**Buck Converter Basic Function**

Before going to buck converter design tutorial, we will discuss first how buck converter works in order to fully understand the following tutorial. A buck converter is a switching converter with a voltage output lower than voltage input. It is also called as a step-down switching converter.

A buck converter has only four main parts. They are the switch (Q1 in below figure), diode (D1 in below figure), inductor (L1 in below figure) and capacitor filter (C1 in below figure). The input voltage VIN must be higher than the output voltage VOUT to qualify as a buck converter.

A buck converter is functioning as a voltage regulator but utilizing the switching action of a semiconductor part like BJT, MOSFET or IGBT. Q1 will switch on and off continuously, D1 acts as a freewheel diode, L1 will charge and discharge energy while C1 will store energy. Buck regulator is a low loss voltage regulator and with efficiency of more than 90% when properly designed.

**Buck Converter Basic Operation**

Buck converter operates by continuously turning ON and OFF a semiconductor switch like BJT, MOSFET or IGBT. The turning ON and OFF of the switch is determined by the duty cycle. The ideal duty cycle of a buck converter is simply

Duty Cycle = VOUT / VIN

Buck Converter Basic Operation–PWM is High

When the PWM is at high state, Q1 will conduct at saturation (very low voltage drop). D1 will be reversed biased and not part in the current loop. The current will flow from VIN, going to the channel of Q1, then charging L1 and a portion will charge C1 and finally the main current path will go to the load.

At this time, L1 will charge and the dot side will be at higher potential. L1’s current will ramp up linearly.

Buck Converter Basic Operation–PWM is Low

When PWM is low, Q1 will turn off and not anymore part of the current loop. The dot side of the inductor L1 will become negative potential as the L1 will reversed polarity but maintaining the same direction of current. The current path will be from the D1, to L1 that is discharging at this time, then to the load. At this time also, C1 energy will help providing the need of the load.

**Comprehensive Buck Converter Design Tutorial**

Basic function and operation of a buck converter has been tackled. So, here we go to our main topic which is buck converter design tutorial. Below is the outline of this buck converter design tutorial.

- Inductor Ripple Current Derivation
- Duty Cycle Derivation
- Inductor RMS Current Derivation
- Inductor DC Current Derivation
- Switch RMS Current Derivation
- Switch DC Current Derivation
- Diode RMS Current Derivation
- Diode DC Current Derivation
- Switch and Diode Voltage Derivation
- Switch Power Losses Derivation
- Switch Thermal Considerations
- Diode Power Losses Derivation
- Diode Thermal Considerations
- Inductor Power Losses Derivation
- Capacitor Ripple Current Derivation
- Efficiency Equation Derivation
- Sample Design with Parts Selection
- Design Template

**1. Inductor Ripple Current Derivation**

To derive the inductor current equations, it is important to know its waveform. By the way, a buck converter is can be categorized as CCM, TM or DCM. CCM stands for continuous conduction mode while TM stands for transition mode or sometimes called as boundary mode. On the other hand, DCM stands for discontinuous conduction mode. CCM and TM are having the same analysis while DCM requires different one. For high power applications, it is unlikely to intentionally operate the buck converter at DCM mode. This will result to a very high losses and impractical. However, there is a time that buck converter will enter DCM mode, and this is when the load is very light. So, the design point or component selection will be based on the heavy load and this is mostly at CCM. So, in this derivation, we will be considering a CCM operation. Below in green is the current waveform of the inductor operating at CCM. It rises linearly when the PWM signal is high. It then decreases linearly when the PWM signal is low.

When PWM is high, the analysis will be:

The key equation to use is the voltage across an inductor that is

VL = L X di / dt

When PWM is low, the analysis will be:

Both di_Ton and di_Toff will give the same result.

**2. Dutycycle Derivation**

If you examine the inductor current waveform, the rise and the fall are in equal magnitude. Therefore, both equations di_Ton and di_Toff above are can be equated and we derived final the duty cycle.

For more information on how to derive buck converter duty cycle, read the article http://electronicsbeliever.com/buck-converter-duty-cycle-derivation/

**3. Inductor
RMS Current Derivation**

Here, I will teach you all the buck converter inductor design formula. We will start with the inductor RMS current is the total of the RMS of di and Imin in below waveform. We will be doing integration here, but don’t worry I have made the analysis for you already.

**4. Inductor
DC Current Derivation**

Next buck converter inductor design formula will be for the DC current. But if you watch carefully on the buck converter schematic, the inductor is in series to the output load. Thus, the DC level of the inductor current is the same to the DC level of the load. This is the easiest derivation in this buck converter design tutorial 😊.

