1. Introduction

Definition: A Buck Converter is a type of DC-DC converter that steps down a higher input DC voltage to a lower output DC voltage. That is, the output voltage is always less than the input voltage.

Where, D is the duty cycle.

It is also called a Step-Down DC-DC Converter, Step-Down Chopper, or Buck Regulator. The name “Buck” originates from the fact that the inductor in the circuit “Bucks” or opposes the input voltage.

The buck converter efficiently converts a higher DC input voltage $V_{\mathrm{in}}$ into a lower, regulated DC output voltage $V_{\mathrm{out}}$. This is achieved through high-frequency switching, where an electronic switch alternately connects and disconnects the input source to an energy-storage element, typically an inductor.

The switch is controlled using Pulse-Width Modulation (PWM), which regulates the average output voltage by adjusting the ON and OFF durations of the switch.

2. Why Do We Need DC–DC Conversion?

Many electronic systems require DC voltages different from what is directly available from the source. Common scenarios include:

• Battery systems (Fixed voltage) supplying electronics that need regulated, lower voltages.
• Electric drives that require variable DC voltages for motor speed control.
• Power supplies for embedded systems, telecom, and automotive electronics.

DC-DC converters, or choppers, efficiently provide this flexibility by switching power devices between nearly-zero and low-impedance states, minimizing conduction and switching losses when designed properly.

3. Operating Principle of Buck Converter

The operation of the buck converter is based on the principle of storing energy in an inductor. The voltage drop across an inductor is proportional to the change in the electric current flowing through the device. A switching transistor is used between input and output and switches continuously ON and OFF at high frequency. To maintain a continuous output, the circuit uses the energy stored in the inductor.

The solid-state device (Like BJT, MOSFET, IGBT, etc.) acts as a switch for the circuit. There is another switch in the circuit which is a Freewheeling or Flywheel Diode (FD). The combination of these two switches forms a connection with a low-pass LC filter in order to reduce current or voltage ripples. This helps in generating a regulated DC output. A pure resistor is connected across this whole arrangement that acts as the load of the circuit. The figure below shows the circuit representation of the Buck Converter.

The controlled switch is turned on and off by using PWM (Pulse Width Modulation). PWM can be time-based or frequency-based. Time-based modulation is mostly used for buck converters because it is simple to construct and use. The switching frequency remains constant in time-based PWM. Whereas frequency-based modulation introduces variable frequency and often complicates LC filter design.

However, due to Lenz's law, the energy stored within the inductor will oppose the cause which produced it, so an induced current will be generated and the polarity across the inductor will be reversed when the switch changes state.

The Buck Converter circuit consists of the switching transistor together with the Freewheeling or Flywheel Diode (FD) circuit. The whole operation of the circuit can be divided into two modes:

• Mode I: Switch $S_1$ is ON and Diode $F_D$ is OFF.
• Mode II: Switch $S_1$ is OFF and Diode $F_D$ is ON.

4. Mode 1: Switch $S_1$ is ON and Diode $F_D$ is OFF ($0 \le t \le T_{\mathrm{ON}}$)

In this mode of operation, the power MOSFET (i.e., switch $S_1$) is closed and therefore the freewheeling diode (FD) is reverse biased by the supply voltage $V_s$ and therefore FD acts as an open switch. Thus switch $S_1$ allows the flow of current through it.

When a constant dc voltage is applied across the input terminal of the circuit, current flows while the switch $S_1$ is closed whereas the diode FD is reverse biased. Due to this current flow, the inductor $L$ stores energy in the form of a magnetic field. The capacitor also stores charge. The input voltage $V_s$ is applied to the switching node, and the inductor sees the difference between the input and output voltages:

Let us assume that during one complete switching cycle, the switch $S_1$ remains in the ON state for a duration of $T_{ON}$ and in the OFF state for a duration of $T_{OFF}$. The total switching period is:

The duty cycle $D$ is defined as:

Where:

• $T_{ON}$ is the ON interval
• $T_{OFF}$ is the OFF interval
• $V_s$ is the source or input voltage
• $V_o$ is the output or load voltage
• $T$ is the chopping period

5. Inductor Current Ripple $\Delta i_L$ of an Ideal Buck Converter (CCM) During $D T_s$

The voltage across an inductor is related to the rate of change of current through it. By definition:

ON Interval, Switch Closed, Duration $D T_s$

Applying Kirchhoff’s Voltage Law (KVL) around the loop when the switch $S_1$ is closed:

Write the ordinary differential equation (ODE) and separate variables:

Integrate both sides over the ON interval from $t=0$ to $t = D T_s$, with current limits from $i_L(0)$ to $i_L(DT_s)$:

Evaluating both integrals explicitly:

Defining the change in inductor current $\Delta i_L = i_L(DT_s) - i_L(0)$:

6. Mode 2: Switch $S_1$ is OFF and Diode $F_D$ is ON ($T_{\mathrm{ON}} \le t \le T$)

The second mode of operation begins when the switch $S_1$ is turned OFF. As a result, the inductor—which had stored energy during the previous interval—now releases this stored energy by acting as a source. The polarity of the inductor voltage reverses, which forward-biases the freewheeling diode $FD$ and allows it to conduct automatically.

