The Boost Converter is a non-isolated DC-DC converter topology which is used to derive output voltages that are greater in magnitude than the converter's input voltage. There are numerous articles available to understand the functioning of the boost converter and this post specifically contains detailed steps required to design and construct it.
Converter Specifications :
Vin (min) - 20 V DC
Vin (max) - 30 V DC
Vout - 75 V DC / ( 0.4 A )
Switching Frequency ( Fs ) - 80 kHz
Selection of the switch-mode controller :
In order to select the switch-mode controller IC, it is essential to find the maximum duty cycle at which the converter is expected to operate. The converter will operate at the maximum duty cycle at minimum input voltage and at rated load on the output. The converter efficiency is assumed to be 0.8 i.e. 80%.
[1]
Hence, a controller IC needs to be selected whose duty cycle can reach the maximum required duty cycle whenever required. For that reason, the UC3843 converter IC is selected. It is a very versatile IC which can be used to control numerous topologies and has a provision to implement current-mode control/ voltage-mode control/ both.
Calculation of the desired Inductance :
While the converter operates, the inductor is subjected to a continuously varying current that flows through it. The ripple current is the maximum allowable swing between the current magnitude with respect to the DC current. Since it is a boost converter, the ripple current through the inductor will be the product of the output ripple current and the converter gain. The ripple current is considered 0.2 i.e. 20% of the rated output current.
[1]
After calculation of the maximum allowable ripple current, the minimum value of the inductor required to stay within the limits of the ripple current can be calculated from the equation below. If the inductor is increased beyond this value, it will lead to further decline in the inductor ripple current.
[1]
Inductor Design :
Once the value of the required inductance is calculated, it is time to move on to the the calculations for the physical design of the inductor. The method used for designing the inductor is called the Area-Product method.
The Area-Product (Ap) of any core is the product of the Effective Cross Sectional Area (Ac) and the Window Area (Aw). i.e. Ap = AwAc
While designing any inductor, it is important to know the following parameters :
- Maximum Current
- Frequency of Operation
- Nature of applied voltage ( Sine, Square, Triangular, PWM, etc. )
The maximum current that the inductor will be subjected to can be found out by the following formula. The inductor has to be designed for this current rating or a higher current in order to avoid core saturation.
The inductor is responsible for storing a certain amount of energy that needs to be free-wheeled during the off-time of the converter to ensure proper voltage regulation at the output. This is the amount of energy that needs to be repetitively stored in it during every switching cycle and signifies the power handling requirement of the inductor.
[2]
This approach goes by calculating the minimum required area product of a ferrite core to successfully achieve the power handling requirement of the application.
All the variables in the equation are handled in the MKS system.
E = Energy handling required in Joules
Window Utilization Factor (Kw)
Some of the window area in which the windings of the inductor are placed is occupied by the bobbin/former, insulation/ Mylar tape and also the enamel insulation on the magnet wire. It is safe to assume that only 60% of the window area will be available to accommodate the windings. (Kw = 0.6)
Crest Factor (Kc)
The crest factor is the ratio of the peak value to the RMS value. The crest factor is dependent upon the type of waveform that the inductor is subjected to.
Square : 1.0
Sine : 1.414
PWM : sqrt(1/Dmax)
Since, the boost inductor is subjected to a PWM waveform with Dmax = 0.7866 (78.66%) for the required application, the resultant crest factor is Kc = sqrt(1/0.7866) = 1.127
Current Density (J)
A lower current density results in lesser copper losses and reduced winding heating during operation. Inductors are designed to operate at current densities ranging between 3 A/sq.mm to 5 A/sq.mm. Operating at a any lower current density is not a problem, but will result in increased winding area requirement. J = (3 A/ 10^-6) = 3 x 10^6
Operating Flux Density (B)
The inductor/transformer is generally designed to operate at 25% of the saturation flux density of a core. Since the core material is ferrite, it is safe to operate the inductor at 0.2 Tesla with 20 kHz switching frequency. When the switching frequency is increased beyond 20 kHz, the operating flux density is de rated in order to avoid switching losses at higher frequencies. I have considered operating the inductor at 0.13 Tesla for the application switching at 80 kHz.
[2]
The pot core P30/19 has an area product of 10160 mm^4, cross sectional area (Ac) of 136 sq.mm, winding area (Aw) of 74.7 sq.mm and is sufficient to handle the amount of power required since it's area product is greater than the required area product. Number of turns is given by :
[2]
Wire gauge selection:
The thickness of the wire is dependent upon the selected current density of operation. The RMS value of the current flowing through the conductor will be the ratio of the peak current to the crest factor.
Irms = Imax/Kc
Hence, Irms = 1.65 A/1.127 = 1.465 A
The cross sectional area of the wire to operate at 3 A/sq.mm with a RMS current of 1.465 A is :
[2]
A magnet wire of 21 SWG has a cross sectional area of 0.51890 sq.mm and is suitable for use at the specified current density. To check whether the winding will be able to fit into the available winding area, a check satisfying the below condition should be performed.
Condition : Available Area > Required Area
[2]
The condition is satisfied, and hence the core can be used to wind the required inductor.
Air Gap Calculation :
There is a necessity to introduce an air gap while constructing the inductor and it is required to avoid core saturation at high inductor currents. The calculation for the air gap :
[2]
Capacitor Selection :
The required output capacitor ( Cout ) can be calculated from a pretty straight forward equation. The output current is driven by the capacitor during the on time of the converter. Considering that the desired output ripple is 20mVpp, the resultant equation is :
[1]
The output capacitor can be 2 x 150 uF Electrolytic capacitors shunted to each other in order to reduce the ESR exhibited by the capacitors. 150uF instead of 100uF ones in order to compensate for the extra ripple created due to the ESR of the capacitor.
The input capacitor can be 2 x 560 uF Electrolytic capacitors shunted to each other in order to reduce the ESR.
Provision of Feedbacks :
Current Sense Resistor : To include cycle by cycle current limiting in case the current tries to exceed the rated input current.
Voltage Divider n/w : To attenuate the voltage to a desired level in order to feed back the output voltage to the switch mode controller.
Schematic of the Boost Converter
The diodes need to be ultra fast rectifiers to exhibit fast switching characteristics and to minimize switching losses.Also, it should be made sure that the diodes and the MOSFETs have a sufficient PIV/Breakdown Voltage respectively to sustain under transient conditions.
The MUR420/ UF5048 or any other ultra fast diodes can be used. I have used an IRFP250 MOSFET since that was the one that I had at home. Any other suitable MOSFET can be used instead of it.
The detailed explanation of the feedbacks and control structure of the converter will be explained in the second part of this post.
References :
[1] "Basic Calculation of a Boost Converter's Power Stage" Texas Instuments Application Note - SLVA372C
[2] "Design of Magnetic Elements for Switched Mode Power Converters" - Umanand, L., Bhat, S.R.
