Transcript Elektroniczne Układy i Systemy Zasilania

SWITCH-MODE POWER
SUPPLIES AND SYSTEMS
Lecture No 8
Silesian University of Technology
Faculty of Automatic Control, Electronics
and Computer Sciences
Ryszard Siurek Ph.D., El. Eng.
Components used in output filters
Electrolytic capacitors
Real capacitor equivalent circuit
UC
iC(t)
C
t
ULC
T

Uw e  U0
L
U
ULC  LC 0
L
ULC  LC
UrC
urc(t)  iC (t)rC
UCC
UC
C
Lc
rc
ULC
UrC
iC(t)
UCC
for the capacitor 100mF/35V
with Ic = 1,25A
C = 100 mF
Uc = 0,1V
rc = 200 mW
Urc = 0,25V
Lc = 100 nH
ULC = 0,0125V
Uw e  U0 2
t  UC (0)
2LC
U
UCC  0 (t  t)2  UC (t)
2LC
ESR - Equivalent Series Resistance
UCC 
Series resistance of the electrolytic trcapacitor has most
significant influence on the output voltage
– special capacitors with low rs are to be used in
switching applications
RMS current value influence on the output capacitor
Flyback converter
Single-ended forward converter
Considering critical current flow and
g = 0,5
I0 = 5A
ID
Imax
ID
I0
I0
t
Imax = 4I0 = 20A
t
T
ID < 20%I0 = 1A
IC
UC
IC
ULC
UCC+ULC
UC > 400 mV
Icrms= 8,16 A
UC
assuming:
rC = 20mW
UC < 20 - 25 mV
Icrms= 0,81 A
T
General rules of electrolytic capacitor selection for
switch-mode applications
capacity
[mF]
2200
4700
6800
nominal rated voltage
[V]
25
50
80
1780
2120
2480
2770
3240
3670
4350
Maximum permissible RMS current value
[mA] for electrolytic capacitors in the
temperature of 85oC or 105oC and frequency
of 120Hz (such current value causes the
capacitor temperature rise < 8 deg)
Kt
2
1
20
40
60
Kf
80
100
[oC]
160-450V
1,4
Icrmsmax=KtKfIrms
63-100V
1,2
1
120
1k
10k
[Hz]
•
select special capacitors with low ESR to keep output voltage ripple small
•
use proper capacitor (or several capacitors connected in paralell) with permissible
RMS current much higher than the maximum RMS current value in real circuit
•
Select capacitors with biggest admissible dimensions as they perform better heat
transfer to the environment (due to power losses on ESR)
•
make external series resitances of electrical leads and connections as low as
possible and symmetrical (traces on PCB, wires, metal buses etc.)
•
place electrolytic capacitors apart from components generating heat (power
resistors, heat sinks etc.)
D1
ZS
rt
rt
UOUT=U0
Output filter inductor
1.
Magnetic material choise depends on:
- operating frequency - for high AC currents (magnetic field) and frequencies
over 1 kHz ferrite materials are generally used due to low power losses, for low
frequencies ferrosilicon cores should be used due to high saturation flux density
Bs (windings with smaller number of turns – lower „copper” losses), modern
technological solutions – nanocrystallic or amorphic cores may be used up to the
frequencies of 100 kHz as they combine adavantages of ferrite and iron cores
(high Bs and extremely low core power losses)
- IDC/IAC relation - core dimensions, air gap width, so called „window area”
- mechanical properties – mounting method, resistance to temperature,
shocks, vibrations itp.
Inductor design procedure
1. Specifying required inductance of the output choke basing on the AC output current
component
L
IL
Io
UIN - U0
t  20Ι0
L
UIN
C
Ro
U0
L
UIN - U0
t
0,2I0
2. Winding wire diameter
usually assumed current density
J
I0

2,5 < J < 5 [A/mm2]
I0
d 2
 J
d2
4
3. Core volume and air-gap selection
B T 
without air-gap
with air-gap
lg
Bs
B
B0
Sw
H
H
H0(I0)
H0 
-Bs
A
M 
 
H1(I1)
I0  ZL
lg
lm
Using Hahn diagrams
Ku  B L
BL
AL.=800
AL.=250
ETD34
AL.=6600
AL  f( 1 )
lg
L  AL  z2
AL.=400
EE30
AL.=1000
AL.=10000
0,1
a)
b)
c)
d)
e)
f)
g)
h)
i)
1,0
10
100
1000
NI [Azw]
Initial core selection (diameters)
assume air-gap lenght (AL)
find the maximum value of ampere-turns IxZ [Azw]
check if the required inductance may be achieved - (1)
if not, try with bigger air-gap (lower AL) and go back to d)
if yes, check if there is enough space for winding in the core window area
if not, select bigger core and start from a)
if yes - output choke is ready
eventualy try with the smaller core if it is to much free room in the window area
(1)
Core selection basing on „AP” (Area Product) – characteristic value
for the core of certain dimentions
AP [cm4]
Sw
100
AP  Sw  Se
l
[cm4 ]
10
Se
For the presented example
1,0
ETD34 – AP=1.185 cm4 , l = 34 mm
0,2
1
2
5
10
20
50 100
I0 [A]
Calculating the number of turns
E  zL
zL  Se
d
dI
L
dt
dt
dΒ dI
L
dt
dt
zL 
L  I
B  S e
przyjmujemy I = I0+0,1I0
oraz B = BS
zLm in 
L  (I0  0.1I0 )
Bs  Se
Air-gap lenght calculation
μ μr  zL2  Se
lg  0
10 2 [cm]
L
mr  permability of the air (=1)
m0  magnetic field constant (4p10-7)
Empirical method
1.
Make the winding with the number of turns zL > zLmin, use wire of maximum possible
diameter and then under the nominal load try to decrease the air gap step by step
measuring the inductor current waveform (output ripple)
2.
Set the air-gap, which gives lowest ripple but without any sign of saturation
IL (UrC)
IL (UrC)
optimal air-gap
IL (UrC)