8.2.1.1 Power Stage

8.2.1.1.1 L_BOOST

The boost inductor value is determined by Equation 4:

Equation 4.

where

• D = Duty cycle
• ΔI = Inductor ripple current
• f_S = Switching frequency

For the example circuit, a switching frequency of 100 kHz, a ripple current of 875 mA, a maximum duty cycle of 0.688, and a minimum input voltage of 85 V_RMS produces a boost inductor value of about 1 mH. The values used in this equation are at the peak of low line, where the inductor current and its ripple are at a maximum.

8.2.1.1.2 C_OUT

Two main criteria, the capacitance and the voltage rating, dictate the selection of the output capacitor. The value of capacitance is determined by the holdup time required for supporting the load after input ac voltage is removed. Holdup is the amount of time that the output stays in regulation after the input has been removed. For this circuit, the desired holdup time is approximately 16 ms. Expressing the capacitor value in terms of output power, output voltage, and holdup time gives Equation 5:

Equation 5.

In practice, the calculated minimum capacitor value may be inadequate because output ripple voltage specifications limit the amount of allowable output capacitor ESR. Attaining a sufficiently low value of ESR often necessitates the use of a much larger capacitor value than calculated. The amount of output capacitor ESR allowed can be determined by dividing the maximum specified output ripple voltage by the inductor ripple current. In this design holdup time was the dominant determining factor and a 220-μF, 450-V capacitor was chosen for the output voltage level of 385 VDC at 250 W.

Power Switch Selection

As in any power-supply design, tradeoffs between performance, cost, and size have to be made. When selecting a power switch, it can be useful to calculate the total power dissipation in the switch for several different devices at the switching frequencies being considered for the converter. Total power dissipation in the switch is the sum of switching loss and conduction loss. Switching losses are the combination of the gate charge loss, C_OSS loss, and turnon and turnoff losses:

P_GATE = Q_GATE × V_GATE × f_s

where

• Q_GATE = Total gate charge
• V_GATE = Gate drive voltage
• f_S = Clock frequency

Equation 6.

where

• C_OSS = Drain source capacitance of the MOSFET
• V_OFF = Voltage across the switch during the off time (in this case V_OFF = V_OUT)

Equation 7.

where

• I_L = Peak inductor current
• t_ON and t_OFF = Switching times (estimated using device parameters R_GATE, Q_GD and V_TH)

Conduction loss is calculated as the product of the R_DS(on) of the switch (at the worst-case junction temperature) and the square of RMS current:

Equation 8.

where

• K = temperature factor found in the manufacturer's R_DS(on) vs junction temperature curves

Calculating these losses and plotting against frequency gives a curve that enables the designer to determine which manufacturer's device has the best performance at the desired switching frequency, or which switching frequency has the least total loss for a particular power switch. For this design example, an IRFP450 HEXFET™ from International Rectifier was chosen because of its low R_DS(on) and its V_DSS rating. The IRFP450 R_DS(on) of 0.4 Ω and the maximum V_DSS of 500 V made it an ideal choice. A review of this procedure can be found in the Unitrode™ Power-Supply Design Seminar SEM1200, Topic 6, Design Review: 140 W (Multiple Output High Density DC/DC Converter).

8.2.1.2 Soft Start

The soft-start circuitry is used to prevent overshoot of the output voltage during start up. This is accomplished by slowly bringing up the voltage amplifier output (V_VAOUT), which allows for the PWM duty cycle to slowly increase. Use Equation 9 to select a capacitor for the soft-start pin.

In this example, t_DELAY = 7.5 ms, which yields a C_SS of 10 nF.

Equation 9.

In an open-loop test circuit, shorting the soft-start pin to ground does not ensure 0% duty cycle. This is due to the current amplifiers input offset voltage, which could force the current amplifier output high or low depending on the polarity of the offset voltage. However, in the typical application, there is sufficient amount of inrush and bias current to overcome the current amplifier offset voltage.