When the switch is OFF, the switching-node voltage is zero for an ideal freewheeling path, while the output capacitor maintains the load voltage. Therefore, the inductor voltage is:

The inductor releases the energy stored in its magnetic field during the ON period, maintaining continuous current through the load via the conducting diode $FD$.

7. Inductor Current Ripple $\Delta i_L$ of an Ideal Buck Converter (CCM) During $(1-D)T_s$

Applying Kirchhoff’s Voltage Law (KVL) during the OFF interval:

Integrating over the interval $t = D T_s$ to $t = T_s$:

8. Steady-State Periodic Condition & Volt-Second Balance

In steady-state operation of a buck converter, the inductor current at the end of one switching period is equal to the inductor current at the beginning of that period ($i_L(T_s) = i_L(0)$).

Summing the volt-second contributions during ON and OFF intervals:

Simplifying yields the fundamental voltage gain relation:

9. Derivation of Inductor and Capacitor in Buck Converter

In Continuous Conduction Mode (CCM), the inductor current waveform is triangular in shape, consisting of a ripple component $\Delta i_L$ superimposed on the average current.

Inductor Current Ripple $\Delta i_L$ and Inductor Selection

Rearranging for inductance $L$:

Capacitor Voltage Ripple $\Delta v_c$ and Capacitor Selection

The relationship between the capacitor current and its voltage is $i_c(t) = C \frac{dv_c}{dt}$. By the principle of charge balance, the positive charge transferred to the capacitor during $i_L > I_L$ is:

10. Applications

A Buck converter is primarily used for converting a high DC voltage into a lower DC voltage. Its major applications include:

• Battery-powered systems such as battery chargers for mobile phones, laptops, and power banks.
• Self-regulating power supplies such as Switch Mode Power Supplies (SMPS).
• Point-of-load converters for PCs and motherboards.
• Solar charging systems and MPPT power stages.
• Automotive electronics and LED lighting drivers.
• Power audio amplifier circuits.

11. Conclusion

The Buck Converter, also known as a step-down DC–DC converter, efficiently converts a higher DC input voltage into a lower regulated output voltage using high-frequency switching and energy storage in inductors and capacitors.

By analyzing its operating modes, the converter’s steady-state relationship $V_o = D V_s$ was derived, demonstrating that the output voltage is directly proportional to the duty cycle of the switching signal.

Further, the integration of inductor current ripple and capacitor voltage ripple provided exact formulas for the sizing of $L$ and $C$ values to minimize ripple and ensure continuous conduction mode (CCM).

12. Important Questions & Technical Interview Answers

1. What is a buck converter, and why is it called a step-down DC–DC converter?

   Answer: A buck converter is a switched-mode power converter that changes a higher DC input voltage into a lower regulated DC output voltage. It is called a step-down converter because ideally $V_o = D V_s$, where $0 < D < 1$; therefore, $V_o < V_s$.

2. Draw the circuit diagram of an ideal buck converter and explain the function of each component.

   Answer: The circuit consists of a controlled switch (MOSFET), freewheeling diode, inductor, capacitor, and load. The switch controls input-energy transfer, the diode provides an inductor-current path while the switch is OFF, the inductor limits current ripple and stores energy, and the capacitor smooths the output voltage.

3. Explain the operation of a buck converter during the switch ON interval.

   Answer: The switch conducts and the diode is reverse-biased. The source supplies the load and stores energy in the inductor. The inductor voltage is $V_L = V_s - V_o$, so its current increases linearly.

4. Explain the operation of a buck converter during the switch OFF interval.

   Answer: The switch opens and the diode conducts. The inductor releases its stored energy through the diode, capacitor, and load. The inductor voltage is $V_L = -V_o$, so its current decreases linearly while remaining continuous in CCM.

5. What is Continuous Conduction Mode (CCM), and what condition must the inductor current satisfy in CCM?

   Answer: CCM is the operating mode in which inductor current flows continuously throughout the complete switching cycle. Its minimum value must remain greater than zero: $I_{L,\min} > 0$.

6. Explain how switching frequency, inductance, and capacitance affect the current and voltage ripples.

   Answer: Inductor-current ripple is inversely proportional to $L$ and $f_s$ ($\Delta I_L = \frac{V_o(1-D)}{f_s L}$), while capacitor-voltage ripple is inversely proportional to $C$ and $f_s$ ($\Delta V_o = \frac{\Delta I_L}{8 f_s C}$). Therefore, increasing switching frequency, inductance, or capacitance reduces ripple.

7. How would you choose an inductor for a practical buck converter?

   Answer: Select inductance for an acceptable ripple current (typically 20% to 40% of load current), then verify that the saturation current rating exceeds the peak inductor current ($I_{peak} = I_o + \Delta I_L/2$) and the RMS current rating exceeds operating current.

8. What is the difference between a synchronous and a non-synchronous buck converter?

   Answer: A non-synchronous buck uses a diode as the low-side freewheeling device, while a synchronous buck replaces it with a controlled low-$R_{DS(on)}$ MOSFET. Synchronous designs significantly reduce conduction losses ($I^2 R_{DS(on)}$ vs $V_F \cdot I$), improving efficiency especially at low output voltages.