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Due Date: 23rd Nov 2014 Date submitted: 23rd Nov 2014
Mohammed AL Nasser 201101137
John Leek
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Electronics manufacturing and design
Bachelor Engineering Technology
ENB6071
Switch mode power supply
Abstract:
The purpose of this assignment was to build and test a small switch mode power supply based on push-pull topology and to simulate particular parts of the circuit. The circuit was supplied with 10 and 15 volts in order to output (25v) without a conspicuous power loss. Several tests were performed on the circuit by varying the load resistor -and hence varying the power at the output- in order to measure the efficiency of the circuit.
Introduction:
In this document, an explanation of how the power supply works will be presented. Some calculations of the wire size, number of turns and losses of the transformer will be demonstrated. The components values of the feedback resistor, compensation and soft start capacitors, snubber circuit and oscillator frequency will be calculated discussed. At the end of this paper, plots of the efficiency of the circuit will be included.
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ContentsAbstract:.........................................................................................................................................2
Introduction:...................................................................................................................................2
How the SMPS works:.....................................................................................................................6
Design specification........................................................................................................................6
Skin effect:..................................................................................................................................7
Proximity effect transformer:.....................................................................................................7
Calculations for the transformer:...................................................................................................8
Wire size (with respect to current density (j)):...........................................................................8
Number of turns:........................................................................................................................8
Explanation and reason:.......................................................................................................10
..............................................................................................................................................10
Question1: why an inductor was used in the output circuit?...............................................11
Calculations of (primary and secondary) loss:-.........................................................................11
Wire losses:...........................................................................................................................11
Core losses:...........................................................................................................................12
Total losses of the transformer:................................................................................................12
Transformer core size calculation:............................................................................................13
Power in of the transformer:................................................................................................13
Power out of the transformer:..............................................................................................14
Components values:.....................................................................................................................15
Calculation of feedback resistor value:.....................................................................................15
Calculation of compensation components:..........................................................................15
Soft start circuit values:............................................................................................................16
Correct oscillator frequency/ configuration:.............................................................................16
Output filters design.................................................................................................................17
Simulation results:....................................................................................................................18
Snubber components values:...................................................................................................20
Output frequency after snubber circuit:...................................................................................22
Mosfet power loss calculation:.................................................................................................22
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Power loss due to its resistance of the MOSFET:..................................................................22
Output switching losses:.......................................................................................................23
Input switching losses:..........................................................................................................23
Diode loss calculation:..............................................................................................................24
The forward voltage drop times the forward current:..........................................................24
The losses caused by the forward & reverse recovery time of the diode:............................24
Measurements of performance:...................................................................................................25
Plots of output voltage vs. output power:................................................................................25
Measurements of efficiency:....................................................................................................27
Plot of efficiency:......................................................................................................................28
Automatic test (Labview results):.........................................................................................29
Appendix A:..................................................................................................................................30
MATLAB code of the Vout vs. Pout:..........................................................................................30
Appendix B:..................................................................................................................................31
MATLAB code of the load test efficiency plots:........................................................................31
Appendix C:...................................................................................................................................33
MATLAB code of the Automatic efficiency test:.......................................................................33
Appendix D:..................................................................................................................................34
Core size calculations:...............................................................................................................34
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Table of figure:Figure 1: skin effect.........................................................................................................................7Figure 2: proximity effect................................................................................................................7Figure 3: Transformer core magnetic data N97............................................................................10Figure 4: Error ± Amplifier connection..........................................................................................15Figure 5: oscillator period graph...................................................................................................16Figure 6: Output LCR filter............................................................................................................17Figure 7: Simulation of the Current and Vout...............................................................................18Figure 8: simulation of the resonate frequency............................................................................19Figure 9: output before snubber circuit........................................................................................20Figure 10: Output after snubber circuit........................................................................................22Figure 11: output voltage vs. output power (10v)........................................................................25Figure 12: output voltage vs. output power (15v)........................................................................26Figure 13: plot of efficieny (load test)with the two supplies (10v,15v).........................................28Figure 14: Automatic efficiency test.............................................................................................29
Table of tables:Table 1: How the circuit works technically.....................................................................................6Table 2: Design specification..........................................................................................................6Table 3: results of the simulation.................................................................................................18Table 4: A comparison between the simulated and experimental results....................................19Table 5: measurment of efficiency with supply 10v......................................................................27Table 6: measurements of efficiency with 15v.............................................................................27
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How the SMPS works:
Table 1: How the circuit works technically.
