10.11  Buck converters

The module

The modules in our kits are the CC/CV variant of the XL4015 board: two blue multi-turn potentiometers, a large toroidal inductor, two electrolytic capacitors and a row of small LEDs. One potentiometer sets the output voltage (constant voltage, CV). The other sets a current limit (constant current, CC), used e.g. to charge batteries; we turn it to its maximum so that it never limits us. The screw terminals are marked IN+, IN−, OUT+ and OUT−. Label input and output with a marker the first time you use a module, since the silkscreen is easy to misread upside down, and input and output swapped destroy the module.

The XL4015 chip itself has these ratings from its datasheet:¹

Step 1: Turn the current limit to maximum

With nothing connected to the module, turn the current potentiometer clockwise until it clicks. Multi-turn potentiometers click at every turn once they reach their end stop, so a few extra turns after the first click are harmless and make sure the limit is at its maximum.

Step 2: Set the output voltage with no load

1. Nothing on OUT+ and OUT− except the multimeter probes.
2. Connect IN+ and IN− to the car’s rail and ground (or to a bench supply at 12 V with the current limit at about 0.5 A), with the main switch off.
3. Set the multimeter to DC volts, red probe on OUT+, black on OUT−. Switch on and read the starting voltage.
4. Turn the voltage potentiometer while watching the meter. On our modules counter-clockwise lowers the voltage. The potentiometer has 10 to 15 turns over its range, so several turns may pass before the reading changes noticeably.
5. Stop at 7.0 V ± 0.1 V. If you overshoot, turn back a little.
6. Tap the potentiometer gently with the screwdriver: the reading must not jump.
7. Switch off. Write 7.0 V on a piece of tape on the module.

Step 3: Connect the loads and measure again

1. With the switch off, connect the 470 µF bulk capacitor across OUT+ and OUT− close to the servo connector: the stripe on the capacitor marks the negative lead. Use a capacitor rated 16 V or more.
2. Connect the servo’s red wire to OUT+ and its brown wire to OUT−.
3. Connect OUT+ to VIN of the ESP32 and OUT− to its GND. Read the next section before the ESP32 is ever connected to USB at the same time.
4. Switch on and measure the voltage at the servo connector and at VIN. Both should be within 0.1 V of the no-load setting. A larger drop means a poor connection or a wire that is too thin.

The bulk capacitor supplies the short current peaks the servo draws when it starts to move, which the wires and the converter cannot follow instantly. Without it, those peaks pull the 7.0 V rail down far enough to reset the ESP32.

USB and VIN at the same time

The ESP32 board has two power inputs: the 5 V of the USB connector and the VIN pin. On most DevKit boards the USB 5 V reaches the VIN node through a diode, often a Schottky diode. The diode points from USB to VIN, so it conducts when USB is higher and blocks when VIN is higher. With 7.0 V on VIN, the diode blocks and the laptop is safe.

On boards without the diode, VIN and the USB 5 V are the same copper. With the car switched on and the USB cable plugged in, the buck converter’s 7.0 V then drives current into the laptop’s USB port, which can damage the port or the laptop. A second problem exists with or without the diode: with the car switched off and USB plugged in, the laptop feeds VIN at about 4.7 V, and with it the servo and the output of the buck converter. The servo then moves weakly on USB power, and the car is not off even though the switch is.

Find out which kind of board you have before connecting both. Plug in only USB, nothing on VIN, and measure from VIN to GND:

A board without the diode can be repaired by cutting the trace from the USB 5 V to VIN and soldering a Schottky diode across the gap, anode on the USB side.

Pre-flight checklist

Before the first power-up of a newly wired circuit:

1. Output set to 7.0 V with no load and confirmed with the multimeter.
2. IN+ and IN− connected with correct polarity to the rail and ground.
3. OUT+ and OUT− correct at the servo, the bulk capacitor and the ESP32 VIN.
4. All grounds connected to the common ground.
5. Bulk capacitor at the servo, 470 µF, at least 16 V, stripe to ground.
6. With power off, the multimeter in continuity mode does not beep between OUT+ and OUT−.
7. USB to VIN behaviour of the ESP32 board checked.
8. After power-up: 7.0 V measured at the load.

