Implementing a system-level power design can be a time-consuming process, even when the design solution relies on off-the-shelf power supplies. Though they're sometimes viewed as black boxes with inputs and outputs, power supplies internally rely on feedback. So, they must be treated as control systems. The stability of these systems is additionally affected by external factors such as load and noise variations.

Designing-in a power supply often requires that someone, either the systems or the power-supply designer, perform a lengthy stability analysis. Power-supply operation must be evaluated for various load conditions. Unfortunately, performing such analysis with the traditional Bode-plot approach is an iterative process that can take weeks or even months to complete.

The use of safe-operating-area curves offers a simpler, quicker method of stability analysis. However, it's in-tended only for loads that are essentially capacitive and cannot be used with the more complex loads that are becoming more common. Yet as loads become more complex, stability analysis for power supplies becomes even more important to ensure a regulated output.

By developing a graphical analysis tool known as the Young Stability Curve (YSC), Lu-cent Technologies of Murray Hill, N.J., has addressed the analysis challenge. Named for Chris Young, the team leader of the Bell Labs group that developed the tool, the YSC lets board-level designers quickly and accurately determine whether a given power converter is stability-compatible with the intended load.

"Not only does the Young Curve help you design a particular power supply into your system," Young explains, "it also helps you determine the best power supply in terms of stability, output impedance, crossover frequency, regulation, and audio susceptibility."

Stability analysis with this method begins with two sets of YSCs generated by the power-supply vendor. These YSCs depict the magnitude and phase response of the power supply for given values of phase margin *(see the figure)*. To determine load stability, designers plot their load-impedance magnitude on the first set of curves *(step 1 in the figure)* and the load-impedance phase on the second set *(step 2)*.

Designers locate the point where their load-impedance magnitude intersects with the YSC magnitude, a point that represents the system's crossover frequency *(step 3)*. Looking at the second set of curves, designers locate the point at which the load-impedance phase and the YSC phase intersect at the crossover frequency *(step 4)*. The value of phase at that point is the phase margin, a key measure of system stability, for the selected load *(step 5)*. A rule of thumb is that the phase margin must be at least 45° to assure stability.

The YSC method is expected to sharply reduce the time required for stability analysis of power supplies and power systems. According to Young, analysis with the YSC technique takes from about half a week to a week and a half. That's roughly a quarter of the time required to perform stability analysis in-house using existing methods. More time, perhaps up to 14 weeks, is usually required if the power-supply customer cannot do the analysis and relies on the power-supply vendor.

The basis for the YSC technique is a control loop model that reduces power-supply modeling to just two parameters. One is Z_{OL}, the ability of the power supply to provide voltage and current. The other is AB, the supply's ability to increase or decrease the output power. When Z_{L}, the load impedance, is known, it becomes possible to characterize loop gain as:

When compared against measured results, the phase results generated by this model were accurate to within 1°.

With this control model in hand, Young's group then took advantage of the fact that stability analysis is centered around unity gain or zero phase shift. From this concept, the team derived the following equation:

where G = gain = 1 and Θ = phase margin. In equation two, the stability and power-supply parameters are separated from load information. From this equation, the load-independent YSCs shown in the figure were generated by plotting the information on the right-hand side of this equation for every 15° of phase margin. By plotting the load impedance on top of these curves, it's possible to quickly determine both the phase margin of the system and its bandwidth.

The company has created YSCs for its more popular power supplies. Lucent plans to offer YSCs along with future product introductions. For more about the Young Stability Curve and a list of YSC-characterized power supplies, go to *http://power.lucent.com/stability*.