9.2.4.4.2 Loop Compensation Design Steps

With the small signal models coming out, the next step is to calculate the compensation network parameters with the given inductor and output capacitance.

1. Set the Cross Over Frequency, ƒ_C
   • The first step is to set the loop crossover frequency, ƒ_C. The higher crossover frequency, the faster the loop response is. It is generally accepted that the loop gain cross over no higher than the lower of either 1/10 of the switching frequency, ƒ_SW, or 1/5 of the RHPZ frequency, ƒ_RHPZ. Then calculate the loop compensation network values of R_C, C_C, and C_P by following below equations.
2. Set the Compensation Resistor, R_C
   • By placing ƒ_Z below ƒ_C, for frequencies above ƒ_C, R_C | | R_EA ~= R_C and so R_C × G_EA sets the compensation gain. Setting the compensation gain, K_COMP-dB, at ƒ_Z, results in the total loop gain, T_(s) = G_PS(s) × H_EA(s) × He(s) being zero at ƒ_C.
   • Therefore, to approximate a single-pole roll-off up to f_P2, rearrange Equation 22 to solve for RC so that the compensation gain, K_EA, at f_C is the negative of the gain, K_PS, read at frequency f_C for the power stage bode plot or more simply:
   Equation 26.
   where
   • K_EA is gain of the error amplifier network
   • K_PS is the gain of the power stage
   • G_EA is the amplifier’s trans-conductance, the typical value of G_EA = 195 µA / V
3. Set the compensation zero capacitor, C_C
   • Place the compensation zero at the power stage R_OUT ,C_OUT pole’s position, so to get:
   Equation 27.
   • Set ƒ_Z = ƒ_P, and get the
   Equation 28.
4. Set the compensation pole capacitor, C_P
   • Place the compensation pole at the zero produced by the R_ESR and the C_OUT, it is useful for canceling unhelpful effects of the ESR zero.
   Equation 29.
   Equation 30.
   • Set ƒ_P2 = ƒ_ESR, and get the
   Equation 31.
   • If the calculated value of C_P is less than 10 pF, it can be neglected.
   Designing the loop for greater than 45° of phase margin and greater than 6-dB gain margin eliminates output voltage ringing during the line and load transient. The R_C = 15 kΩ , C_C = 6.8 nF, C_p = 10 pF for this design example.