The main attributes of the components of CRM PFC AC-DC converter, such as output capacitor and inductor value, need to be governed. Then, the power losses on each component should be estimated to calculate the efficiency of the CRM PFC circuit.
2.4.1 Analysis and Design of CRM PFC Power Stage
The design basic specifications are shown in Table 2.2. Then, the main elements of the CRM PFC power stage can be determined.
TABLE 2.2
SPECIFICATIONS OF THE CRMPFCAC-DC CONVETER
Parameter Specification Rated Output Power (Pout) 100 W
Input Voltage (Vg,rms) 110 Vac Line Frequency (fline) 60 Hz Minimum Switching Frequency (fsw) 40 kHz
Output Voltage (Vout) 400 Vdc Output Voltage Ripple (ΔVout) < 1 %
System Efficiency (η) 90%
Hold-Up Time (tholdup) 20 ms
The design flows for the main components are as shown in below. There are many factors involved in the design process. However, the equations below are intended to provide a framework for the design.
Determination of Output Capacitor
There are two methods to decide the output capacitor value. One way focuses on the ripple of the output voltage. There are two factors induce the output voltage ripple. One is introduced by the MOSFET switching frequency and the other one is caused by the rectified line voltage which has 120 Hz ripple. The output voltage ripple generated by the MOSFET switching frequency is much smaller than the ripple generated by the rectified line voltage.
Assuming the line current is pure sinusoidal. The relationship between average inductor current during a switching period (iL(t)) and input power (Pin) is represented as
)
the input instantaneous power is
(2-13)
Therefore, the current flowing through the output capacitor (ic(t)) is ) .
Substituting (2-13) into (2-14)
[
2⋅sin2( )−1]
.Integrated both sides of (2-15) can be given as
[
( )]
0.5 sin(2 t)where Vout(t) is equal to [Vout + Δvout,ripple(t)], the combination of output voltage DC term and AC term. The ripple of output voltage is
out
the peak-to-peak value of output voltage ripple (ΔVout,ripple) can be got
, .
According to the output voltage ripple specification from Table 2.2, the output capacitance can be given as below
μF.
400 166 60
Another considers the effect of hold-up time. Hold-up time is an important factor related to the amount of energy that the output capacitor needs to store. Generally, hold-up time range from 16 to 50 ms. A great majority of the industry requirement is 20 ms. This takes into consideration the minimum voltage the PFC pre-regulator will allow the output voltage to drop to while sustaining the output load (Usually is down to 95 % of output voltage). The energy storing in output capacitor can be expressed by below energy equation
( )
.According to the specification of hold-up time, the output capacitor can be decided as
F.
380 256 400
Comparing above results of two methods, the output capacitor can be determined by larger one which is 300 μF as shown in Fig. 2.7. The output ripple can be
recalculated
V.
2 . 400 2 60 2 300
100
, =
⋅
⋅
= ⋅
Δvoutripple μ π (2-22)
2.2 V
25 ms 2.2 V
25 ms
Fig. 2.7. The simulation of the hold-up time and output voltage ripple.
Vout Vout
Vin Vin
vL vL
vL iL
Vin
Vin -Vout
ton toff
IL
Switch on Switch off
t
t IL,pk
Vout Vout
Vin Vin
vL vL
vL iL
Vin
Vin -Vout
ton toff
IL
Switch on Switch off
t
t IL,pk
Fig. 2.8. Switching Sequences of the CRM PFC power stage.
Determination of Inductor
The off-time of the MOSFET is based on the input line voltage and the inductance, which also dictates the operating frequency range. The design of the inductor is based on the
switching frequency. As shown in Fig. 2.8, the off-time of the MOSFET is
Combining (2-11) and (2-23), the switching frequency (fsw) is
[ ]
.The CRM PFC AC-DC converter has variable switching frequency from (2-24).
Therefore, the minimum switching frequency will occur at the peak of line voltage.
pk
where Vin,pk is the input peak voltage and IL,pk is the peak inductor current. And the average inductor current during a switching period can be represented as
.
According to Table 2.2, the specification of the lowest switching frequency is 40 kHz.
Substituting (2-26) into (2-25), the relationship between inductance and the lowest switching frequency is as follow
2 .
From (2-27), the inductance should be lower than 835 μF. In this thesis, the inductance is decided as 800 μF. Because that the boost converter operates in the CRM, the relationship between the rectified line voltage and output voltage is
) 1 (
1 V t Vout D⋅ in
= − (2-28)
where D is the duty cycle of the switch. The minimum duty cycle which occurs at the peak of line voltage can be calculated by (2-28).
% 400 61
1 156
1 ,
min
=
−
=
−
=
out pk in
V D V
(2-29)
The peak of inductor current (IL,pk) can be expressed as
rms g
out rms
g pk
L V
I P I
, ,
, =2⋅ 2⋅ =2⋅ 2⋅ (2-30)
When the line voltage is 110 Vrms, the inductor current peak is 2.57 A. The typical waveforms of the CRM PFC AC-DC converter are shown in Fig. 2.9. At the zero-crossing of line voltage, the energy stored in the inductor is not enough to drive the resonant capacitor to the output voltage. At this critical input line voltage level, the line current distortion will occur.
Fig. 2.9. Typical waveforms of CRM PFC AC-DC converter.
2.4.2 Calculation of Current RMS Values for Power Components
The efficiency of the CRM PFC power stage is an important issue. Therefore, the RMS current on each component are significant for design procedure [12]-[14].
Rectifier Bridge
The diode of rectified bridge can be approximated by the serial connection of a forward voltage (VF) and a resistance (RF). The current flowing through the rectifier bridge (Iin) is equal to the inductor current (IL). The inductor current waveform is shown in Fig. 2.10.
Assuming the switching frequency is much higher than the line frequency. Then, the instantaneous peak value of inductor current is
.
The RMS value of the inductor current triangle over the corresponding switching period Ts (iL,rms(θ)) is represented by
Fig. 2.10. The waveform of inductor current.
As the consequence, the RMS value of the inductor current is
Then, the power consumption of the four diodes of the rectifier bridge, Ploss,br, can be estimated as follow
2 .
MOSFET and Current Sensing Resistance
CRM PFC AC-DC converter presents a challenge because of the high peak currents which will introduce higher switching conduction losses. The power consumption on the switching current sensing resistance should be concerned either. The waveform of switching current is shown in Fig 2.11. The RMS value of the switching current triangle over the corresponding switching period Ts (iQ,rms(θ)) can be as
The CRM PFC operates at the border of the CCM and DCM, then the expression gives the duty cycle in a CRM AC-DC converter applications.
T
ssin .
As the consequence, the RMS value of the MOSFET current is
[ ]
The conducting switch can be equivalent to a resistance, Rds,on. The power loss on both switch and current sensing resistance, Rsense, is as follow
Ploss,on =
[
Rds,on +Rsense]
⋅IQ,rms2. (2-38) Diode RMS CurrentThe freewheeling diode of CRM PFC AC-DC converter will be a fast recovery one. The diode current waveform is shown in Fig. 2.12. The RMS value of the diode current over the corresponding switching period Ts, is given by
where the ratio of switching off-time over one switching cycle is
As the consequence, the RMS value of the diode current is
and the average current flowing through the diode is equal to the output average current.
, .
The diode can be also approximated to a serial connection of a forward voltage, VFD, and a resistance, RFD. Therefore, the power consumption can be estimated as
Ploss,diode =VFD⋅ID,avg +RFD⋅ID,rms2. (2-42) Output Capacitor
The capacitor current is the difference between the diode current and the current absorbed by the load as shown in Fig. 2.13.