**5. Switch RMS Current Derivation**

The switch on the buck converter is could be a BJT, MOSFET or IGBT. In this tutorial let us use MOSFET as it is the most popular one in low to medium power applications. The current waveform of the MOSFET looks like below.

The RMS current of Q1 is the sum of the RMS of the area A1 and A2. A1 is a triangle while A2 is rectangle.

**RMS of Area A1**

**RMS of Area A2**

So, the RMS of the switch current will be

Simplifying to get rid of Imax

**6. Switch DC Current Derivation**

RMS current of the MOSFET is always higher than the DC current and it is the value to use in computing the power dissipation to get the worst case. However, the DC level is may be needed for whatever reason a designer to come up. So, let us include it in this buck converter design tutorial.

The total DC level is also the sum of the DC level of A1 and A2 in the above waveform.

Rewriting the equation to exclude Imax

**7. Diode RMS Current Derivation**

Referring to below waveform, we can calculate the RMS current of the diode. The diode will conduct only when the MOSFET is not conducting.

**8. Diode DC
Current Derivation**

We will still use above waveform in the determination of the DC current of the diode.

**9. Switch and
Diode Voltage Derivation**

VQ1 max = VIN max + VSpike

Vspike is due to the parasitic inductance and it can be assumed to be 40-70% of VIN.

VD1 max = VIN max + Vspike

Vspike is due to the parasitic inductance and it can be assumed to be 50-120% of VIN.

**10. Switch
Power Losses Derivation**

The switch power losses are composed of two factors. First is conduction loss and the second is switching loss. Conduction loss is due to the fixed voltage drop on the switch while the switching loss is due to the switching action of the switch. In this tutorial we emphasize to use a MOSFET. So, belo equations are valid for the MOSFET.

**Conduction
Loss**

**Switching Loss**

**Total MOSFET Power Loss**

**11. Switch Power Stress and Thermal Considerations**

Power stress of the switch is just actual power dissipation divided by power capability.

Pstress = Pdissipation actual / Pdissipation capability

Power dissipation capability is can be derived from the datasheet information.

**For without heatsink (the switch is not mounted
on a heatsink):**

Pdissipation capability = (Tjmax – Tamax) / Rthjc

Where;

Tjmax – maximum junction temperature of the device

Tamax – maximum ambient temperature of operation

Rthjc – thermal resistance from junction to case

In case needed to compute for the device actual junction temperature, it can be done as below:

Tjactual = (Pdissipation capability X Rthjc) + Tamax

**For with heatsink (the switch is mounted on a heatsink):**

Pdissipation capability = (Tjmax – Tcmax) / (Rthjc + Rthchs +Rthhsa)

Where;

Tjmax – maximum junction temperature of the device

Tcmax – maximum allowed case temperature

Rthjc – thermal resistance from junction to case

Rthchs – thermal resistance from case to heatsink. This is the thermal resistance of the material that bond the heatsink and the case.

Rthhsa – thermal resistance from heatsink to air. This actually the thermal resistance of the heatsink used.

The actual device junction temperature is can be computed as:

Tjactual = [Pdissipation capability X (Rthjc + Rthchs +Rthhsa)] + Tcmax

**12. Diode Power Losses Derivation**

Ploss diode = Irms X VF

**13. Diode Power Stress and Thermal Considerations**

Power stress of the diode is just actual power dissipation divided by power capability.

Pstress = Pdissipation actual / Pdissipation capability

Power dissipation capability is can be derived from the datasheet information.

**For without heatsink (the diode is not mounted on
a heatsink):**

Pdissipation capability = (Tjmax – Tamax) / Rthjc

Where;

Tjmax – maximum junction temperature of the device

Tamax – maximum ambient temperature of operation

Rthjc – thermal resistance from junction to case

In case needed to compute for the device actual junction temperature, it can be done as below:

Tjactual = (Pdissipation capability X Rthjc) + Tamax

**For with heatsink (the diode is mounted on a heatsink):**

Pdissipation capability = (Tjmax – Tcmax) / (Rthjc + Rthchs +Rthhsa)

Where;

Tjmax – maximum junction temperature of the device

Tcmax – maximum allowed case temperature

Rthjc – thermal resistance from junction to case

Rthchs – thermal resistance from case to heatsink. This is the thermal resistance of the material that bond the heatsink and the case.

Rthhsa – thermal resistance from heatsink to air. This actually the thermal resistance of the heatsink used.

The actual device junction temperature is can be computed as:

Tjactual = [Pdissipation capability X (Rthjc + Rthchs +Rthhsa)] + Tcmax

**14. Inductor Power Losses Derivation**

The power loss of the inductor is composed of two parts: DC and AC losses. In low switching frequency and low power, AC loss is small and thus simply not included in the calculation. But for very high switching frequency, you can assume a switching loss almost the same to the DC loss. DC losses is also sometimes referred to copper loss while switching loss is also called core loss.

