How to Calculate a Buck Converter Circuit

In this post I have explained the method of dimensioning or calculating inductors in buck converter circuits in order to ensure an optimal performance from these devices.

We take the example of IC 555 buck converter typologies, and try to understand the optimizing techniques through equations and manual adjustments, for achieving the most optimal output response from these converter designs.

You may want to summarize the details from the following articles, before embarking on the present article which deals with the inductor designing methods.

How Boost Converters Work

How Buck Converters Work

Basic Buck Converter Equations

The crucial specifications needed to design a buck converter are as given below::

• Input Voltage (V_in)
• Output Voltage (V_out)
• Output Current (I_out)
• Switching Frequency (f_s)

Duty Cycle Calculation

Now, the crucial element required for calculating the inductor, is the duty cycle. We can use the following formula for calculating the duty cycle:

D = V_out / V_in

The next crucial thing for calculating the buck inductor is the Ripple Current, which can be calculated in the following manner:

Target Inductor Ripple Current (Δ_IL): As a rule of thumb, you can choose 10% of output current.

Calculating the Buck Inductor

Now, finally we can calculate the buck inductor, using the following formula:

L = (V_OUT × (1 - D)) / (Δ_IL × f_s)

Next, we need to calculate the output filter capacitor, which requires the Ripple Voltage ΔV_OUT

As a rule of thumb, we can take the Voltage Ripple (Δ_Vout) as 1% of output voltage.

Now, we can calculate the value of the output capacitor in the following manner:

Output Filter Capacitance Calculation for Buck Converter:

C_OUT = Δ_IL / (8 × f_s × Δ_Vout)

When we design a buck converter, the output ripple voltage Δ_Vout is mainly affected by two things, the inductor ripple current ΔIL and the output capacitor C_out.

You might be wondering where that factor of 8 came from.

It appears when we use an estimate to connect the peak-to-peak ripple voltage, peak-to-peak ripple current, and capacitance value. We assume that the ripple waveform is shaped like a triangle, which is a popular method in these computations.

So, in simple terms, number 8 is simply the result of reducing our arithmetic while preserving everything relevant to how the output ripple acts in continuous conduction mode (CCM).

Choose an output capacitor rated at least 250 μF with a voltage rating above 100V and low ESR.

Diode Selection

Reverse Voltage: Greater than input voltage with a safety margin.
Average Current Rating: Should be 1.5 times higher than the output current.

Switch (MOSFET) Selection

For the MOSFET to work efficiently, make sure to consider the following parameters:

Voltage Rating VDS of the MOSFET should be higher than the input voltage, typically 1.2-1.5 times.

Current Rating I_D of he MOSFET must be selected so that the MOSFET can handle peak current.

The R_DS(on) value must be selected to be minimum to reduce conduction losses.

By appropriately adjusting any one of the above parameters it becomes possible to tailor the output voltage from the converter. This adjustment could be implemented manually or automatically through a self adjusting PWM circuit.

Although the above formulas clearly explain how to optimize the output voltage from a buck converter, we still do not know how the inductor can be built for getting an optimal response in these circuits.

Solving an Example Buck Converter Design

Let's say we want to design a buck converter with 60V input and 12V output with 5 Amp current, let's calculate the above discussed parameters.

Given Specifications

• Input Voltage (V_in): 60V
• Output Voltage (V_out): 12V
• Output Current (I_out): 5A
• Switching Frequency (f_s): Let us assume 100 kHz (a common choice for this power range)

Duty Cycle Calculation

• Formula: Duty Cycle (D) = V_out / V_in
• Calculation: D = 12 / 60 = 0.2
• Result: Duty Cycle (D) = 20%

Inductor Selection

• Target Inductor Ripple Current (ΔIL): Assume 10% of output current, so:
• Δ_IL = 0.1 × I_out = 0.1 × 5 = 0.5 A
• Inductance Calculation:
• Formula:
• L = (V_out × (1 - D)) / (Δ_IL × f_s)
• Calculation:
• L = (12 × (1 - 0.2)) / (0.5 × 100,000) = (12 × 0.8) / 50,000 = 9.6 / 50,000 = 0.000192 H
• Result:
• Inductance (L) = 192 μH
• Choose an inductor with a value close to 192 μH, rated for at least 5A current.

Output Capacitor Selection

• Target Voltage Ripple (Δ_Vout): Let us assume 1% of output voltage, so:
• Δ_Vout = 0.01 × V_out = 0.01 × 12 = 0.12 V
• Output Capacitance Calculation:
• Formula:
• C_out = Δ_IL / (8 × f_s × Δ_Vout)
• Calculation:
• C_out = 0.5 / (8 × 100,000 × 0.12) = 0.5 / 9600 = 52.08 μF
• Result:
• Output Capacitance (Cout) = 52 μF
• Choose an output capacitor rated at least 52 μF with a voltage rating above 12V, and low ESR for handling ripple current.

Diode Selection

• Reverse Voltage: Greater than input voltage (60V), with a safety margin.
• Average Current Rating: Should be higher than the output current, so choose a diode rated for at least 5A (ideally 6A for reliability).

Switch (MOSFET) Selection

• Voltage Rating: Higher than the input voltage, typically 1.2 to 1.5 times Vin (60V), so choose a MOSFET rated for at least 80-90V.
• Current Rating: Should be able to handle peak current, so at least 8A (10A is recommended for safety).
• Low RDS(on): To reduce conduction losses and increase efficiency.

Final Results for our example 60V to 12V Buck Converter Design

• Duty Cycle: 20%
• Inductor: 192 μH
• Output Capacitor: 52 μF (voltage rating > 15V)
• Diode: Reverse voltage > 60V, current rating > 5A
• MOSFET: Voltage rating > 80V, current rating > 5A, low R_DS(on)

Using Practical Trial and Error Method

You may find many elaborate and researched formulas for settling this issue, however no new hobbyist or any electronic enthusiast would be interested to actually struggle with these complex formulas for the required values, which could actually have more possibility of providing erroneous results due to their complexities.

The better and more effective idea is to "calculate" the inductor value with an experimental set up and through some practical trial and error process as explained in the following paragraphs.

The inductor L may be initially made arbitrarily.

The rule of the thumb is to use the number of turns slightly higher than the supply voltage, therefore if the supply voltage is 12V, the number of turns could be around 15 turns.

1. It must be wound over a suitable ferrite core, that could be a ferrite ring or a ferrite rod, or over an EE core assembly.
2. The thickness of the wire is determined by the amp requirement which initially won't be a relevant parameter, therefore any relatively thin copper enameled wire would work, may be around 25 SWG.
3. Later on as per the current specs of the intended design, more number of wires could be added in parallel to the inductor while winding it in order to make it compatible with the specified ampere rating.
4. The diameter of the inductor will depend on the frequency, higher frequency would allow smaller diameters and vice versa. To be more precise, the inductance offered by the inductor becomes higher as frequency is increased, therefore this parameter will need to be confirmed through a separate test using the same IC 555 set up.

Basic Circuit Diagram Buck Converter