# Interleaved Power Factor Correction Calculations

## Interleaved Power Factor Correction Calculations using UCC28063

Figure 1 at below is an example and describes calculation for the selection of components for 350W two-phase interleaved transition-mode PFC circuit with the use of UCC28063 PFC controller. Interleaved Transition Mode PFC using UCC28063

### 1) First detail input specifications have to be defined.

·        Mains voltage range (Vac rms):
VACmin = 85Vac   and   VACmax = 265Vac

·        Output voltage (Vout):
Vout = 400V

·        AC line frequency (fline):
fline = 47 to 63Hz

·        Power Factor at maximum load (P.F.):
P.F. = 0.95

·        Output wattage (Pout):
Pout = 350W

η = 95%

·        Minimum switching frequency (fmin):
fmin = 45kHz

### 2) Inductor selection

The selection of boost inductor depends on inductor ripple current requirements at the peak of low line.
For this we have to calculate the boost converter duty cycle at the peak of low line (DPEAK_LOW_LINE);

DPEAK_LOW_LINE = (Vout – VACmin √2) / Vout
= [400 – (85 x 1.414)] / 400
= 0.699

To avoid audible noise the minimum switching frequency of the converter (fmin) under low line conditions occurs at the peak of low line and usually it is set in between 25 kHz and 50 kHz. For this design example, fmin is set to 45 kHz. Now L1 and L2 values can be calculated by;

L1 = L2 = [η x (VACmin)² x DPEAK_LOW_LINE] / (Pout x fmin)
= [0.95 x (85V)² x  0.699] / (350W x 45kHz)
= 304µH

Now calculate peak inductor current (ILpeak) and RMS current of inductor;

Peak inductor current = ILpeak = (Pout x √2) / (VACmin x η)
= (350W x 1.414) / (85V x 0.95)
= 6.128Apk

RMS current of inductor = ILRMS = ILpeak / √6
= 6.128 / √6
=2.502ARMS

The converting time can be set by constant on time (TON) and zero-current detection (ZCD). Auxiliary windings on L1 inductor and L2 inductor is detect when the inductor currents are zero.
There should be at least 2 V at the peak of high line to reset the ZCD comparator after every switching cycle; this can be achieved by proper turn’s ratio. The turns-ratio of each auxiliary winding is;

Np / Ns = (Vout – VACmax √2) / 2V
= [400 – (265V x 1.414)] / 2V
= 13

### 3) ZCD Resistor Selection (Rza, Rzb)

The minimum value of the ZCD resistors is selected based on the internal clamps maximum current ratings of 3mA, as shown in below equation

Rza = Rzb ≥ [(Vout x Ns) / (Np x 3mA)]
= Rzb ≥ [400V / (13 x 3mA)
= 10.2kΩ
In this design the resistor value for Rza and Rzb are set to 10 kΩ (standard resistor value chosen).

### 4) To set “High Voltage Output Sense” (HVSEN) pin

·        UCC28063 driver IC has PWMCNTL (PWM control output) pin, which is an open-drain output and use to deactivate lower side converter while the PFC output capacitor (Cout) is charging.
·        When voltage at HVSEN pin rises more than 2.5V, PWMCNTL pulls to ground because of increase of impedance at this pin.
·        A voltage divider from the boost voltage (output voltage) to the HVSEN pin to ground is required to set the working point of PWMCNTL.
·        Below equations shows, how to set the PWMCNTL pin to trigger when the output voltage is within 95% of its nominal value.

Vout _trig = Vout x 0.95 = 400 x 0.95 = 380V

·        Resistor Re sets up the high side of the voltage divider and programs the hysteresis of the PWMCNTL signal.
·        Here Re can be select to provide 99V of hysteresis.

Re = Hysteresis / 12µA = 99V / 12µA = 8.25MΩ
= 2.74MΩ + 2.74MΩ + 2.74MΩ = 8.22MΩ
(Three resistors can be used in series to achieve calculated resistance to meet voltage requirements as shown in above equation).