8.2.1.3 Multiplier

The output of the multiplier of the UCC2818A-Q1 is a signal representing the desired input line current. It is an input to the current amplifier, which programs the current loop to control the input current to give high power factor operation. As such, the proper functioning of the multiplier is key to the success of the design. The inputs to the multiplier are VAOUT, the voltage amplifier error signal, I_IAC, a representation of the input rectified ac line voltage, and an input voltage feed-forward signal, V_VFF. The output of the multiplier, I_MOUT, can be expressed as:

Equation 10.

where

• K = Constant typically equal to 1/V

The Electrical Characteristics table covers all the required operating conditions for designing with the multiplier. Additionally, curves in Figure 10, Figure 11, and Figure 12 provide typical multiplier characteristics over its entire operating range.

The I_IAC signal is obtained through a high-value resistor connected between the rectified ac line and the IAC pin of the UCC2818A-Q1. This resistor R_IAC is sized to give the maximum I_IAC current at high line. For the UCC2818A-Q1, the maximum I_IAC current is about 500 μA. A higher current than this can drive the multiplier out of its linear range. A smaller current level is functional, but noise can become an issue, especially at low input line. Assuming a universal line operation of 85 V_RMS to 265 V_RMS gives a R_IAC value of 750 kΩ, because of voltage-rating constraints of a standard 1/4-W resistor, use a combination of lower-value resistors connected in series to give the required resistance and distribute the high voltage amongst the resistors. For this design example, two 383-kΩ resistors were used in series.

The current into the IAC pin is mirrored internally to the VFF pin where it is filtered to produce a voltage feed-forward signal proportional to line voltage. The VFF voltage is used to keep the power-stage gain constant, and to provide input power limiting. See the TI application report SLUA196 for detailed explanation on how the VFF pin provides power limiting. The following equation can be used to size the VFF resistor R_VFF to provide power limiting where V_IN(min) is the minimum RMS input voltage, and R_IAC is the total resistance connected between the IAC pin and the rectified line voltage.

Equation 11.

Because the VFF voltage is generated from line voltage, it needs to be adequately filtered to reduce THD caused by the 120-Hz rectified line voltage. Refer to Unitrode Power-Supply Design Seminar, SEM-700 Topic 7 (Optimizing the Design of a High Power Factor Preregulator). A single pole filter was adequate for this design. Assuming that an allocation of 1.5% total harmonic distortion from this input is allowed, and that the second harmonic ripple is 66% of the input ac line voltage, the amount of attenuation required by this filter is:

Equation 12.

A ripple frequency (f_R) of 120 Hz and an attenuation of 0.022 requires that the pole of the filter (f_P) be placed at:

Equation 13.

The following equation can be used to select the filter capacitor C_VFF required to produce the desired low-pass filter.

Equation 14.

The R_MOUT resistor is sized to match the maximum current through the sense resistor to the maximum multiplier current. The maximum multiplier current, or I_MOUT(max), can be determined by the equation:

Equation 15.

I_MOUT(max) for this design is approximately 315 μA. The R_MOUT resistor can then be determined by:

Equation 16.

In this example, V_RSENSE was selected to give a dynamic operating range of 1.25 V, which gives an R_MOUT of roughly 3.91 kΩ.

8.2.1.4 Voltage Loop

The second major source of harmonic distortion is the ripple on the output capacitor at the second harmonic of the line frequency. This ripple is fed back through the error amplifier and appears as a third harmonic ripple at the input to the multiplier. The voltage loop must be compensated not just for stability but also to attenuate the contribution of this ripple to the total harmonic distortion of the system (see Figure 2).

Figure 2. Voltage Amplifier Configuration

The gain of the voltage amplifier, G_VA, can be determined by first calculating the amount of ripple present on the output capacitor. The peak value of the second harmonic voltage is given by the equation:

Equation 17.

