Measurement of loop gain with the digital modulator

A General Framework for Automated Tuning of Digital Controllers in Multi-phase Dc-Dc Converters

“…Real-time system identification [25], [26], is used here due to its immunity to parameter uncertainty. The authors have set forth a system identification technique that enables the real-time parameter estimation in situ (in-place), without requiring expensive external test equipments such as network analyzer [26].…”

Closed-loop performance comparisons of switching regulators with current-injected control

“…The open-loop gain expression can be determined by substituting a test vector y es) for the state vector X es) in Equation 4, and combining this with Equation 3 resulting in a set of transfer function s (10) The open-loop gain of each individual loop corresponds to a diagonal element of the matrix formed in Equation 10. For a two-loop system the corresponding open-loop gains are G1(s) H 1 (s) X 1 (s) /V 1 (s) and G2(s) H2(s) � X2(s) /V2(s) .…”

“…All open-loop measurements presented in this paper were taken in the common path, after the comparator, using digital modulation techniques [10] .…”

“…By subst ituting Equations 7a and 7b into Equation 10, it can be shown for the current injected-controlled buck regulator circuit of Figure 2, that after summing the individual loop gains …”

Reconsideration of loop gain measurement of DC/DC converters

“…However, this method will yield erroneous measurement result if the perturbation signal at the point where the loop gain is measured contains a pulsating nature [3], [8]- [11]. To overcome this problem, the PSPM, which perturbs the duty cycle signal, is proposed [9]. The PSPM injects a pulse-width perturbation signal to perturb the duty cycle signal, and the perturbed duty cycle signal and the response duty cycle signal are measured by the FRA to obtain the loop gain.…”