The linear regulator, and why we do not use one

The simplest way to get 7.0 V from 12.6 V is a linear regulator: a transistor in series with the load, controlled so that it drops exactly the voltage difference. The current through the transistor is the load current, so the transistor turns the product of the two into heat:

\[ P_\text{loss} = (V_\text{in} - V_\text{out}) I. \]

With the servo and the ESP32 drawing 2 A together, from a full pack,

\[ P_\text{loss} = (12.6 - 7.0) \cdot 2~\text{W} = 11.2~\text{W}, \]

while the load receives \(7.0 \cdot 2~\text{W} = 14~\text{W}\). The efficiency is \(V_\text{out}/V_\text{in} = 7.0/12.6 = 56~\%\), and the regulator needs a heat sink the size of a matchbox to get rid of 11 W. Near the end of the pack, at 9.6 V, the loss is still \(2.6 \cdot 2~\text{W} = 5.2~\text{W}\). Almost half the battery’s energy would go into heating the regulator.

The buck topology

A buck converter avoids that loss by using a switch that is either fully on or fully off. A fully on switch has almost no voltage across it, and a fully off switch carries no current, so in neither state does it dissipate much. Figure 10.11.1 shows the ideal circuit. The switch S connects the input to the node SW for a fraction \(D\) of each switching period \(T\), the duty cycle. The inductor \(L\) between SW and the output resists changes in its current, and the capacitor \(C\) smooths the output voltage. The diode D gives the inductor current a path when the switch is off.

While the switch is closed, SW is at \(V_\text{in}\) and the inductor sees \(V_\text{in} - V_\text{out}\) across it. Its current grows, and the inductor stores energy in its magnetic field. When the switch opens, the inductor current cannot stop instantly: it keeps flowing, now through the diode, which puts SW at about 0 V. The inductor sees \(-V_\text{out}\) and its current falls, while the stored energy goes to the load. The current in the inductor is therefore a triangle around the load current, and the capacitor turns the remaining small ripple into a nearly constant output voltage.

The duty cycle

The voltage across an inductor is \(v_L = L \, \mathrm{d}i_L/\mathrm{d}t\). In steady state the inductor current is the same at the start of every period, so the voltage across it must average to zero over one period: the rise during the on-time equals the fall during the off-time. For the ideal converter this gives

\[ (V_\text{in} - V_\text{out}) D T = V_\text{out} (1 - D) T, \]

and solving for \(D\),

\[ D = \frac{V_\text{out}}{V_\text{in}}. \]

The output voltage is the average of the switched voltage at SW. For the car, with \(V_\text{out} = 7.0~\text{V}\):

The XL4015 measures its output through a voltage divider (the voltage potentiometer is part of it) and adjusts \(D\) continuously so that the divider’s midpoint stays at 1.25 V. As the pack discharges, the duty cycle rises from 56 % to 73 %, and the output stays at 7.0 V.

Efficiency compared

A real converter loses some power in the switch’s on-resistance, in the diode, in the inductor’s winding and in switching itself. The XL4015’s datasheet curve for 12 V to 5 V shows about 90 % efficiency between 1 and 2 A. At 90 %, the 14 W the servo and the ESP32 take at 2 A require

\[ P_\text{in} = \frac{P_\text{out}}{\eta} = \frac{14}{0.90}~\text{W} = 15.6~\text{W}, \]

so the converter loses 1.6 W, against 11.2 W for the linear regulator. The input current from a full pack is \(15.6 / 12.6~\text{A} = 1.24~\text{A}\), less than the 2 A delivered at the output. A buck converter trades voltage for current, the same way a gearbox trades speed for torque, and only a tenth of the power goes missing on the way. A linear regulator always takes the full output current from its input.