In this example, V_OPK = 3.91 V. Assuming an allowable contribution of 0.75% (1.5% peak to peak) from the voltage loop to the THD budget, set the gain equal to:

Equation 18.

where

• ΔV_VAOUT = Effective output voltage range of the error amplifier (5 V for the UCC2818A-Q1)

The network needed to realize this filter is comprised of an input resistor, R_IN, and feedback components C_f, C_Z, and R_f. The value of R_IN is already determined because of its function as one-half of a resistor divider from V_OUT feeding back to the voltage amplifier for output voltage regulation. In this case, the value was chosen to be 1 MΩ. This high value was chosen to reduce power dissipation in the resistor. In practice, the resistor value would be realized by the use of two 500-kΩ resistors in series because of the voltage rating constraints of most standard 1/4-W resistors. The value of C_f is determined by the equation:

Equation 19.

In this example, C_f = 150 nF. Resistor R_f sets the dc gain of the error amplifier and, thus, determines the frequency of the pole of the error amplifier. The location of the pole can be found by setting the gain of the loop equation to one and solving for the crossover frequency. The frequency, expressed in terms of input power, can be calculated by the equation:

Equation 20.

The f_VI value for this converter is 10 Hz. A derivation of this equation can be found in the Unitrode Power Supply Design Seminar SEM1000, Topic 1 (A 250-kHz, 500-W Power Factor Correction Circuit Employing Zero Voltage Transitions).

Solving for R_f becomes:

Equation 21.

or R_f = 100 kΩ.

Because of the low output impedance of the voltage amplifier, capacitor C_Z was added in series with R_F to reduce loading on the voltage divider. To ensure the voltage loop crossed over at f_VI, C_Z was selected to add a zero at 1/10th of f_VI. For this design, a 2.2-μF capacitor was chosen for C_Z. The following equation can be used to calculate C_Z:

Equation 22.

8.2.1.5 Current Loop

The gain of the power stage is:

Equation 23.

The value of R_SENSE was selected to provide the desired differential voltage for the current sense amplifier at the desired current limit point. In this example, a current limit of 4 A and a reasonable differential voltage to the current amplifier of 1 V gives a R_SENSE value of 0.25 Ω. V_P in this equation is the voltage swing of the oscillator ramp, 4 V for the UCC2818A-Q1. Setting the crossover frequency of the system to 1/10th of the switching frequency, or 10 kHz, requires a power-stage gain at that frequency of 0.383. In order for the system to have a gain of 1 at the crossover frequency, the current amplifier must have a gain of 1/G_ID at that frequency. G_EA, the current amplifier gain is then:

Equation 24.

R_I is the R_MOUT resistor, previously calculated to be 3.9 kΩ (see Figure 3). The gain of the current amplifier is R_f/R_I, so multiplying R_I by G_EA gives the value of R_f, in this case approximately 12 kΩ. Setting a zero at the crossover frequency and a pole at one-half the switching frequency completes the current loop compensation.

Equation 25.

Equation 26.

Figure 3. Current Loop Compensation

The UCC2818A-Q1 current amplifier has the input from the multiplier applied to the inverting input. This change in architecture from previous TI PFC controllers improves noise immunity in the current amplifier. It also adds a phase inversion into the control loop. The UCC2818A-Q1 takes advantage of this phase inversion to implement leading-edge duty cycle modulation. Synchronizing a boost PFC controller to a downstream dc-to-dc controller reduces the ripple current seen by the bulk capacitor between stages, reducing capacitor size and cost and reducing EMI. This is explained in greater detail in a following section. The UCC2818A-Q1 current amplifier configuration is shown in Figure 4.

