SMPS Power Supplies

Site Directory:


Home
PSpice Simulation
Excel Design files
SMPS Design Help
Get free software

Prometheus Project
Nemesis Project

Discussion Forum
Voltage Loop Design
Solid State Lighting
Design Resources
SMPS terminology
Universities

Jobs

Power Supply Manufacturers db

Power Electronics
News & Forum


Power Lab

LLC Average Model
MOSFET switching
Flyback Design
Current Doubler
GaN or Silicon?
Boost PFC math
EN 50082-1

SMPS on LinkedIn


Privacy Policy
Legal

SMPS Design Notes

Boost Power Factor Correction

15-xx

Chapter 15.

Boost Power Factor Correction

Maximum Peak to Peak Ripple Current in the Boost PFC Inductor:

Because the switching frequency is usually more than three orders of magnitude higher than the line frequency, for a single switching cycle the inductor can be considered as having a triangle AC switching current with the instantaneous line current as a DC bias. After making this approximation, the following equations can be developed:

In general, for an inductor the following equation will apply:

General inductor equation                                             (15-1)

When the switch is ON, the current in the boost inductor will increase from Il to Ih:

Inductor equation, switch ON                                              (15-2)

Where Vi is the instantaneous input voltage.

When the switch is OFF, the current in the boost inductor will decrease from Ih to Il:

Inductor equation, switch OFF                                 (15-3)

We will eliminate now D between equations (15-2) and (15-3):

Inductor equation, duty cycle

Ripple current

General inductor equation

Voltage accross inductor

Inductor equation # 2

PFC ripple current peak to peak                                   (15-4)

To find at what instantaneous input voltage the peak to peak ripple current will have a maximum, we need to analyze the function:

Ripple current function of input voltage

Derivation of the ripple current function                                    (15-5)

From the above equation, we see that:

a) If the instantaneous input voltage can reach half of the boost voltage, the peak to peak ripple current has a maximum in this point. This maximum is:

Maximum peak to peak ripple current                                           (15-6)

The maximum instantaneous RMS value will be:

Ripple current RMS value                     (15-7)

b) If the instantaneous input voltage cannot reach half of the boost voltage, the peak to peak ripple current has a maximum when the instantaneous input line reach its peak.

In a normal design, 85-276Vac, or 176-276Vac, or 85-138Vac, the instantaneous input voltage would always reach a value equal with half of the boost voltage. The only situation when the instantaneous input voltage will not reach half of the boost voltage, is in a 85-136Vac design with 400Vdc boost voltage witch is unusual. This particular case will not be discussed further.

RMS Ripple Current in the Boost PFC Inductor:

Re-write the formula (15-4) function of time:

Instantaneous peak to peak ripple current

The RMS value of this current will be:

RMS ripple current formula 1

RMS ripple current formula 2

RMS ripple current formula 3

RMS ripple current formula 4

RMS ripple current formula 5

RMS ripple current formula 6

RMS ripple current formula 7

RMS ripple current formula 8

Boost Power Factor Correction RMS ripple current formula

Boost PFC Inductor Calculation:

We will try now to determine a formula for calculating the boost inductor having as input data: PFC output power, PFC boost voltage, Minimum AC input voltage, PFC switching frequency and Maximum boost ripple current as a percentage from the peak Input AC current:

Ripple current, percentage from peak

Ripple current, percentage from peak formula 1

PFC boost inductor funtion of ripple current and frequency formula 1

PFC boost inductor funtion of ripple current and frequency 2                                         (15-8)

Maximum Boost PFC Inductor Peak Current:

PFC input voltage and current

Power Factor Correction (PFC) instantaneous input current

Power Factor Correction (PFC) instantaneous input current 2

Analyzing the above equation, the conclusion will be that the inductor peak current will occur at the minimum AC line voltage (V rms ), and when the instantaneous line voltage reaches its peak. Therefore, the maximum peak current in the boost inductor will be:

Peak Boost PFC Inductor Current formula 1

Maximum Power Factor Correction Peak Current

Now, going back to the equations (15-2) and (15-3) and eliminating ripple current, we will have the following equation for the Boost duty cycle:

Boost PFC Duty Cycle Formula                                                  (15-9)

© SMPS Power Supplies

Constantin Darius Livescu

www.SMPS.com

SMPS Power Supplies
Copyright © SMPS Power Supplies ™. All rights reserved.