https://www.analog.com/en/index.html POWER MODULES 23 www.power-mag.com Issue 2 2024 Power Electronics Europe From the transfer function (Equation 1), the second-order LC filter will introduce double poles with resonant frequency. From the typical Bode plot shown in Figure 1, there is a sharp 90° phase delay at the resonant frequency. To ensure stability, the resonant frequency should be 4 to 5 times higher than the control loop bandwidth. This is to avoid a 90° phase delay that could cause instability. Also, to provide enough attenuation for the switching frequency ripple, this resonant frequency should be set 4 to 5 times lower than the switching frequency so the LC filter can provide enough filtering. There is a trade-off between attenuation gain at switching frequency and the control loop bandwidth. However, this methodology helps in selecting a resonant frequency with the optimal LC value. To maintain similar load transient performance, the output impedance should remain consistent before and after adding the LC filter. This means the output capacitance should be roughly the same with or without the LC filter. As a rule of thumb, the capacitance of C2 in Figure 1 can be kept similar to the design without the LC, and C1 can use a much smaller capacitance value so that C1 can dominate the resonant frequency location. Since C1 is much smaller than C2, Equation 2 can simplify into Equation 3: C1 is recommended to be at least one-tenth the value of C2. Once C1 is chosen, the Lf value can be calculated using the resonant frequency in Equation 3. By checking the availability of real components, the optimum C1 and Lf values can be decided. Components Selection Considerations The selections of the capacitor and inductor components are critical in an effective second-order LC filter design. The second-order LC filter needs to provide large enough attenuation at the switching frequency. Since the switching frequency is high (1MHz to 3MHz) in an ultralow noise µModule regulator, the inductor and capacitor in the second-order LC require a good high frequency characteristic. The C2 selection requirement is similar to the design without the LC, so it is not discussed here. The C1 and Lf selection criteria is provided below. C1 capacitor selection criteria. 1. The self-resonant frequency of C1 must be higher than the switching frequency. The impedance of C1 at the switching frequency is the key factor for the second-order LC design. A ceramic capacitor is recommended, and its impedance vs. frequency curve can be referred to determine its self-resonant frequency. Usually, a typical 0603 or 0805 size ceramic capacitor would be ideal, and their self-resonant frequency must be above 3MHz. 2. The rms current rating should be high enough to withstand the current flow. Assuming that all the AC ripple goes through C1, the ceramic capacitor should be able to handle a large rms ripple current. The ceramic capacitor’s temperature rise vs. current curve can be referred to determine current capability. For a 0603 size capacitor, ~4Arms is a good rule of thumb. Lf inductor selection criteria 1. For output current below 8A, a ferrite bead is recommended due to its great high frequency characteristic and compact size. Ferrite beads are also helpful to dampen very high frequency spikes.1 For output current above 8A, or if a large inductance is required, it can be difficult to find a proper ferrite bead, so the traditional shielded inductor is recommended. 2. Select a ferrite bead/inductor with a sufficient rms current rating (for example, 8Arms current rating for output current below 8A). The inductor value is recommended to be less than 10% of the inductor of the µModule device. Ultralow Noise µModule Design Example Figure 2 shows a design example of the LTM4702. It features ultralow electromagnetic interference (EMI) emissions and ultralow rms noise. Its switching frequency is adjustable from 300kHz to 3MHz. In the design example, it is set to 2MHz to optimise noise performance for a 12VIN to 1VOUT application. According to the proposed LC filter design method, the resonant frequency of a second-order LC is set to 400kHz to 500kHz, 4 to 5 times smaller than the switching frequency. Figure 2. The LTM4702 example circuit and a board photo.
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