Figure 4. Current Amplifier Configuration

8.2.1.5.1 Start Up

The UCC2818 version of the device is intended to have VCC connected to a 12-V supply voltage. The UCC2817A has an internal shunt regulator enabling the device to be powered from bootstrap circuitry, as shown in the typical application circuit of Figure 1. The current drawn by the UCC2818A-Q1 during undervoltage lockout, or start-up current, is typically 150 μA. Once V_CC is above the UVLO threshold, the device is enabled and draws 4 mA typically. A resistor connected between the rectified ac line voltage and the VCC pin provides current to the shunt regulator during power up. Once the circuit is operational, the bootstrap winding of the inductor provides the V_CC voltage. Sizing of the start-up resistor is determined by the start-up time requirement of the system design.

Equation 27.

where

• I_C = Charge current
• C = Total capacitance at the V_CC pin
• ΔV = UVLO threshold
• Δt = Allowed start-up time

Equation 28.

Assuming a 1-s allowed start-up time, a 16-V UVLO threshold, and a total V_CC capacitance of 100 μF, a resistor value of 51 kΩ is required at a low line input voltage of 85 V_RMS. The IC start-up current is sufficiently small as to be ignored in sizing the start-up resistor.

8.2.1.5.2 Capacitor Ripple Reduction

For a power system where the PFC boost converter is followed by a dc-to-dc converter stage, there are benefits to synchronizing the two converters. In addition to the usual advantages, such as noise reduction and stability, proper synchronization can significantly reduce the ripple currents in the boost circuit output capacitor. Figure 5 shows the impact of proper synchronization by showing a PFC boost converter together with the simplified input stage of a forward converter. The capacitor current during a single switching cycle depends on the status of the switches Q1 and Q2 and is shown in Figure 6. With a synchronization scheme that maintains conventional trailing-edge modulation on both converters, the capacitor current ripple is highest. The greatest ripple current cancellation is attained when the overlap of Q1 offtime and Q2 ontime is maximized. One method of achieving this is to synchronize the turnon of the boost diode (D1) with the turnon of Q2. This approach implies that the boost converter leading edge is pulse width modulated, while the forward converter is modulated with traditional trailing-edge PWM. The UCC2818A-Q1 is designed as a leading edge modulator with easy synchronization to the downstream converter to facilitate this advantage. Table 1 compares the I_CB(rms) for D1/Q2 synchronization as offered by UCC2818A-Q1, versus the I_CB(rms) for the other extreme of synchronizing the turnon of Q1 and Q2 for a 200-W power system with a V_BST of 385 V.

Figure 5. Simplified Representation of a Two-Stage PFC Power Supply

Figure 6. Timing Waveforms for Synchronization Scheme

Table 1. Effects of Synchronization on Boost Capacitor Current

	VIN = 85 V		VIN = 120 V		VIN = 240 V
D(Q2)	Q1/Q2	D1/Q2	Q1/Q2	D1/Q2	Q1/Q2	D1/Q2
0.35	1.491 A	0.835 A	1.341 A	0.663 A	1.024 A	0.731 A
0.45	1.432 A	0.93 A	1.276 A	0.664 A	0.897 A	0.614 A

Table 1 shows that the boost capacitor ripple current can be reduced by about 50% at nominal line and about 30% at high line with the synchronization scheme facilitated by the UCC2818A-Q1. Figure 7 shows the suggested technique for synchronizing the UCC2818A-Q1 to the downstream converter. With this technique, maximum ripple reduction as shown in Figure 6 is achievable. The output capacitance value can be significantly reduced if its choice is dictated by ripple current or the capacitor life can be increased as a result. In cost-sensitive designs where holdup time is not critical, this is a significant advantage.

An alternative method of synchronization to achieve the same ripple reduction is possible. In this method, the turnon of Q1 is synchronized to the turnoff of Q2. While this method yields almost identical ripple reduction and maintains trailing edge modulation on both converters, the synchronization is much more difficult to achieve and the circuit can become susceptible to noise as the synchronizing edge itself is being modulated.

Figure 7. Synchronizing to a Downstream Converter