When the circuit supplied with (10v to 15v) at (100 KHz).Part Function
PWM switching regulator Generates (5v) pulses in pins (16 and 13) at 100 KHz.
Mosfet driverIncreases the current to boost charging
capacitance of the MOSFETs and open the gate of the each MOSFET faster.
Mosfets
When the MOSFET driver close the gate of the MOSFET using high current it allows the current
flows through the primary windings to the ground. The result of the two Mosfets operation will
generate a push-pull signal.
Transformer Produce magnetic flux from both primary windings when the gate of the MOSFET is closed.
Diode bridge Rectify the secondary transformer output signal to convert it to a DC signal.
RLC filter Smooth the output rectified signal.
Snubber circuit Reduces the ringing from the output of the bridge to increases the efficiency of the circuit.
Feedback circuit Maintain the output voltage to output a 25v.
Design specificationThe calculation was carried to design a DC to DC push-pull converter with the following specification:
Table 2: Design specification.
Specification ValueOperation frequency 100 KHzMaximum output Power 30 WattsMinimum input Voltage 10 VoltsMaximum input voltage 15 VoltsOutput voltage with a load current of 250mA min 25 VoltsNo load output voltage As set voltageOutput voltage ripple 0.01% V outSoft start circuit This is required
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Efficiency >78% @ Pout > 5Watts
Skin effect:Increasing the wire diameter will only increase the resistance of the wire, while the
effective area will be only on the skin of the wire (skin depth). This effect was occurred in the secondary windings.
Figure 1: skin effect.
Proximity effect transformer:Proximity effect is the uneven current distribution in the conductor. As it shown blow,
the current will flow only on one side of each wire. This effect was occurred in the two primary windings.
Figure 2: proximity effect.
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Calculations for the transformer:
Wire size (with respect to current density (j)):
isec=Pv=30
25=1.2 A
j= AmpArea
Where:
Current density (j) = 10
Amp = 1.2A
10= 1.2Area
Area=1.210
=0.12mm2
Area=π r2
0.12=π r2
r=0.195mm
d=0.390mm
Number of turns:Primary turns:
N primary=Vmaxf∗β∗A
Where:
Switching frequency (f) = 100 kHz.
Flux density (B) = 0.35 Tesla.
Area (A) = 31 mm2.
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Vmax = 15v.
N p=15
(100∗103 )∗( 3501000 )∗( 31
1000000)=13.8≈14 turns
Vout=25+(2∗diodeVf )
Diode forward voltage drop = 0.7v
didoeVf=0.7≈1v
Vout=25+(2∗1)=27 v
Secondary turns:
N secondary=Np∗Vout
Vin (minimum )∗2∗Dutycycle
Where:
N primary = 13.8
Vout = 27
Vin= 10v
Duty cycle = 0.45
Ns= 13.8∗2710∗2∗0.45
=41.4≈ 42turns
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Explanation and reason:Saturation is when the magnetic field (H) stops increasing the magnetization of the
material, so the total magnetic flux density (B) will level off.
When the magnetic core saturates, the inductance of the transformer will change with the change of the driving current, so this considered as unwanted departure from the ideal behavior. As a result, when the core saturates the current will keep flowing until the temperature of the transformer raises.
As it is described in the BH curves, the maximum flux density for N97 is (550 mT). As results, the core will start to saturate when the flux density exceed (550 mT).
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Figure 3: Transformer core magnetic data N97.
Question1: why an inductor was used in the output circuit?To produce DC current and to keep the current flowing during the (off) periods. In
another word, to reduce ( DvDt ), which is (ration of voltage with respect to time).
Calculations of (primary and secondary) loss:-
Wire losses:
Pwire=I 2∗R
R=turns∗¿∗condactor resistance
Where:
In: length per turn = 0.04 m (measured using a ruler).
Conductance = 0.1382 Ω/m (from core wire tables, Appendix E - Work book).
Primary power loss:
Rprimary=14∗0.04∗0.1382=0.07Ω
Pwire=(1.5 )2∗0.07=0.1575w
Secondary power loss:
Rsecondary=42∗0.04∗0.1382=0.23Ω
Pwire=(1.2 )2∗0.23=0.3312w
Comments:
The procedure was preceded, due to the similarity in results:
Calculated current = J∗Area=10∗0.137=1.37 A .
Secondary current = PoutVout
=3025
=1.2 A.
