9.1.1 Feedback Compensation

The open loop response of a boost regulator is defined as the product of modulator transfer function and feedback transfer function. When plotted on a dB scale, the open loop gain is shown as the sum of modulator gain and feedback gain. The modulator transfer function of a current mode boost regulator including a power stage transfer function with an embedded current loop can be simplified as one pole, one zero, and one right-half-plane (RHP) zero system.

Modulator transfer function is defined as follows:

Equation 16.

where

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• 
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• n is the number of the phase.

If the equivalent series resistance (ESR) of C_OUT (R_ESR) is small enough and the RHP zero frequency is far away from the target crossover frequency, the modulator transfer function can be further simplified to one pole system, and the voltage loop can be closed with only two loop compensation components, R_COMP and C_COMP, leaving a single pole response at the crossover frequency. A single pole response at the crossover frequency yields a very stable loop with 90 degrees of phase margin.

The feedback transfer function includes the feedback resistor divider and loop compensation of the error amplifier. R_COMP, C_COMP, and optional C_HF configure the error amplifier gain and phase characteristics, create a pole at origin, a low frequency zero and a high frequency pole.

Feedback transfer function is defined as follows:

Equation 17.

where

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• 

The pole at the origin minimizes the output steady state error. Place the low frequency zero to cancel the load pole of the modulator. The high frequency pole can be used to cancel the zero created by the output capacitor ESR or to decrease noise susceptibility of the error amplifier. By placing the low frequency zero an order of magnitude less than the crossover frequency, the maximum amount of phase boost can be achieved at the crossover frequency. The high frequency pole should be placed beyond the crossover frequency since the addition of C_HF adds a pole in the feedback transfer function.

The crossover frequency (open loop bandwidth) is usually selected between one twentieth and one fifth of the f_SW. In a simplified formula, the estimated crossover frequency can be defined as:

Equation 18.

where

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For higher crossover frequency, R_COMP can be increased, while proportionally decreasing C_COMP. Conversely, decreasing R_COMP while proportionally increasing C_COMP, results in lower bandwidth while keeping the same zero frequency in the feedback transfer function.

The modulator transfer function can be measured by a network analyzer and the feedback transfer function can be configured for the desired open loop transfer function. If the network analyzer is not available, step load transient tests can be performed to verify acceptable performance. The step load goal is minimum overshoot/undershoot with a damped response.