·        Below equation shows calculation for Resistor Rf, which is used to program the PWMCNTL active threshold;

Rf = 2.5V / {[(Vout _trig – 2.5V) / Re] – 12µA]
= 2.5V / {[(380V – 2.5V)/ 8.22MΩ] – 12µA}
= 73.69kΩ
= 73.2kΩ     (Standard resistor value has been selected)

·        Below equation shows calculation for minimum output voltage Vout_min, PWMCNTL output will continue to work until Vout_min is reached;

Vout_min = [2.5V (Re + Rf)] / Rf
= [2.5V (8.22M+ 73.2k)] / 73.2k
= 283.2V
= 283V

·        Below equation shows the value of Over Voltage Protection threshold which can be achieved by Re and Rf values;

Vovp = [4.87V (Re + Rf)] / Rf
= [4.87V (8.22M+ 73.2k)] / 73.2k
= 551V

### 5) Selection of Output capacitor (Cout)

Holdup requirements decide output capacitor (Cout) of our circuit, below equation explains this;

Cout ≥ [2(Pout/η)(1/fline)] / [Vout² - (Vout_min)²]
= [2(350/0.95)(1/47)] / [400² - (283V)²]
= 196µF

Two 100μF capacitors were used in parallel for the output capacitor.
Cout = 200µF

The low-frequency peak-to-peak output voltage ripple (Vripple) is approximately 14 V for this size capacitor, as shown in below equation;

Vripple = (2 . Pout / η) [1 / (Vout x 4π x fline x Cout)]
= (2 . 350W / 0.95) [1 / (400V x 12.56 x 47 x 200µF)]
= 15.60Vppk
= 16Vppk

A capacitor should withstand the low-frequency RMS current (ICout_100Hz) and the high-frequency RMS current (ICout_HF); calculations of both as follows;

ICout_100Hz = Pout / (Vout x η x √2)
= 350W / (400V x 0. 95 x 1.414)
= 0.6513 Arms

Note: In the capacitor data sheet the low- and a high-frequency RMS current rating is already available.

### 6) For Peak Current Limiting; Selection of resistor Rs

·        Inrush and overload conditions cause failure of MOSFET’s, but this IC saves the MOSFET’s as this IC has inbuilt peak limit comparator, which is use to sense the input current.
·        We had set the peak current limit (Ipeak) threshold to 120% of the nominal maximum current. Below equation gives details;
Ipeak = (2Pout x √2 x 1.2) / (η x VACmin)
= (2 x 350W x √2 x 1.2) / (0.95 x 85V)
= 14.7A

·        Value of current sensing resistor can be calculated as;

Rs = 200mV / Ipeak = 13.5mΩ
A metal film current sense resistor will work for us. 500mW resistor will give surge protection.

·        Power loss across current sense resistor (Prs) is calculated by below equation;

Prs = [Pout / (VACmin x η)]² Rs
= [350W / (85 x 0.95)]² 13.5mΩ
= 0.25W

·        Surge rating is the important specification for the selection of current-sense resistor. The resistor should sustain the short circuit current.
·        Thermal energy resulting from current flow required to melt the fuse, can be calculate by; I²t
Where; I = RMS current and t = period of current flow

### 7) Selection of power components; MOSFET’s M1, M2 and Boost Diodes D1, D2

for the calculations and selections of the components value for designing transition-mode PFC pre-regulators.

Selecting MOSFET;
Below are the some major MOSFET selection considerations;
§  Consider; low RDSON
§  Consider; RDSON*Qg and RDSON*EOSS
§  The device switching losses can be reduce by fast turn ON/OFF switching.
§  Consider low output capacitance Coss for low switching energy and to increase light load efficiency.
§  Drain-source breakdown voltage VBR(DSS) to handle spikes or overshoots.
§  Low thermal resistance RthJC.
§  Since body diode never conducts in the CCM boost converter, the body diode commutation speed and reverse recovery charge are not important.

Drain to Source RMS current of power MOSFET is given by;

Select “Power MOSFET” of;
Drain-Source Voltage (VDS) = 500V
Continuous Drain Current (ID) = 11A

Selecting boost diode;
§  Care to be taken while selecting boost diode for CCM converter because this diode is hard commutated at a high current i.e. the diode turns off while there is still forward current flowing through, and the reverse recovery can cause substantial power loss, noise and current spikes.
§  Reverse recovery can be a problem for high switching frequency and high power density power supplies.
§  At low line, the diode conduction duty cycle is quite low, and the forward current is quite high according to the average current. For this reason, diode in CCM boost are fast recovery with low reverse recovery charge, followed by Vf operating at high forward current.