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Core losses:Core material number: N97
By knowing the frequency required (100 KHZ):
core loss=Eev∗Ve
Where:
Core volume (Ve) = 1460 mm2. (From Appendix D – work book).
Spectral irradiance = (Eev) = 300 Kw per m3. (From Appendix B(transformer core magnetic) – work book
core loss=300 Kwm3 ∗1460mm3
core loss=0.438w
Total losses of the transformer:T=(2∗primary power loss )+secondary power loss+core loss
And by substituting in the total losses of the transformer equation:
T=(2∗0.1575 )+0.3321+0.438=1.0851w
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Transformer core size calculation:
Power in of the transformer:
Ap=Ac∗Aw=[ 11.1∗PinKt∗∆B∗fs ]
1.143
∗104 (mm4 )
Where:
Pin = power in (watts).
Kt = constant of topology = 0.141
∆ B = Magnetic flux density wing (typically 0.2 to 0.3 T).
Fs = switching frequency (Hz).
Ap = Area product (mm4).
Ae = core area (mm2) = 31 mm2.
Aw = winding area (mm2) = 28.1 mm2.
The maximum power in of the transformer (the value of (power in) was obtained from the MATLAB code):
Pin=45.0378watts
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Power out of the transformer:
Pout=0.001∗Bmax∗fs∗Ae∗AcDcma
Where:
Bmax = magnetic flux density = 350mT
Ae = core area = 31 mm2.
Dcma = 500 circular mil per RMS current
Fs = switching frequency = 100 kHz.
Ac = winding area square = 28.1 mm2.
Pout=0.001∗3500∗100000∗0.31∗0.281500
Pout=60.977watts
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Components values:
Calculation of feedback resistor value:
Figure 4: Error ± Amplifier connection
Voltage divider rule was used to calculate the values of the two resistors used in the feedback and by assuming R1=1KΩ:
VoutVin
= R1R2+R1
By using the voltage divider formula, the input voltage value is 25v and it was required to reduce the input (25v) to (2.5v) output.
2.525
= 1000R2+1000
0.1= 1000R2+1000
R2=10000.1
−1000
R2=9000=9kΩ
The feedback resistors:
R1= 1kΩ.
R2= 9kΩ.
Calculation of compensation components:The output signal at (pin3) of the switching regulator was oscillating when the voltage
increased. A compensation capacitor was connected at pin 3 to stabilize the signal and stop the oscillating.
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C compensation = 100nF
Soft start circuit values:In the soft start circuit in the switching regulator (pin4), an equation was used to calculate the values:
C∗V=i∗t
By performing a variety of capacitor to obtain an acceptable time, the capacitor value was used in the circuit = 10uF, and by substituting in the formula above:
t=C∗Vi
=10∗10−6∗2.5100∗10−6 =0.25 s=250ms
The function of the soft start capacitor is to protect the transistors and diodes inside the switching regulator from high current when the power supply is turned on.
Correct oscillator frequency/ configuration:
Figure 5: oscillator period graph.
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As it shown in figure 5, the frequency at each driver output is half the oscillator frequency. The switching frequency is (100 KHz):
The oscillator frequency (200 KHz), and the period (5us), and the capacitor is 1nF. From the graph the value of the resistor used almost (8KΩ).
The values used in the circuit:
Switching frequency: 100 KHz.
Oscillator frequency: 200 KHz.
Oscillator period: 5us.
RT: 6.8 KΩ.
CT: 1nF.
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Output filters design
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Figure 6: Output LCR filter.
A 2nd order low pass filter circuit was designed on Altium software to determine the frequency response:
Calculating value of the inductor:
L=(Vpeak−Vout )∗∆ t
∆ i
Where:
Vpeak = 30v.
Vout = 25v.
∆ t=5∗10−6 s.
∆ i = 0.12 A.
L=(30−25 )∗5∗10−6
0.12=208.33∗10−6 H
The value of the inductor used in the circuit (L=227 uH).
Output capacitor calculations:
Cmin≥
18∗∆ i∗t
∆Vout
Where: (from Equation 20. in AN2794 application note).
∆Vout=2.5mV
∆ i=0.12 A
t=4.5∗10−6s
Cmin≥
18∗0.12∗4.5∗10−6
2.5∗1 0−3 =27uF
The values of the output filter components:
C= 27uF.
L=227uH.
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Simulation results:Table 3: results of the simulation.
