# PFC Controller Modeling: For Buck, Boost, and SMPS Designs

If we look back sixty years ago at consumer electronics, we gain an interesting view of power supply technologies. Older power supplies for televisions relied on vacuum tube shunt regulators and flyback transformers that delivered 15 to 30 kilovolts to a cathode ray tube (CRT). Everything in low and high voltage power supplies emitted heat; “efficiency” simply didn’t exist as a priority.

However, the emergence of digital, optical, and wireless telecommunications systems changed everything. During 1978, participants in the International Telecommunications Energy Conference began addressing the need for energy-efficient and cost-effective power systems for the public switched telephone network.

Today, we see an electronics industry clearly focused on power supply efficiency, reducing power consumption, and mitigating electromagnetic interference. That focus also becomes apparent through the regulatory pressures placed on improving standby power consumption as well as active mode efficiency. As an example, electrical equipment produced in Europe and Japan complies with the IEC 61000-3 standard. The international Energy Star 6.0 requirement addresses standby power requirements. Each of those points increases the need for optimal power factor correction functions that maximize the available amount of effective power.

## PFC Controllers: Power Efficiency in Power Supply Circuits

Efficiency in the simplest form tells us that if the output power of a power supply circuit equals 75 watts and the input power equals 100 watts, the efficiency equals 75 percent. However, the quest for methods to reduce electrical power consumption goes beyond the output power of a circuit equaling a fraction of the input.

Effective power represents the average of the instantaneous product of current and voltage over a cycle and is the power dissipated due to a resistive load. In other words, effective power translates into the portion of the power that performs work. The effective power drawn by a load will have a lower value than the product of the voltage across the load and the current flowing through the load.

## Power Factors and RMS Voltage Values

Connecting a reactive load across an AC power supply results in some the power returning to the source. When we calculate the apparent power of the circuit, we use RMS (Root Mean Square or the square root of the mean square) values. For alternating currents, the RMS value equals the value of direct current that would produce the same average power dissipation in a resistive load.

Apparent power represents the product of the RMS value of current multiplied by the RMS value of voltage and is the total amount of power supplied to an electric circuit. The RMS voltage of a sinusoidal waveform equals the peak voltage value multiplied by 0.7071.

The power factor (PF) of a circuit equals the effective power divided by the apparent power. We express effective power in watts and the apparent power in volt-amps.

PF = Effective Power (watts) / Apparent Power (VA) or

True Watts / Volts x Amps

We can also define power factor as the phase displacement of voltage and current or as the cosine of the phase angle between the voltage and current waveform.

PF = CosƟ

If both the current and the voltage remain in phase and have a perfect sinusoidal shape, the power factor equals 1.0 or the maximum possible value of power factor. Typical power factor ratios produce values less than one expressed in a decimal format. If both the current and voltage have a perfect sinusoidal shape but are out-of-phase, the power factor equals the cosine of the phase angle and a value of less than one.

*Hopefully your circuit’s power supply doesn’t require a full arc flash prevention suit.*

A low power factor tells us that device, computer, or appliance consumes more than the applied power. This over-consumption translates to wasted power generation. Power factor correction (PFC) shapes the input current waveform of an off-line power supply for the purpose of maximizing the real power arriving from the line voltage.

As a result, a power correction circuit increases the power factor. With power factor correction in place, the load presented by a computer, device, or appliance emulates a pure resistor. As a result, the drawn—or wasted--reactive power has a minimal or zero value.

## PFC Controller Modeling with SMPS

Switched-mode power supplies consist of a half-wave or full-wave rectifier input circuit followed by a capacitor that maintains a voltage of approximately the peak voltage of the input sinusoidal wave until the next peak charges the capacitor. Alternating current at the input of the capacitor flows only if the input AC voltage ranges higher than the capacitor voltage. Because the capacitor serves as a capacitive load, the circuit draws current from the input only at the peaks of the input waveform.

Because the energy in the current pulse must sustain the load until the next peak, the capacitor receives a significant charge over a short time period. With the capacitor slowly discharging the energy into the load, the current pulse ranges from five to ten times more than the average current. However, the alternating current pulses also contain high frequency components that distort the sinusoidal waveform.

From the perspective of the line voltage, the power supply appears as a non-linear impedance with the current and voltage in phase. The higher harmonic content of the current pulses, though, contributes to the apparent power and drives the power factor to a distortion factor of approximately half the maximum power factor value or .5 to 6.

## Power Factor Corrected, Harmonic Distortion, and Converters

Power Factor Correction (PFC) reshapes the current and reduces the unwanted total harmonic distortion (THD). When we speak about power factor correction, we can use either passive or active power factor correction to accomplish the task. Placing an inductor between the input rectifier and the storage capacitor in a lower voltage power supply can keep harmonics below specified limits.

Power supplies that handle high voltages, though, require an active power factor correction circuit. Using a typical switched mode power supply as an example, placing a switched-mode boost converter between the input rectifier and the storage capacitor shapes the input current waveform so that it matches the input voltage waveform.

Boost and buck converters make up the most-used PFC topologies. A boost converter places a filter inductor on the input side of the power supply to establish a smooth continuous input current waveform. With a continuous input current, filtering becomes easier. Boost converters may operate in either the continuous conduction mode (CCM), discontinuous conduction mode (DCM), or the critical conduction mode (CrCM). Of those three modes, most PCB designs use the CCM boost topologies.

*Understanding harmonics fundamentals will inarguably help in your power supply designs*

The CCM operation uses a large filter inductor that maintains the full load inductor current ripple between 20 to 40 percent of the average input current. As a result, the circuit achieves a lower peak current, reduced device conduction losses, lower turn-off losses, and a smooth, lower amplitude high frequency ripple current. In contrast, CrCM uses constant on-time control. The line voltage and the operating frequency change across the 60 Hz cycle and—in turn—produce a high input ripple current. While the CCM boost topology can work for low, medium, and high power designs, the higher input ripple current limits the use of the CrCM boost topology to low and medium power supplies.

Buck converters work as step-down converters and have an output voltage less than the input voltage. A typical buck converter operation begins with the switching on of a power transistor. As the input current increases, it flows through the filter inductor, filter capacitor, and a load resistor. Because of the reliance on only one transistor, buck converters offer simplicity and high efficiencies that range to 90 percent. Although the inductor in a buck converter limits the rate of change of load current, buck converters have a discontinuous input current and always require a smoothing input filter.

With Cadence’s suite of design and analysis tools, you’ll be sure to find any power supply and power efficiency demands met with ease and grace. Working through the OrCAD PSpice Simulator, you’ll be able to model and simulate your power supplies long before you begin layout for components to ensure proper voltage and heat regulations have been met.

If you’re looking to learn more about how Cadence has the solution for you, talk to us and our team of experts.