Switching Converters
Buck, boost, and buck-boost DC-DC converters — switching at high frequency to achieve efficiencies above 90%, far exceeding any linear regulator.
1. Why Switching Regulators?
A linear regulator dissipates \((V_{in} - V_{out}) \times I_{load}\) as heat. Converting 12 V to 5 V at 1 A wastes 7 W — 58% of input power lost. A switching regulator cycles an ideal switch at high frequency (typically 100 kHz–several MHz), storing energy in an inductor and capacitor between cycles. Because the switch dissipates zero power (ideal: ON → zero voltage, OFF → zero current), efficiency can exceed 95%.
Buck (Step-Down)
D < 1 → V_out < V_in
Boost (Step-Up)
D > 0 → V_out > V_in
Buck-Boost
Inverts polarity
2. Buck Converter Circuit
When the switch is ON (time \(DT_s\)), energy builds in \(L\); when OFF, \(L\)maintains current via the freewheeling diode D1. The average inductor voltage must be zero in steady state (volt-second balance), giving \(V_{out} = D V_{in}\).
3. Inductor Current Ripple & CCM/DCM
In Continuous Conduction Mode (CCM), the inductor current never reaches zero. The peak-to-peak ripple is:
\[ \Delta I_L = \frac{V_{in}\,D\,(1-D)}{f_s\,L} \qquad \text{(buck, CCM)} \]
CCM/DCM boundary: the converter enters Discontinuous Conduction Mode (DCM) when \(I_{load} < \Delta I_L / 2\). In DCM, the voltage conversion ratio becomes load-dependent and control is more complex.
Output voltage ripple from the capacitor:
\[ \Delta V_{out} = \frac{\Delta I_L}{8 f_s C} = \frac{V_{in}\,D\,(1-D)}{8\,f_s^2\,L\,C} \]
Output ripple decreases with higher \(f_s\), \(L\), and \(C\)
4. Boost & Buck-Boost Converters
Boost (Step-Up)
The switch connects the inductor to ground during ON time, building up current. When switched OFF, the inductor voltage adds to \(V_{in}\), forward-biasing the diode and charging the output capacitor to a higher voltage:
\[ V_{out} = \frac{V_{in}}{1-D} \qquad (V_{out} > V_{in}) \]
At D = 0.5 → \(2V_{in}\). At D = 0.8 → \(5V_{in}\). Used in battery chargers, LED drivers, power factor correction.
Buck-Boost (Inverting)
Inverts the output polarity. The output magnitude can be above or below \(V_{in}\):
\[ V_{out} = -\frac{D}{1-D}\,V_{in} \]
Non-inverting variants (SEPIC, Cuk) avoid polarity inversion at the cost of complexity. Used when \(V_{in}\) may be above or below \(V_{out}\)(e.g., single-cell Li-ion to 3.3 V).
Control Loops
Switching converters use feedback control to regulate output voltage despite varying load and input. The most common architectures are: voltage-mode control (compare output to reference, adjust PWM duty cycle) and current-mode control(inner current loop for fast response, outer voltage loop for regulation). The power stage transfer function has a second-order LC pole that must be compensated with a Type-II or Type-III error amplifier for stability.
Python Simulation
Buck converter: inductor current and output voltage waveforms vs duty cycle, V_out vs D for buck and boost, inductor current ripple vs L, efficiency vs load, and output voltage ripple vs C.
Click Run to execute the Python code
Code will be executed with Python 3 on the server