Ripple

The inductor current rises and falls by the same amount \(\Delta i_L\) in each period. During the off-time the inductor sees \(-V_\text{out}\) for \((1-D)/f\) seconds, so

\[ \Delta i_L = \frac{V_\text{out} (1 - D)}{L f}. \]

The XL4015 datasheet’s application circuit uses \(L = 47~\mu\text{H}\) (the module’s toroid is of similar size). At \(f = 180~\text{kHz}\) and a full pack (\(D = 0.556\)),

\[ \Delta i_L = \frac{7.0 \cdot 0.444}{47 \cdot 10^{-6} \cdot 180 \cdot 10^{3}}~\text{A} = 0.37~\text{A} \]

peak to peak. The ripple is largest when the input is highest, because \(D\) is smallest there. The output capacitor absorbs this triangle. For an ideal capacitor the resulting voltage ripple would be \(\Delta V = \Delta i_L / (8 f C)\), less than a millivolt with 470 µF, but real electrolytic capacitors have a series resistance (ESR) of the order of 0.1 Ω, and \(\Delta i_L \cdot \text{ESR}\) gives a ripple of some tens of millivolts at 180 kHz. The oscilloscope shows it as a small sawtooth on the 7.0 V, with sharp spikes at every switching edge. Neither the servo nor the ESP32’s own regulator notices it.

When the input sags: dropout

A buck converter can only lower a voltage. The XL4015 can raise its duty cycle up to 100 %, switch permanently on, and then the output follows the input minus the voltage drop across the switch and the inductor. The datasheet gives this minimum dropout as 0.3 V. The converter therefore holds 7.0 V as long as its input stays above about 7.3 V, and below that the 7.0 V rail follows the input down. Below 8 V the chip is also outside its specified input range.

The rail sags when the motor starts, as shown in Internal resistance and voltage sag. With a resistance of 0.06 Ω in the battery path, a 30 A start drops a full pack from 12.6 to 10.8 V and the converter does not notice. Near the cutoff, the same start takes 9.6 V down to 7.8 V, close to the dropout. An aged pack with twice the internal resistance takes it to 6.0 V, and the servo and the ESP32 sag with it.

The bulk capacitor does not help against this. It supplies the servo’s current while the voltage falls at the rate

\[ \frac{\mathrm{d}V}{\mathrm{d}t} = \frac{I}{C} = \frac{2}{470 \cdot 10^{-6}}~\text{V/s} = 4.3~\text{V/ms}, \]

so it holds the rail through microsecond peaks, not through a motor start lasting tens of milliseconds. A sagging rail is fixed at its cause: shorter and thicker battery wiring, a fresh pack, and firmware that ramps the motor up over some tens of milliseconds instead of switching it on at full duty.

The ESP32’s own 3.3 V regulator

The ESP32 runs on 3.3 V. The DevKit board makes it from VIN with a linear regulator, on most boards an AMS1117-3.3, the part used on Espressif’s own DevKitC.² The AMS1117 needs its input at least 1.1 to 1.3 V above its output (its dropout), so VIN must be above about 4.6 V, and its absolute maximum input is 15 V.³ As a linear regulator it turns \((V_\text{in} - 3.3~\text{V}) I\) into heat.

The ESP32 draws about 240 mA while transmitting on Wi-Fi⁴ and less on average. With 0.2 A from the 7.0 V rail, the regulator dissipates

\[ P = (7.0 - 3.3) \cdot 0.2~\text{W} = 0.74~\text{W}. \]

The AMS1117 datasheet gives a thermal resistance from junction to air of 55 to 80 °C/W when the tab is soldered to a generous copper area, and a small DevKit board has less copper than that. With 80 °C/W the junction runs \(0.74 \cdot 80 = 59~\text{K}\) above the air, about 85 °C in a 25 °C room: warm, and within the 125 °C limit. Fed directly from a full pack instead, the regulator dissipates

\[ P = (12.6 - 3.3) \cdot 0.2~\text{W} = 1.9~\text{W}, \]

and the junction would rise about 150 K above the air. The regulator’s thermal protection switches it off before that, the ESP32 resets, the regulator cools, and the cycle repeats. 12.6 V is also uncomfortably close to the 15 V absolute maximum, and some clones are rated lower. That is why VIN is fed from the 7.0 V of the buck converter and not from the rail. Any VIN voltage from about 5 to 7 V works; we use 7.0 V because the servo wants that voltage and one converter feeds both.