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Examine the inductive nature of voltage-control loops

27 Feb 2015  | Steve Sandler

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The regulator impedance can, therefore, be represented by three terms as:

Equation 10

The relationship between load current and the effective inductance can be seen by substituting for Equation 1 for Rj.

Equation 11

Using the example of figure 1, with S=628 radians/sec (100Hz) and G=5000, the simulated output impedance is shown for three different output currents in figure 3.

Figure 3: Closed-loop output impedance for three different load currents, illustrating the load current dependency. As the dynamic junction resistance gets small compared with Ro the current dependency is greatly reduced, as seen here. The +6dB/octave region confirms the inductive nature of the closed loop.

The impedance calculated using the exact solution of Equation 4 and the impedance calculated using the partial fraction result of Equation 4 are plotted together in figure 4, which confirms that the two solutions are equivalent.

Figure 4: The result of Equation 4 (red solid trace) and the partial fraction result of Equation 10 (blue dotted trace) confirm the equality of the two equations.

Output impedance measurements, performed on a voltage reference at two different currents, are shown in figure 5. These measures results clearly show the three impedance regions, as well as the sensitivity to operating current.

Figure 5: Voltage reference output impedance at two operating currents shows the sensitivity to output current and also shows the 3 distinctive impedance regions.

About the author
Steve Sandler is the founder and former CEO of Analytical Engineering Inc., the predecessor of AEi Systems. He has over 30 years experience in the design and analysis of power conversion equipment for military and space applications. Mr. Sandler is also the CEO of Picotest, a company that distributes test equipment including the Signal Injector product line designed for testing linear and switching power supplies.

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