4 Loop Stability With Post Filter Feedback

Since the ferrite bead filter is now inside the class-D loop, there are extra poles added in the system, which adversely affects the stability of the loop. The user needs to take into account extra guidelines to choose the correct configuration of the filter, which can make sure that the class-D loop is stable. To find a stable configuration of the EMI filters, the equivalent model of the EMI filter needs to be drawn. The filter needs to be approximated into a second order filter as shown in Figure 1-1. Ferrite beads impedance can be divided into three main regions, for example, inductive, resistive, and capacitive. These regions can be easily determined by looking at impedance plots of ferrite bead data sheet (as shown in Figure 4-1), where Z is the impedance, X is the reactance and R is the resistance of the bead.

For the region of the impedance plot where the bead appears mostly inductive (region 1 in Figure 4-1), the L_EQ can be calculated by using the Equation 1, where X_L = impedance of bead at frequency ‘f’. Best practice to take the impedance value at least a decade away from the peak impedance value for accurate calculations. For example, impedance shown in Figure 4-1 at 10MHz for MPZ1608S221A is 70Ω. The L_EQ can be calculated as 1.11µH.

The C_PAR can be estimated in a method similar to L_EQ, by looking at region where the bead appears mostly capacitive (region 2 in Figure 4-1). The C_PAR can be estimated using Equation 2 where X_C = impedance of the bead at frequency ‘f’. It is best to take impedance value at least a decade away from the peak impedance value for accurate calculations. For most beads the C_PAR is less than 5pF and has no impact on the stability of the loop. User should do the calculations and make sure that this holds true for the bead selected for the use case. For example, impedance shown in Figure 4-1 at 1GHz for MPZ1608S221A is 150Ω. So the C_PAR can be calculated as 1pF.

The R_PAR can be approximated as the peak impedance of the bead. For ease of calculations, the R_DC is approximated as zero here, and the entire peak impedance is estimated as R_PAR. In Figure 4-1, the R_PAR can be calculated as 250Ω

The total output cap (C_EQ) needs to include the intentional cap added by the user for the filtering and the parasitic caps due to any other additional elements at output of the ferrite bead such as ESD diodes, board routings, and so on.

Using the model of the filter, the filter cutoff frequency and the Q-factor can be calculated using the following equations:

Table 4-1 summarizes the stability criteria for TI’s Post filter feedback class-D amplifiers. Users need to make sure that the stability criteria for the selected filter satisfy the guidelines in Table 4-1 for proper functioning of class-D amplifier.

Note that some EMI Filter data sheets provide the impedance derating profile across different dc bias currents. For example, as shown in Figure 4-2, the 2506036017Y2 data sheet provides the impedance curve of the EMI filter for different dc currents of 0A, 0.2A, 0.5A, 1A, and 2A. Hence if the Class-D is to be used in high speaker current applications up to 2A, it is required to verify the stability across each of these settings. Verify the Class-D loop stability of the amplifier in PFFB across the range of bias currents to make sure no instability at any intermediate operating point of the loop