Calculating Inductors in Buck Boost Converters

In this post we try to understand the method of dimensioning or calculating inductors in buck boost converter circuits in order to ensure an optimal performance from these devices.

We take the example of IC 555 boost converter and 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.

In a few of my earlier posts we comprehensively studied regarding how SMPS buck and boost converters work, and we also deduced a few fundamental formulas for evaluating the important parameters like voltage, current and inductance in these converter circuits.

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 Boost Equations

For calculating inductors in buck boost SMPS circuits, we could derive the following two concluding formulas for a buck converter and for a boost converter respectively:

Vo = DVin ----------  For Buck Converter

Vo  = Vin / (1 – D) ----------  For Boost Converter

Here D = Duty Cycle, which is = Transistor ON time / ON + OFF time of each PWM cycle

Vo = Output Voltage from the converter

Vin = Input supply voltage to the converter

From the above derived formulas, we can understand that the 3 basic parameters which can be used for dimensioning the output in an SMPS based circuit are:

Main Parameters Associated with Buck Boost Converter

1) The Duty cycle

2) The Transistor ON/OFF time

3) And the Input Voltage level.

This implies that 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 or boost converter, we still do not know how the inductor can be built for getting an optimal response in these circuits.

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.

Configure a Boost Converter Using IC 555

A simple IC 555 based boost and buck converter designs  are shown below which could be used for determining the best possible inductor value for a particular SMPS boost converter circuit.

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.

Circuit Diagram Boost Converter

Optimizing the Potentiometer Controls

The above set up shows a basic IC 555 PWM circuit, which is equipped with separate potentiometers for enabling an adjustable frequency, and an adjustable PWM output at its pin#3.

Pin#3 can be seen connected to a standard boost converter configuration using the TIP122 transistor the inductor L, the diode BA159 and a capacitor C.

The transistor BC547 is introduced to limit the current across the TIP122 so that during the adjustment process when the pots are being tweaked the TIP122 is never allowed to cross the breakdown point, thus the BC547 safeguards the TIP122 from excessive current and makes the procedure safe and foolproof for the user.

The output voltage or the boost voltage is monitored across C for a maximum optimal response during the entire testing process.

The IC 555 boost converter could be then manually optimized through the following steps:

• Initially, set the PWM pot to produce the narrowest possible PWM at pin#3, and the frequency is adjusted to about 20kHz.
• Take a digital multimeter fixed over above 100 V DC  range and connect the prods across C with appropriate polarity.
• Next, gradually adjust the PWM pot and monitor as long as the voltage across C continues to rise. The moment you find this voltage dropping, restore the adjustment to the previous position which yielded the highest possible voltage on the pot, and fix this pot/preset position as the optimal point for the selected inductor.
• After this, tweak the frequency pot similarly for further optimization of the voltage level across C, and set it to achieve the most effective frequency point, for the selected inductor.
• For determining the duty cycle one could possibly check the PWM pot resistance ratio, which would be directly proportional to the mark space ratio of the pin#3 output duty cycle.
• The frequency value could be learned through a frequency meter or by using the frequency range across the given DMM if it has the facility, this could be checked at pin#3 of the IC.

Your inductor parameters are now determined and could be used for any boost converter for the best optimal response.

Determining Current for the Inductor

The current spec of the inductor could be increased by simply using many parallel wires while winding it, say for example you could use around 5 nos of 26SWG wires in parallel for empowering the inductor to handle 5amps of current. and so on.

The next diagram shows the process of optimizing and calculating inductors in SMPS, for a buck converter application.

Circuit Diagram Buck Converter

The same process applies for this set up too, as was done with the above explained boost converter design.

As can be seen the output stage is now altered with a buck converter set up, the transistors are now replaced with PNP types and the positions of the inductor, diode changed appropriately.

Thus, by using the above two methods anybody can determine or calculate inductors in buck boost smps circuits without using complex and unfeasible formulas.