Load resistors (Ω)
Load current (A)
Delta current ∆IL (inductor) (mA)
Resonate frequency (Hz)
Output voltage (V)
Time one (us)
100 0.25 38 2.39 25.1 4.6580 0.34 38 2.39 25.1 4.6550 0.5 38 2.39 25.1 4.6522 1.14 38 2.39 25.1 4.65
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Figure 7: Simulation of the Current and Vout.
From the simulation figures, the results of the (RLC) simulation were obtained. Different load resistors were used in the simulation.
Table 4: A comparison between the simulated and experimental results.
Method Load resistors (Ω) Load current (A) Output voltage (V)Simulation 100 0.25 25.1Experimental 10v 100 0.249 24.9Experimental 15v 100 0.25 25
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Figure 8: simulation of the resonate frequency.
Snubber components values:
Frequency of the ringing before adding Cadded :
Figure 9: output before snubber circuit.
From figure 9, the frequency of the ringing before snubber circuit equals (
f 1= 1180∗10−9 =5.56∗106 Hz ¿.
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Frequency of the ringing after adding Cadded :
cadded=0.47∗10−9F (The value of the added capacitor was assumed).
f 2= 1360∗10−9=2.778∗106 Hz
Calculating Cstray:
( f 1f 2 )
2
=1+Cadde d
C stray
( 5.6∗106
2.778∗106 )2
=1+ 0.47∗10−9
Cstray
C stray=0.15∗10−9 f
Snubber components value used in the SMPS:
The value of the capacitor used in the snubber circuit must 10 times the value of Cstray :
C = 0.15*10-9 * 10
C1= 1.5*10-9 F
The value of the resistor used:
R1 = 6.2 KΩ (the value of the resistor was assumed)
The diode used in snubber circuit:
D1 = STTH1R02QRL
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Output frequency after snubber circuit:
Figure 10: Output after snubber circuit.
After adding the snubber circuit in the SMPS, the ringing in the output signal was reduced. The
frequency of the ringing (f=1
130∗10−9 =7.7∗106Hz ¿ .
Mosfet power loss calculation:
Power loss due to its resistance of the MOSFET:
Prds (on )=Rds (on )∗I 2dc
Where: (from the datasheet)
Rds (on) = 6mΩ.
I2dc = 1.5A (for each MOSFET).
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Prds (on )=(6∗10−3 )∗(1.5 )2=9∗10−3w .
Output switching losses:
Psw (mosfet )=Vds∗Ids∗(tr+tf )∗fswit ching2
Where: (from the datasheet)
Vds = 9mv.
Tr = 60*10-9 s.
Tf = 57*10-9 s.
Fswitching = 100 KHz.
Psw (mosfet )=(9∗10−3 )∗(1.5 )∗( (60∗10−9 )+(57∗10−9 ))∗100∗103
2=52.65∗10−6w .
Input switching losses:
Pin ( loss )=Cin∗V 2gs2
Where: (from the data sheet)
Cin = 6860pF.
Vgs= ±20v.
Pin (loss )=(6860∗10−12)∗(20 )2
2=0.1372w .
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Diode loss calculation:
The forward voltage drop times the forward current:
Pconduction loss=Vd∗If
Where:
Vd = 0.7v ≈1v (the drop voltage o the diode was considered as 1v for each diode).
If = 1.5A.
Pconduction loss=2∗(1 )∗(1.5 )=3w .
The losses caused by the forward & reverse recovery time of the diode:
Pswitching (Diode)=Vsec∗Iout∗(tfr+trr )∗fswitching
2
Where: (from the datasheet)
Vsec = 30v.
Iout = 1.2 A.
Tfr = 50ns.
Trr = 15ns.
Fswitching = 100 KHz.
Pswitching (Diode)=(30)∗(1.2)∗((50∗10−9)+(15∗10−9))∗100∗103
2=0.117w
Due to there are two switching diodes (Pswitching = 0.117 * 2 = 0.234 watts).
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Measurements of performance:
Plots of output voltage vs. output power:
With supply = 10v:
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Figure 11: output voltage vs. output power (10v).
With supply = 15v:
From both figures above, while increasing the output power, a small drop in voltage will be occurred in the output.
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Figure 12: output voltage vs. output power (15v).
Measurements of efficiency:
Table 5: measurment of efficiency with supply 10v.