**15. Output Capacitor Selection**

Below output capacitance (C1) calculation is generic. However, specific controllers may have their own equation to derive the value of the output capacitance as this has something to do with the loop compensation. Considering no effect of ESR, equation below is can be used to determine the size of output capacitor.

C1 = di / (Fsw X Vripple)

For electrolytic capacitors the ESR is huge, so it needs to consider it in the analysis. The calculated capacitance above should have an ESR of not higher than below equation.

ESR = Vripple / di

Where;

ESR – equivalent series resistance

di – inductor ripple current

Fsw – switching frequency

Vripple – allowable output ripple voltage

**Ripple Current**

The selected output capacitor should have a ripple current rating of higher than the result of below equation.

Where;

Irms_inductor – inductor RMS current

I_load – load current

**16. Buck Converter Efficiency Equation Derivation**

Buck converter efficiency is can be computed using below equation.

Efficiency = (Pout / Pin) X 100%

Pout = Iout X Vout

Pin = Pout + Ploss total

Efficiency = [Iout X Vout / (Pout + Ploss total)] X 100%

Where;

Iout – load current

Vout – output voltage

Pout – total power losses

**17. Buck Converter Design Tutorial – Sample Design with Parts Selection**

We are done with all the necessary equations. Let us apply this buck converter design tutorial to actual design scenario.

**Given Values: **

By setting the %inductor_ripple to 100% means the converter operation is in the transition mode or boundary mode. But in this sample design we will set to 10% only that means a CCM operation.

**Dutycycle Calculation**

**Inductance Calculation**

For very detailed explanations on how the inductor of a buck converter derived, read the tutorial http://electronicsbeliever.com/sizing-the-inductor-of-buck-converter-and-setting-its-operation/

**Inductor
Ripple Current Derivation**

**Peak Current Calculation**

MOSFET Q1, Diode D1 and the inductor L1 will have the same peak current.

**Inductor RMS Current**

*Design Note 1: **Choose an inductor that has the value of L1_selected, with a RMS current rating higher than Irms_inductor and a saturation current rating higher than Imax.*

**Inductor Power Losses**

**MOSFET Q1 RMS and DC Current**

*Design Note 2: **Select a MOSFET with an RMS current or DC current higher than Irms_Q1. The peak current rating must be higher than Imax. The selected MOSFET should have voltage rating higher than the maximum input voltage. The rule of thumb is to select a voltage rating of twice the maximum input voltage. For instance, a MOSFET of 30V rating is can be used to a maximum input voltage of 12V.*

**MOSFET Q1 Power Losses**

To know the power losses, below information must be known:

**Conduction Loss**

**Switching Loss**

**Total Power Loss of Q1**

**MOSFET Q1 Power Capability Without Heatsink**

To know if the selected MOSFET Q1 is able to handle the **Ploss_total_Q1** above, the following information should be known.

**MOSFET Q1 Power Capability with Heatsink**

For with heat sink, additional informations must be known. For more detailed explanation regarding heat sink, kindly visit the tutorials provided by the link below. http://electronicsbeliever.com/heat-sink-thermal-resistance-calculation-easy-explanation/

**Diode D1 RMS and DC Current**

*Design Note 3: **The selected diode should have current continuous current rating higher than Irms_diode. The peak current rating must be higher than Imax. The peak inverse voltage rating of the diode must be higher than the maximum input voltage. A diode of 50V is suitable to an input voltage of up to 24V for instance.*

**Diode D1 Power Loss**

To know if the selected diode D1 is able to handle the **Ploss_diode** above, the following informations should be known.

**Diode D1 Power Capability without Heatsink**

**Diode D1 Power Capability with Heatsink**

For with heat sink, additional informations must be known.

For more detailed explanation regarding heatsink, kindly visit the tutorials provided by the link below. http://electronicsbeliever.com/heat-sink-thermal-resistance-calculation-easy-explanation/

**Output Capacitor C1 Selection**

Select a standard value capacitor higher than the computed.

**Buck Converter Efficiency Calculation**

Finally, the buck converter efficiency is

**Operation Mode Checking**

A buck converter is can be a CCM, DCM or transition mode. In CCM, the current of the inductor will not touch zero. On the other hand, the current on DCM will go below zero while the current on the transition mode is just exactly at zero mode.

**18. Design Template**

All the calculations in this buck converter design tutorials are incorporated to a design template in Mathcad format. You don’t need to do very deep analysis instead you just provide the information needed in each field then you can see the calculation result immediately. This is a proven design template that I used in many projects launched in the market. For more information about this design template, visit http://electronicsbeliever.com/downloads/buck-converter-design-template-mathcad/