parasitic EMI antenna. This underlines the importance to keep the PDN impedance number under control.

**Ed.:** The original publication displayed an incorrect formula for the impedance of a PDN. We regret any confusion.

- Eric Bogatin,
*Signal and Power Integrity Simplified*, 2009.