There are two methods to design a suitable control loop for the TPS4021x device. The first (and preferred, if equipment is available) is to use a frequency-response analyzer to measure the open-loop modulator and power stage gain and to then design compensation to fit that. The usage of these tools for this purpose is well-documented with the literature that accompanies the tool and is not discussed here.

The second option is to make an initial guess at compensation, and then evaluate the transient response of the system to see if the compensation is acceptable to the application or not. For most systems, an adequate response can be obtained by simply placing a series resistor and capacitor (R_FB and C_FB) from the COMP pin to the FB pin as shown in Figure 7-6.

Figure 7-6 Basic Compensation Network

The natural phase characteristics of most capacitors used for boost outputs combined with the current mode control provide adequate phase margin when using this type of compensation. To determine an initial starting point for the compensation, the desired crossover frequency must be considered when estimating the control to output gain. The model used is a current source into the output capacitor and load.

When using these equations, the loop bandwidth should be no more than 20% of the switching frequency, f_SW. A more reasonable loop bandwidth would be 10% of the switching frequency. Be sure to evaluate the transient response of the converter over the expected load range to ensure acceptable operation.

Equation 21.

Equation 22.

Equation 23.

where

• K_CO is the control to output gain of the converter, in V/V
• g_M is the transconductance of the power stage and modulator, in S
• R_OUT is the output load equivalent resistance, in Ω
• Z_OUT is the output impedance, including the output capacitor, in Ω
• R_ISNS is the value of the current sense resistor, in Ω
• L is the value of the inductor, in H
• C_OUT is the value of the output capacitance, in μF
• R_ESR is the equivalent series resistance of C_OUT, in Ω
• f_SW is the switching frequency, in Hz
• f_L is the desired crossover frequency for the control loop, in Hz

These equations assume that the operation is discontinuous and that the load is purely resistive. The gain in continuous conduction can be found by evaluating Equation 22 at the resistance that gives the critical conduction current for the converter. Loads that are more like current sources give slightly higher gains than predicted here. To find the gain of the compensation network required for a control loop of bandwidth f_L, take the reciprocal of Equation 21.

Equation 24.

The GBWP of the error amplifier is only specified to be at least 1.5 MHz. If K_COMP multiplied by the f_L is greater than 750 kHz, reduce the desired loop crossover frequency until this condition is satisfied. This ensures that the high-frequency pole from the error amplifier response with the compensation network in place does not cause excessive phase lag at the f_L and decrease phase margin in the loop.

The R-C network connected from COMP to FB places a zero in the compensation response. That zero should be approximately 1/10^th of the desired crossover frequency, f_L. With that being the case, R_FB and C_FB can be found from Equation 25 and Equation 26.

Equation 25.

Equation 26.

where

• R1 is in f_L is the loop crossover frequency desired, in Hz
• R_FB is the feedback resistor in C_FB is the feedback capacitance in μF

Though not strictly necessary, it is recommended that a capacitor be added between COMP and FB to provide high-frequency noise attenuation in the control loop circuit. This capacitor introduces another pole in the compensation response. The allowable location of that pole frequency determines the capacitor value. As a starting point, the pole frequency should be 10 × f_L. The value of C_HF can be found from Equation 27.

Equation 27.

The error amplifier GBWP will usually be higher, but is ensured by design to be at least 1.5 MHz. If the gain required in Equation 24 multiplied by 10 times the desired control loop crossover frequency, the high-frequency pole introduced by C_HF is overridden by the error amplifier capability and the effective pole is lower in frequency. If this is the case, C_HF can be made larger to provide a consistent high-frequency roll off in the control loop design. Equation 28 calculates the required C_HF in this case.

Equation 28.

where

• C_HF is the high-frequency roll-off capacitor value in μF
• R_FB is the mid-band gain-setting resistor value in Ω