Power Electronics & Voltage Regulator Design
Synchronous Buck Converter Ripple & CCM Formula
Calculate Step-Down Buck Converter Duty Cycle D = V_out / V_in, Peak-to-Peak Inductor Current Ripple (V_in - V_out)*D / (f_MHz * L_uH), Peak Switch Current, and Critical CCM Inductance.
Size step-down Buck inductors cleanly using the exact 1 MHz * 1 uH = 1 Ohm-s identity!
Point-of-load (PoL) CPU/GPU voltage regulators use Synchronous Buck DC-DC converters to step down an intermediate 12 V rail to low-voltage core rails V_out < V_in! In Continuous Conduction Mode (CCM), inductor volt-second balance sets Steady-State Duty Cycle D = V_out / V_in. Expressing switching frequency in MHz (10^6 Hz) and filter inductance in microhenries uH (10^-6 H) cancels powers of ten identically (1 MHz * 1 uH = 1 V/A!), giving Peak-to-Peak Inductor Ripple Current Delta_I_L (A) = ((V_in - V_out) * D) / (f_MHz * L_uH), Peak High-Side MOSFET Current I_peak = I_load + Delta_I_L / 2 (which must stay below inductor saturation current I_sat!), and Critical Boundary Inductance L_crit_uH = ((V_in - V_out) * D) / (2 * I_load * f_MHz)!
Verify on Input_Bus V_in = 12.0 V (B2), Regulated_Core V_out = 3.0 V (B3 -> Duty Cycle D = 3 / 12 = 0.2500 = 25.0% in E2), Switching_Freq f_sw = 0.50 MHz (500 kHz, B4), Inductance L = 4.50 uH (B5), and DC_Load_Current I_load = 2.00 A (B6): Peak-to-Peak Ripple Delta_I_L is ((12 - 3) * 0.25) / (0.50 * 4.50) = 2.25 / 2.25 = 1.00 A (E3); Peak MOSFET/Inductor Current is 2.00 + 0.50 = 2.50 A (E4); and Critical CCM Inductance is 2.25 / (2 * 2.00 * 0.50) = 1.125 uH (E5, well below 4.50 uH so inductor current stays continuous)!
| Synchronous Buck Metric (Vin=12V, Vout=3.0V, f=0.50MHz, L=4.50uH, Iload=2.0A) | Formula | Verified Output |
|---|---|---|
| CCM Step-Down Duty Cycle D | V_out / V_in | 0.2500 (25.00%) |
| Peak-to-Peak Ripple Delta_I_L | ((V_in - V_out) * D) / (f_MHz * L_uH) | 1.00 A (50% Ripple Ratio) |
| Peak Switch / Core Current I_pk | I_load + Delta_I_L / 2 | 2.50 A (Check < Inductor I_sat!) |
| Critical CCM Inductance L_crit | ((V_in - V_out)*D) / (2 * I_load * f_MHz) | 1.125 uH (5.625 uH @ Iload=0.4A) |
Buck Inductor Ripple & Critical CCM Inductance Formula
Enforce strict step-down topology 0 < V_out < V_in ("Invalid Step-Down (Vout >= Vin)"—stepping up requires a Boost or Buck-Boost topology!) and positive f_MHz, L_uH, and I_load!
=LET(v_in, B2, v_ot, B3, f_mh, B4, l_uh, B5, i_ld, B6, IF(OR(v_in <= 0, v_ot <= 0, f_mh <= 0, l_uh <= 0, i_ld <= 0), "Invalid Buck Input", IF(v_ot >= v_in, "Invalid Step-Down (Vout >= Vin)", LET(dt_c, v_ot / v_in, ROUND(((v_in - v_ot) * dt_c) / (2 * i_ld * f_mh), 3)))))Light-Load Discontinuous Threshold Check (I_load = 0.40 A)
Drop DC_Load_Current to 0.40 A in cell B6: Critical Inductance rises to 5.625 uH (> 4.50 uH installed), explaining why synchronous buck controllers enable Diode-Emulation / Pulse-Skipping at light load to block reverse inductor current!
=IF(ISTEXT(E3), E3, ROUND(B6 + E3 / 2, 2))Try the example
Use the original values or change them to test your understanding.