Switching power supplies
A buck converter that delivers 12 V at 2.4 A rises to 15.4 V when the load drops to 0.77 A, without touching the duty cycle: it has entered discontinuous conduction. That is why every switching supply needs feedback.
01The principle
A linear supply regulates by dissipating the difference between input and output, as seen in linear regulated power supplies. A switching supply, by contrast, chops the voltage with a switch that opens and closes at a fixed frequency, and filters the result with an inductor and a capacitor, which ideally dissipate nothing. With the duty cycle \( D \), the fraction of the period during which the switch conducts, the ratio between output and input is set. Efficiency reaches 85 to 97 %, and the size of the magnetic components falls as the frequency rises. A more practical introduction is on the switching power supplies page of the technician program.
02The topologies
In steady state, the average voltage across the inductor is zero: the continuous-conduction relations follow from that balance.
| Topology | Vo/Vi in continuous conduction | Use |
|---|---|---|
| Buck (step-down) | \( D \) | Points of load, processor regulators |
| Boost (step-up) | \( 1/(1-D) \) | Batteries to higher voltages, power factor correction |
| Buck-boost | \( -D/(1-D) \) | Inverted outputs, or outputs both higher and lower than the input |
| Flyback | \( \frac{N_s}{N_p}\,\frac{D}{1-D} \) | Isolated supplies up to about 100 W: chargers |
| Forward | \( \frac{N_s}{N_p}\,D \) | Isolated supplies of hundreds of W |
| Half bridge, full bridge, LLC | depends on the topology | High power, high efficiency |
Isolated supplies use a high-frequency transformer; in the flyback that transformer is actually a coupled inductor that stores the energy in its air gap, as seen in magnetic materials.
03Continuous and discontinuous conduction
If the load is light, the inductor current reaches zero before the period ends: this is discontinuous conduction. There the voltage ratio stops being \( D \) and starts to depend on the load. In the buck converter, with \( K = 2L/(R\,T) \):
A 24 V, 100 kHz buck converter with a 100 μF output capacitor, operating open loop. The curve is the inductor current over three periods; the dashed line, the load current.
04Control, rectification and noise
The output is regulated with a loop that adjusts \( D \). In voltage-mode control, an error amplifier compares the output with a reference and a pulse-width modulator generates \( D \); the LC filter adds two poles and the loop is compensated as seen in stability and compensation. In current-mode control, an inner loop limits the peak switch current in each cycle: the plant becomes first order and the overcurrent protection is automatic.
At a low output voltage, the drop of the freewheeling diode eats up a good part of the efficiency; it is replaced by a MOSFET that conducts in synchronism, synchronous rectification. Supplies that draw more than about 75 W from the line include a boost stage for power factor correction, which forces the input current to follow the sinusoidal shape of the voltage. Fast edges generate conducted and radiated interference, which is controlled with input filters, careful layout of the board and shielding.
05In the laboratory
With a laboratory buck converter at a fixed duty cycle, vary the load and measure the output voltage and the inductor current with a current probe; identify the transition to discontinuous conduction.
Measure the efficiency of a commercial power supply as a function of load, with a diode and with synchronous rectification.
Apply a load step to a feedback-regulated supply and measure the overshoot and the settling time of the output.
06Common mistakes
- Using Vo = D Vi with a light load. In discontinuous conduction the output rises.
- Choosing the inductor without looking at its saturation current. The peak, not the average, is what saturates the core.
- Calculating the ripple from the capacitance alone. The equivalent series resistance of the capacitor usually dominates.
- Making large loops with the switched current. They are antennas; the input loop must be as small as possible.
07Self-assessment
What duty cycle does a boost converter need to go from 12 to 48 V?
D = 0.75.
In the lab, with D = 0.5 and 22 μH, what current ripple is there in continuous conduction?
\( \Delta I = 12 \cdot 0.5 \cdot 10\ \mu s / 22\ \mu H \approx 2.73 \) A.
At what load resistance does it enter discontinuous conduction?
When \( 2L/(RT) < 1 - D \): with R greater than 8.8 Ω.
What advantage does current-mode control have?
It simplifies the compensation of the voltage loop and limits the switch current in each cycle.
08Further reading
- Robert W. Erickson and Dragan Maksimović. Fundamentals of Power Electronics. 3rd ed., Springer, 2020. The analysis of DC-DC converters, their modeling and their control.
- Abraham I. Pressman, Keith Billings and Taylor Morey. Switching Power Supply Design. 3rd ed., McGraw-Hill, 2009. The practical design of switching power supplies, including their transformers.
- Sanjaya Maniktala. Switching Power Supplies A–Z. 2nd ed., Newnes, 2012. The design details that the formulas do not tell you.