To convert a 12V DC input to a regulated 5V output using a classic inverting buck-boost converter, the required ideal duty cycle is 29.4%, yielding a switch ON-time of 2.94 µs at a 100 kHz switching frequency. The foundational formula used to derive this is D = V_out / (V_in + V_out). Substituting our exact query values (using magnitudes for the inverting topology): D = 5 / (12 + 5) = 5 / 17 = 0.2941. However, on the bench, ideal math fails to account for semiconductor voltage drops. When we factor in a realistic 0.4V Schottky diode forward voltage ($V_f$) and a 0.1V MOSFET drain-source drop ($V_{ds}$), the real-world duty cycle shifts to 31.2%, calculated as D = (V_out + V_f) / (V_in - V_ds + V_out + V_f) → 5.4 / (11.9 + 5.4) = 0.312.
| Input Voltage ($V_{in}$) | Ideal Duty Cycle | Real Duty Cycle (w/ $V_f$ & $V_{ds}$) | Switch ON-Time (@ 100kHz) |
|---|---|---|---|
| 9.6V (-20%) | 34.2% | 36.0% | 3.60 µs |
| 10.8V (-10%) | 31.6% | 33.5% | 3.35 µs |
| 12.0V (Nominal) | 29.4% | 31.2% | 3.12 µs |
| 13.2V (+10%) | 27.5% | 29.2% | 2.92 µs |
| 14.4V (+20%) | 25.8% | 27.3% | 2.73 µs |
Core Conversion Formulas and Real-World Assumptions
The calculations above rely on one critical assumption that fixes the answer: Continuous Conduction Mode (CCM). In CCM, the inductor current never falls to zero during the switching cycle. This assumption holds true only if your inductor is sized correctly for the minimum expected load current. If the load drops below the critical current threshold, the converter enters Discontinuous Conduction Mode (DCM), and the simple voltage-ratio formulas become invalid.
Furthermore, the "real-world" adjustments assume specific component characteristics. The 0.4V diode drop assumes a standard Schottky rectifier like the SS34. If you are designing a synchronous buck-boost converter (using a second MOSFET instead of a diode, like the TI TPS63020), that 0.4V drop shrinks to roughly 0.05V (the $I \times R_{DS(on)}$ drop of the low-side FET), pushing your real-world duty cycle much closer to the ideal 29.4%. Always check your specific controller's datasheet for internal compensation networks, as some ICs measure output voltage before the inductor's DC resistance (DCR) drop, requiring an additional offset in your feedback resistor divider.
Topology Shifts: Inverting vs. 4-Switch Non-Inverting
The classic buck-boost topology inverts the output polarity (a positive 12V input yields a negative 5V output). In modern embedded systems, engineers usually require a positive-to-positive conversion. This shifts the math and the hardware topology entirely.
| Criterion | Classic Inverting | 4-Switch Non-Inverting | SEPIC (Single-Ended Primary-Inductor) |
|---|---|---|---|
| Output Polarity | Inverted (-V) | Same as Input (+V) | Same as Input (+V) |
| Duty Cycle Formula (CCM) | $D = V_{out} / (V_{in} + V_{out})$ | Buck: $D = V_{out}/V_{in}$ Boost: $D = 1 - (V_{in}/V_{out})$ | $D = V_{out} / (V_{in} + V_{out})$ |
| Switch Voltage Stress | $V_{in} + V_{out}$ | $V_{in(max)}$ | $V_{in} + V_{out}$ |
| Inductor Count | 1 | 1 | 2 (or 1 coupled) |
| Typical Use Case | Negative bias rails, op-amp supplies | Battery-powered USB 5V rails | Low-noise, non-isolated LED drivers |
When using a 4-switch non-inverting buck-boost (like the Analog Devices LTC3130), the controller dynamically shifts between buck mode and boost mode based on the input voltage. If your 12V battery sags to 10V while regulating a 12V output, the IC seamlessly transitions into boost mode, altering the active switching nodes and changing the effective duty cycle formula mid-operation.
When Voltage Conversion Math Becomes Meaningless
There are specific operating conditions where plugging numbers into the standard buck-boost conversion formulas yields useless or dangerous results:
- Discontinuous Conduction Mode (DCM): If your load current drops below the inductor's ripple current threshold ($\Delta I_L$), the inductor fully discharges before the switching cycle ends. In DCM, the output voltage becomes dependent on the load current and inductance value, not just the duty cycle. The CCM formulas will predict a stable 5V, but your bench measurement will show 7V or higher, potentially destroying your load.
- Right-Half-Plane Zero (RHPZ): In continuous conduction mode, the classic inverting buck-boost and boost topologies exhibit a RHPZ in their control-to-output transfer function. This introduces a 90-degree phase lag. If you attempt to design a feedback compensation network with a crossover frequency higher than the RHPZ frequency, the control loop will oscillate violently. The math for the steady-state duty cycle remains correct, but the dynamic conversion (transient response) becomes unstable.
- Exceeding Maximum Duty Cycle Limits: Most PWM controllers cap their maximum duty cycle between 85% and 95% to prevent transformer/inductor saturation and allow time for bootstrap capacitor recharging. If your calculation demands a 98% duty cycle (e.g., trying to boost 3.0V to 50V), the converter will physically fail to reach the target voltage, regardless of what the formula dictates.
FAQ: How does this conversion shift for 120V vs 230V vs 3-Phase?
A frequent point of confusion on the bench is applying DC-DC switching regulator math to AC mains. Switching buck-boost converters do not apply to AC mains voltages. Applying 120V AC or 230V AC directly to a standard buck-boost IC will result in catastrophic failure.
If you need to "buck" or "boost" 120V, 230V, or 3-phase AC line voltage (for example, bucking a 240V supply down to 208V for industrial HVAC equipment), you are not using a switching converter. You are using an AC buck-boost transformer (an autotransformer configuration). The conversion ratio for AC autotransformers is strictly dictated by the physical turns ratio ($N_p / N_s$) of the copper windings and Faraday's Law of Induction, completely independent of PWM duty cycles, switching frequencies, or inductor saturation currents. For AC-to-DC conversion from mains, you must look toward isolated Flyback or Forward switching topologies, which utilize entirely different transfer functions.
