The final result for minimum capacitance will be as shown below. The capacitor is designed such that the maximum input voltage will be with stand by capacitor voltage. Ideally both are considered equal i. The ESR factor contributes to capacitor loss. The ESR factor can be reduced for better efficiency by two methods. Either by paralleling capacitors or by choosing capacitor with low ESR. By putting the value of q in this equation, the result will be as given below.

I o is considered as I o max. Therefore, the above equation become. This is the required capacitance value while the RMS current rating equation can be found as. The following table shows all the important equations required for the designing of Buck converter.

To design a buck converter that will convert volt input DC to 2. For such conversion we have some known data and some parameters are required. Proper selection of components is must for successful conversion from 12v to 2. This example will help to design buck converter for any conversion ratio. The duty cycle D can be found from the output input voltage ratio.

Critical inductance can be found from previously found equation. The critical inductance can be chosen as. The peak current rating can be found according to the equation. I Lmax 1. Forward diode current according to the given equation will be. Maximum switch voltage according to the equation derived above. While maximum switch current. Minimum capacitance required for the converter according to the equation will be.

Near value for this required capacitance can be. Voltage rating of capacitor. Losses for the buck converter must be considered when the efficiency estimation is required for it. Several major losses that are to be considered are given below and discussed briefly one by one. This on resistance greatly contributes in over losses.

The two graphs given below show the exponential increase of on state resistance. The other graph shows the increase of on-state resistance with increase in temperature. Drain current in this case 7. Switching losses are related with the transition time of the switch. During the transition time, both current and voltage are non-zero.

Therefore, the main switching losses are due to overlapping of current and voltage. The given graph show that how losses occurs in transition states. The voltage across the switch approaches to zero with a specific slope while current across it increase. During this time losses occur. The same case is with turning OFF the switch. During this time current approaches to zero with a specific slope while voltage drop across it increases.

This is how transition losses occur during transition time. According to the above discussion the overall power losses P loss is equal to the power losses during turn-on time and turn-off time. We know that losses during turning-on time is.

While losses during turn-off time is. By putting both these values in the above equation, we will get the following result. By taking common term, the final form for the overall switching losses will become. Whereas the gate drive losses come from two parameters i. By considering both, the mathematical form for gate drive losses is. Losses that occur when diode is completely on or when diode is completely in off state.

Static losses that occur when diode is in on state are known as forward static losses. In contrast, the losses occur in off state is known as reverse static losses. For more precise value of the diode forward loss, the rms loss that occurs due to diode dynamic resistance , rd is added. All these calculations were for forward losses. While losses for reverse state are. This section will discuss the losses associated with diode connected in practical buck converter.

The same is the case with diode as it is for switch discussed previously. This section will discuss losses associated in both turn-on time and turn-off time. The losses associated in turn-on time are characterized by forward recovery time t fr and by low value of peak forward voltage V FP. By knowing above two value from the data sheet, the on-loss P ON can be calculated from the given equation. The losses associated in turn-off time are associated with the time for which diode voltage and current overlaps.

This overlap manly contributes in reverse recovery time. This is really important equation for calculating turn-off losses in non-ideal case. Some of unknown values required for the above equation can be found from the following equations. There can be at most three inductors in buck converter that are storage inductor, coupled inductor and filter inductor.

Therefore, the losses of all these inductors are considered in buck converter. In most of buck converters, the coupled inductor is not used but storage inductor and filter inductor are must. Therefore, losses of their two inductors are considered. Some of the losses that occur in magnetic components are as given as. Above is the general form of Steinmetz equation whereas the modified form of this equation is as.

There are two main type of losses associated with inductor i. This section will discuss inductor copper loss while core losses are discussed separately. Inductor copper loss, as its name suggests that these losses are associated with the winding of the inductor. As the winding is made of copper wire therefore, it is known as inductor copper losses. These losses are resistive in nature because the winding have some resistance. These losses are not significant that is why these are ignored for ideal buck converter while considered for more precise calculations.

Inductor copper losses occur due to the resistance of the winding. Core losses of an indicator in buck converter are mainly affected by three factors i. The general form of the formula for inductor core loss is given as. Values required for these constants need be as low as possible for low core losses. Some of well-known manufacturers and companies provide with very low values of these coefficients for better efficiency. This resistance contributes to power loss in buck converter known as Capacitor ESR loss.

R ESR. A buck converter has already been designed in this article. But that example was for pure ideal buck converter which does not exist in practical life. This section will show how to use previously derived equations to compute the values of different components required for buck converter.