RMS current for boost diode is given by;

Select “Ultrafast Recovery Diode” of;
Peak Repetitive Reverse Voltage (VRRM) = 600V
Average Rectified Forward current (IF) = 3A

### 8) Protection for Brownout

·        A control should be there on PFC circuit i.e. PFC circuit should shut down when applied input voltage falls below a particular voltage for defined time and PFC should again restart when applied input voltage rises to a particular voltage.
·        We can program our circuit at 75% of minimum operating input voltage to go in brownout protection by selecting Ra and Rb.
·        The brownout hysteresis comparator in UC28063 is programmed by Ra resistor, 17V of hysteresis can be provided by calculating and proper selection of Ra resistor value.
·        Calculations for Ra and Rb are shown in below equations.
Ra = Hysteresis / 2µA
= 17V / 0.000002A
= 8.5MΩ
= 2.87MΩ + 2.87MΩ + 2.87MΩ = 8.61MΩ
(Three resistors can be used in series to achieve calculated resistance to meet voltage requirements as shown in above equation).

= 133kΩ (standard resistor value has been selected)

After placing above calculated resistor values PFC circuit will shut down when applied input voltage falls below 66VRMS (longer than 440msec) and PFC will again restart when applied input voltage rises to 78VRMS.

### 9) Setting of converter ON time

·        The minimum frequency fMIN determines the maximum on-time Ton as shown in below equation;

·        Highest boost inductance (L1max) and Power output (Pout) confirms operation timing.
·        Calculate the timing resistor Rt as shown in below equation;

·        Maximum frequency can be calculated as;
fMAX = 133kΩ / (2µs x 123 kHz) = 540 kHz

### 10)    Output Voltage (Vout) programming

·        We have to minimize the loading effect on the power line when PFC is not working, this will be done by a proper value of resistor Rc;

Rc = 2.74MΩ + 2.74MΩ + 3.01MΩ = 8.49MΩ
Vref = 6V
(Three resistors can be used in series to achieve calculated resistance to meet voltage requirements).

·        Resistor Rd is then calculated depending on Rc, the reference voltage; Vref and the required output voltage; Vout.

Rd = (Vref x Rc) / (Vout –Vref)
= (6V x 8.49M) / (400 – 6V)
= 129.2 kΩ
= 130kΩ (standard resistor value has been selected)

·        Output over-voltage protection threshold can be calculated by following equation;

Vovp = 6.48V[(Rc + Rd)/Rd]
= 6.48V[(8.49M + 130kΩ) / 130kΩ]
= 429.67V

### 11) Compensation of Voltage loop

Resistor value Rz should be such that, it should confirm best power factor and low harmonic distortion on the input current. Resistor Rz should attenuate low-frequency ripple to less than 2% of the voltage amplifier output range.

The trans-conductance amplifier small-signal gain is;
gm = 50µsec

The voltage-divider feedback gain can be calculated as shown in below equation;
H = Vref / Vout
= 6V / 400V = 0.015

The Rz resistor value can be calculated as shown in below equation;
Rz = 100mV / (Vripple x H x gm)
= 100mV / (16V x 0.015 x 50µsec)
= 8.3 kΩ
Standard resistor value is Rz = 8.2 kΩ

Cz is then set to add 45° phase margin at 1/5th of the line frequency, as shown in below equation;
Cz = 1 / [2π x (fline / 5) x Rz]
= 1 / [2π x (47Hz / 5) x 8.2kΩ]
= 2µF
Standard capacitor value is Cz = 2.2µF

Cp is sized to attenuate high-frequency switching noise, as shown in below equation;
Cp = 1 / [2π x (fMIN / 2) x Rz]
= 1 / [2π x (39 kHz / 2) x 8.2kΩ]
= 995pF
Standard capacitor value is Cp = 1000pF

### Conclusion

Above mentioned interleaved Power Factor Correction Calculation will help for the selection of components for 350W two-phase interleaved transition-mode PFC circuit with the use of UCC28063 PFC controller.