Switching Dynamics Intermediate Power Electronics

Buck-Boost DC-DC Switching Regulator

Explore inductor energy storage, Continuous vs Discontinuous mode, and voltage inversion.

Adjust duty cycle and load resistance in real time to observe the magnetic flux accumulation during MOSFET switch-on, and rapid diode freewheeling energy dump to output capacitor during switch-off.

Governing Physical Law & Equations

V_{out} = -V_{in}\frac{D}{1 - D}, \quad \Delta I_L = \frac{V_{in} D}{L f_{sw}}

Ideal voltage transfer ratio and peak-to-peak inductor current ripple.

Law: Conservation of Energy & Volt-Second Balance | Standard Reference: IEEE Std 1573 / IEC 62040 (Switching Mode Power Regulators)

Adjustable System Parameters

Parameter	Nominal Value	Dynamic Range	Physical Role
PWM Duty Cycle (D)	0.6	0.15 to 0.85	Ratio of MOSFET ON-time to total switching period
Input Voltage (V_in)	12 V	5 to 48 V	DC primary source voltage
Switching Freq (f_sw)	100 kHz	20 to 300 kHz	MOSFET gate drive switching frequency
Power Inductor (L)	120 µH	10 to 300 µH	Energy storage choke (dictates CCM vs DCM threshold)

Analytical Proof & Derivation

By inductor volt-second balance in steady state: ∫₀^(T_s) v_L(t) dt = 0. During switch-on (D T_s), v_L = V_in. During switch-off ((1-D) T_s), v_L = V_out. Therefore, V_in (D T_s) + V_out (1 - D) T_s = 0, directly giving V_out = -V_in [D / (1 - D)]. Peak ripple is ΔI_L = (V_in D) / (L f_sw).

Verification Benchmark

Power benchmark: V_in = 12 V, D = 0.60 gives ideal V_out = -12 × (0.6/0.4) = -18.00 V. For L = 120 µH, f_sw = 100 kHz, inductor ripple ΔI_L = (12 × 0.60) / (120e-6 × 100e3) = 0.60 A. Numerical solver matches exact analytical value.

Field Engineering Insights

To guarantee Continuous Conduction Mode (CCM), inductor must exceed L_crit = (1 - D)² R_load / (2 f_sw). In DCM mode, the output voltage becomes load dependent and dynamic transient regulation degrades.