Buck Converter Circuit Design

2023-03-31 | By Jack Hannum

License: Apache License, Version 2.0 Power Supplies Arduino ARM mbed

So, we’ve established what’s going to drive the buck converter and what load the buck converter will serve. Now, we can get to the fun part: the power electronics design. As I’ve mentioned ad nauseam, the converter we’re going to design is a buck converter. I’ve hinted that the buck converter acts as a DC transformer; it steps a higher DC voltage down to a lower one while increasing current to ensure power is preserved. I’ve mentioned that it does so in a controlled way- that it can keep a steady output voltage despite changes in load and input voltage. I’ve noted that it has some limitations - namely that it would be hard for it to make a huge step down in voltage, such that we can’t go directly from the ~170V we’d get by directly rectifying the mains voltage to the 3.3V we need to run a microcontroller. But I haven’t given you any details of how the buck converter works, much less how to design one. That changes with this post. This is the circuit for the buck converter:

Basic Power Conversion:

The buck converter is the simplest power electronic converter; it lowers the output voltage relative to the input voltage by switching rapidly between two circuit configurations using switches; one configuration connects the source to the load, while the other connects the load to ground. The duty cycle determines how much of a switching period the source is connected to the load; the average output voltage approaches the input voltage as the duty cycle approaches 1 (100%), indicating a continuous connection between source and load. An L-C filter reduces the amount of switching harmonics present and makes the output voltage and current continuous; without the filter, the output voltage would fluctuate between 0 and the source voltage, and the load would receive pulses of current rather than the smooth, continuous current devices need to operate well [1].

PWM Basics:

PWM stands for Pulse Width Modulation, and it’s a technique to create a continuous spectrum of voltages out of two or more discrete source voltages. For the buck converter, the two voltage levels we’ll combine to get the targeted average voltage are the source/input voltage and ground (0V). As before, the duty cycle determines the amount of time that the load receives the high level each period; for the remainder of the switching period T_s, the load is connected to ground. The average output voltage can be calculated from the duty cycle and the two voltage levels:

In the case of the buck converter V_LO=0 and V_HI=V_g. So, the average voltage applied to the load over one switching period T_s is: V= DV_g . A similar argument can be made for the input and load/inductor current to get the relation I_g=DI. An example of PWM working at 10kHz is shown below.

Note how the average value changes when we change the duty cycle. Getting the average value is done here using a digital moving average filter set to the switching frequency, but in the physical converter, it will be done with an LC network tuned to limit switching ripple in the output voltage and inductor current. The PWM frequency is the switching frequency, and the PWM period is the switching period. For this converter, we’ll use a PWM frequency of 10kHz, which gives us a period of 100μs. I’ll justify this selection in the next article when we select the transistors we’ll use to implement this converter.

Designing the converter circuit passives:

Thus far, I’ve used capital letters to denote steady-state DC average quantities. Switching converters also create switching ripple around these DC average quantities, specifically the output voltage V and inductor current I. The switching ripple seen by the load is attenuated by the LC output filter of the buck converter, and thus the switching ripples are determined by these passives, as well as the switching frequency and system inputs. Often, we start from a specification for inductor current ripple ∆I and output voltage ripple ∆V. These specifications might come from what the load we’re supplying can tolerate or interface standards and other regulations if we’re connecting to a bus shared by many devices. We then design the passives to meet those specifications. For this application, I’ve decided that 10% of nominal current is acceptable for the inductor current ripple, and 10% of nominal output voltage is acceptable for output voltage ripple. Numerically, this means the output voltage will vary between 2.97-3.63V, and the inductor current will vary between 0.45-0.55A. We can design the passives to meet this requirement.

In a buck converter, the output voltage ripple is caused by the inductor current ripple and is thus a function of it:

From the specifications given earlier, the inductor L= 2.7mH and the output capacitor C=15.2μF.

[1] R. W. Erickson and D. Maksimović, Fundamentals of Power Electronics. Springer Nature, 2020. doi: 10.1007/978-3-030-43881-4.

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