This example will show that how to design non-ideal buck converter for given parameters. We will design a non-ideal buck converter for the given parameters according to the previous discussion and derived equations. Given parameters. Nominal output voltage of the system is. Nominal input voltage of the system is. Maximum output power is. Switching frequency is.

Maximum ripple percentage is. Minimum percent CCM is. Calculations for Designing. Nominal duty cycle for the non-ideal buck converter is. Inductor value selection: The critical inductance formula is a little bit different that is. Conclusion: We have already discussed that the value of inductor must not be chosen less than Critical inductance.

Therefore, the value of inductor can be any value greater than this critical value. Hence choosing Lo as. Calculating peak inductor current according to the above discussion is.

When does Maximum Power Transfer occur? Answer: conjugate matched impedance Z f. You have Voc and Isc coming from the PV in two distinct impedances, "open circuit and short circuit". How do you achieve maximum power transfer? Moritz von Jacobi published the maximum power transfer theorem around ; it is also referred to as "Jacobi's law".

The theorem results in maximum power transfer, and not maximum efficiency. For a voltage converter, you want maximum efficiency but for a power converter like a PV you want maximum power transfer to capture all the power that is available. This is done by conjugate impedance matching a switched inductor using primary PWM to store energy from a PV current source with a capacitor load on input such that the average impedance of the switched inductor over one cycle is EQUAL R but opposite reactance, X f at some frequency , f.

Then can expect Jacobi's Law to work. However for voltage regulation and high efficiency, in voltage step down or up converters you want any load to have minimal effect on the regulated voltage. Go read. Using a simple switched voltage converted from 24 or 36 to 12V assumes a low impedance source to have high efficiency. Solar Panels can be modeled as sun controlled current sources high impedance with a zener voltage limit Voc when open circuit. You can convert the Norton equivalent circuit to a Thevenin with some load testing and actually limit the current load if the input power gets reduced using a few transistors and zener with an optical PD to regulate the current limit.

But most people buy an MPPT convertor to do this. Some hunt for max power by sensing current and voltage in and out, others use an algorithm based on pulsed no load Voc and other methods are documented in this forum. Whereas a SMPS voltage converter assumes the source is a low impedance voltage source to achieve maximum efficiency. The input current to a SMPS depends on the demand charge for the battery charger.. SO there must be two separate conversions. One for effectively matched impedance to the PV that limits current out with solar input.

One for voltage regulation and output current to the battery according to State of Charge and current limits imposed. So an ideal PV converter needs 2 stages of regulation to utilize the maximum power transfer theorem because the PV is not a voltage source. It is possible to combine these two regulators into 1 by using one or more Photo Diodes PD for redundant feedback.

BTW other newable power sources also have this characteristic where the impedances must be matched at maximum power transfer. Wind, water , nuclear? For example excess load would act as a brake to window power turbine and thus reduce the available wind energy and optimum RPM at max Hp. When the conditions are such that the power is in excess of what can be used, the switch opens up.

It does it in pulses as it attempts to regulate the voltage. Hence the name pulse-width modulation. It is never fully off - just the duty cycle changes to adjust.

So yes, power is not used but it is power that couldn't have been used. Like when the battery is full and there is no other load, like an inverter.. PWM pulse-widths are continually changing depending on the load and type of battery. You don't want sealed lead-acid batteries bursting, nor do you want open flooded batteries boiling dry. So it quenches the power to keep things regulated.

In the end you get all the power you can be used but any reduction is not due to inefficiency. It is under program control. Wikipedia definition of PWM with diagrams. Here is today's plot of my secondary PWM charger with a 50 Watt panel on a 12 Volt marine battery - it powers the motors which aim my soar panel pairs. The downward spikes are when the motors 3 of them activate to reposition the panel pairs.

The PWM charge controller is just one piece in the overall system. Every single device or connection in the system is going to lose some power. Doesn't matter what kind of controller you use. That's just physics. Increased Efficiency.

Programmable Fixed Frequency of kHz kHz. Improved ease of use. Optimize the design for size, cost or efficiency. Wide Input Voltage 4.

Allows use in many versatile applications. Adapts to changes in battery voltage. I constructed the buck converter shown below. As i saw, in most buck converter schematics the pulse generator is connected like i did positive side on the transistor gate and negative on the drain.

My problem is that when i measure the gate voltage is a pulse of approximately 10Volts isntead of the 5Volts i gave to V2 of the pulse generator Furthermore, if i would like to construct it to a pcb and connect a pwm pulse width modulation signal from a microcontroller instead of pulse generator of PSpice how will this connection be done?

Thank you. Hence as per your circuit measuring gate voltage with repect to ground will give more voltage than pulse applied since voltage at source terminal wil add up in measurement..