Type III Compensator Design for Power Converters

Jan 1, 2011 12:00 PM
Liyu Cao Ametek Programmable Power

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Type II compensators are widely used in the control loops for power converters. However, there are cases where the phase lag of a power converter can approach 180 degrees, while the maximal phase from a type II compensator at any frequencies is at most zero degree. Thus in these cases, the type II compensator cannot provide enough phase margin to keep the loop stable, and this is where a type III compensator is needed. A type III compensator can have a phase plot going above zero degree at some frequencies, and therefore it can provide the required phase boost to maintain a reasonable phase margin.

Although the concept of the type III compensator has been around for years, an in-depth analysis on the compensator is not easy to find. There are some design procedures described in the literature [1,2,3,4]. However, these procedures are usually empirically derived, and the derivation processes are not provided, which make it difficult to follow and evaluate these procedures.

An analog implementation of type III compensators is shown in Fig. 1, where six passive circuit components are needed. The transfer function of the Type III compensator in Fig. 1. is given by:

Equations 1-6 Select figure to enlarge.

where C₁₂ is the parallel combination of C₁ and C₂,

The Type III compensator has three poles (one at the origin) and two zeros. In practice, it is usually arranged to have two coincident zeros and two coincident poles, and the loop crossover frequency is placed somewhere between the zeros and poles. For this kind of design, the transfer function in Equation (1) can be rewritten as:

where the zero's and pole's frequencies are given by:

and the constant gain K is given by:

Equations 7-13 Select figure to enlarge.

The amplitude of the transfer function in Equation (3) at a given frequency ω can be calculated as:

The phase of the transfer function in Equation (3) at a given frequency ω can be calculated as:

As can be seen, the phase of C(jω) has two parts: a constant part of -π/2 due to the pole at the origin, and a variable part as a function of frequency ω given by:

Equation (8) can be converted to:

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