Input measurements Output measurements EfficiencyLoad Ω Current in
AVoltage
inV
Power inWatt
Current out A
Voltage out V
Power out Watt
Pout/Pin%
100 0.68 10 6.8 0.249 24.9 6.2 91.268 1.01 10 10.1 0.365 24.9 9.1 90.147 1.48 10 14.8 0.53 24.8 13.1 88.533 1.97 10 19.7 0.73 24.5 18 91.3722 2.89 10 28.9 1.07 23.5 25.1 86.85
Table 6: measurements of efficiency with 15v.
Input measurements Output measurements EfficiencyLoad Ω Current in
AVoltage
inV
Power inWatt
Current out A
Voltage out V
Power out Watt
Pout/Pin%
100 0.49 15 7.35 0.25 25 6.25 85.0368 0.71 15 10.65 0.37 25 9.19 86.2947 1 15 15 0.53 24.7 12.98 86.533 1.39 15 20.85 0.7 24.7 18.48 88.622 2.13 15 31.95 1.12 24.7 27.7 86.6915 3.27 15 49.05 24 24 38.4 78.28
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Plot of efficiency:
The previous figure demonstrates the efficiency of the 30w push-pull DC to DC converter circuit using the load test. The efficiency at both supplies (10v, 15v), was more than 80%. From the assignment sheet in the design specification section, the acceptable efficiency should be more than 78%.
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Figure 13: plot of efficieny (load test)with the two supplies (10v,15v).
Automatic test (Labview results):
In the design specification table, the required efficiency should be more that 78%. The automatic and load test efficiency plot demonstrated the efficiency of the SMPS circuit, which is (>80%).
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Figure 14: Automatic efficiency test.
Appendix A:
MATLAB code of the Vout vs. Pout:%10v:
vout= [24.9,24.9,24.8,24.5,23.5];
pout= [6.2,9.1,13.1,18,25.1];
plot(pout,vout);grid;
xlabel('output power');
ylabel('output voltage');
title('Output voltage Vs output power (10v)');
figure;
%15v:
vout1= [25,25,24.7,24.7,24.7];
pout1= [6.25,9.19,12.98,18.48,27.7];
plot(pout1,vout1);grid;
xlabel('output power');
ylabel('output voltage');
title('Output voltage Vs output power (15v)');
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Appendix B:
MATLAB code of the load test efficiency plots:%load test plots
%10v
pout1 = [6.2,9.1,13.1,18,25.1];
eff1 = [91.2,90.1,88.5,91.37,86.85];
plot(pout1,eff1);
xlabel('Output power(watt)');
ylabel('Efficiency %');
title('Efficiency with 10v supply');
ylim([0 100]);
grid;
figure;
%15v
pout2 = [6.25,9.19,12.98,18.48,27.7,38.4];
eff2 = [85,86.29,86.5,88.6,86.69,78.29];
plot(pout2,eff2);
xlabel('Output power(watt)');
ylabel('Efficiency %');
title('Efficiency with 15v supply');
ylim([0 100]);
grid;
figure;
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%both
plot(pout1,eff1,pout2,eff2);
xlabel('Output power(watt)');
ylabel('Efficiency %');
title('Efficiency Of the SMPS');
legend ('supply = 10v','supply = 15v');
xlim([5 30]);
ylim([0 100]);
grid;
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Appendix C:
MATLAB code of the Automatic efficiency test:%10v
f = dlmread('10v.txt');
vo = f(:,1);
io = f(:,2);
vin = f(:,3);
iin = f(:,4);
pout = vo.*io;
pin = vin.*iin;
eff= (pout./pin)*100;
%15v
f2 = dlmread('15v.txt');
vo2 = f2(:,1);
io2 = f2(:,2);
vin2 = f2(:,3);
iin2 = f2(:,4);
pout2 = vo2.*io2;
pin2 = vin2.*iin2;
eff2= (pout2./pin2)*100;
plot(pout,eff,pout2,eff2); grid;
xlabel('Output power (watts)');
ylabel('Efficiency (%)')
title('plot of efficiency of SMPS')
legend('supply = 10v',' supply = 15v');
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Appendix D:
Core size calculations:%Matlab code to calculate the maximum power in the trasformer.
Kt = 0.141; %constant topology.
deltaB = 0.3; % magneic flux.
fs = 100000; %swtiching fequency Hz.
Aw = 28.1*10^-6; %winding area.
Ae = 31*10^-6; % core area.
Ap = Aw*Ae*(10^8); %product area.
pin = (Ap^(7/8))*((Kt*deltaB*fs)/(11.1)); % power in(watts).
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