Non-invasive Stability Measurement

Non-Invasive Stability Measurement

What is NISM? (Technical Details)

The Non-Invasive Stability Measurement (‘NISM’) is a stability margin measurement method based on the complex output impedance and group delay of closed-loop Device Under Test (DUT). Rather than assessing phase or gain margin, NISM utilizes Stability Margin (See Nyquist related reference below); a more accurate relative assessment for control loop stability. The Stability Margin result is reported as a phase margin equivalent value for a 2nd order system.

The mathematical relationship that allows the precise determination of the control loop stability from output impedance data was developed by Steven M. Sandler of Picotest (See References below). The mathematical solution is based on minor loop gain theory, which makes it equally applicable to measuring the stability of passive input filters, VRM (Voltage Regulator Module), linear and LDO regulators, and switching converters of all types (i.e., Middlebrook stability criteria). It is especially useful, and often the only accurate measurement technique for control loops that cannot be broken and assessed with the traditional Bode plot (e.g., fixed linear regulators, regulators with multiple internal loops, non-linear or time variant, high bandwidth opamp circuits, etc.). Another advantage is that the test can, and in fact, should be made in-circuit, with all applicable impedance loading.

The correlation between phase margin and the impedance-peaking (Q) in the closed-loop output impedance is used to derive the phase margin of the control loop from one closed-loop output impedance measurement by measuring the 𝑄 of an insufficiently damped closed-loop system. A very sensitive way to measure the quality factor 𝑄 is via the group delay (Tg) represented as the phase slope at resonance. The higher the 𝑄, the sharper the phase-turn, respectively the higher the slope of phase at resonance. Group delay 𝑇𝑔=−𝑑φ 𝑑𝜔 is then transformed to a form of 𝑄. The phase margin is then computed from the maximum value of the measured 𝑄(𝑇𝑔) curve close to the loop-crossover frequency respectively close to the peak in output impedance.

The assessment proceeds by recording the impedance and group delay 𝑄(𝑇𝑔) at the circuit point of interest. For regulators, this is at the output of the regulator close to the sense location. . The frequency of the impedance peak, the 𝑄(𝑇𝑔) peak value, and the 𝑄(𝑇𝑔) peak frequency are fed into the mathematical transform which returns the equivalent phase margin. The assessment is akin to evaluating the small-signal transient step load response and assessing the step load related 𝑄, except the NISM assessment is performed in the frequency domain.

A huge benefit of the measurement is that because it is based on impedance, it can be measured ‘in-situ’ with a simple probe measurement and non-invasively, that is without impacting the result. In cases where loop breakage is possible, NISM can confirm the validity of the Bode plot stability margin.

Picotest has published many articles and application notes since we introduced the method. NISM has proven to be a popular and simple technique for determining the stability of voltage references, linear and switching regulators, opamps, class D switching amplifiers, and input filters.

Is The Non-Invasive Stability Measurement As Accurate as a Bode Plot?

Yes. In fact, it’s as accurate in cases where Bode plots are valid and less subject to some of the issues that plague Bode Plot’s accuracy. It's Proven. As noted in this introductory article, “New Technique for Non-Invasive Testing of Regulator Stability”, phase margin can be determined from an output impedance measurement on a VNA, which is then converted to group delay. This is because the phase margin is related to the Q factor and through the group delay information a conversion can be made to phase margin.

NISM VS. BODE PLOTS - A PowerPoint presentation comparing Non-Invasive Stability Measurement (‘NISM’) with traditional Bode Plots. (Adobe PDF)
Companies are focused on Bode plots as the only stability criteria. Yet there are cases where this data is not accessible and/or where it does not provide a relative stability assessment. In these cases, NISM may be the only option and in other cases it provides a better overall assessment than a Bode plot. This presentation provides proof of the accuracy of the NISM testing technique by way of example.

If you would like to find out more on this method please download the videos and application notes listed below.

Reference Material

Videos

Application Notes