CHAPTER THREE
3.2 Sizing Components
3.2.2 Switch Rating
Transistors chosen for use in switching power supplies must have fast switching times and should be able to withstand the voltage spikes produced by the inductor.
Voltage rating: With an ideal switch, the maximum switch voltage (V switchmax) is the maximum voltage input3. But for a non ideal switch, V switchmax = Vinmax + VF where VF is the maximum forward drop across the switch at maximum load current.
27 Current Rating: The switch current rating is calculated based on the average value of switch current. During Ton , the inductor current is equal to switch current. During Toff switch current is equal to zero.
ON OFF ON OFF t (a)
iswitch
(b)
iDiode
t T 2T
Fig 3.4 Current Waveform (a) Inductor Current (b) Switch Current (c) Diode Current
Fig 3.4 shows the current wave forms through the diode, switch and diode.
I
switch= (i
Lmin+ i
Lmax) * t
on/ 2T
(3.8)I
switch= [(i
Lmax- ∆i
L)+ i
Lmax] * DT / 2T = [2i
Lmax- ∆i
L] * D / 2 I
switch= [ i
Lmax- ∆i
L/2] * D = i
L* D
I
switch> i
L* D
max (3.9)28 3.2.3 Diode Rating
It is necessary that the diode should be able to turn off relatively fast. Diodes known as the fast recovery diodes are used in these applications. The diodes average current ID is equal to the load current times the portion of the time the diode is conducting Toff as shown in Fig 3.5. The diode's forward-current specification must meet or exceed the maximum output current3.
iDiode
OFF OFF Fig 3.5 Diode current wave form
I
diode= (i
Lmin+ i
Lmax) * t
off/ 2T
(3.10)
I
diode= [(i
Lmax- ∆i
L)+ i
Lmax] * (1-D)T / 2T = [2i
Lmax- ∆i
L] * (1-D) / 2 I
diode= [ i
Lmax- ∆i
L/2] * (1-D) = i
L* (1-D)
I
diode> i
L* (1-D
min)
(3.11)The maximum reverse voltage on the diode is the maximum input voltage. The current voltage ratings are low enough that a small Schottky diode or a fast recovery diode could be used for this application.
Power dissipation is the limiting factor when choosing a diode. The worst-case average power can be calculated as follows:
Pdiode = (1- Dmin) * iL * VD (3.12)
where VD is the voltage drop across the diode at the given output current IOMAX. Time (s) Current (A)
29 3.2.4 Output Capacitor Selection
The capacitor voltage should withstand the maximum output voltage. Ideally
Vcmax = VO + ∆Vo/2 (3.13)
Where ∆Vo = ripple voltage VO = output voltage
Output capacitance is required to minimize the voltage overshoot and ripple present at the output of a buck converter. Since switched power regulators are usually used in high current, high-performance power supplies, the capacitor should be chosen for minimum loss. Loss in a capacitor occurs because of its internal series resistance and inductance.
Capacitors for switched circuits are chosen on the basis of effective series resistance (ESR). For very high performance power supplies, sometimes it is necessary to parallel capacitors to get a low enough effective series resistance. The maximum allowed output-voltage overshoot and ripple are sometimes specified at the time of design. Thus, to meet the ripple specification for a buck converter circuit, an output capacitor with ample capacitance and low ESR is included.
The output voltage ripple could be reduced by
Reducing the ESR by paralleling capacitors or using capacitors with lower ESR
The current ripple is reduced by increasing the circuit inductance or increasing the switching Frequency
The current ripple in the inductor current flows through the capacitor leaving the average flowing through the load1.
30 ic
ON OFF ON OFF t
Fig 3.6 Capacitor Current Waveform Fig 3.6 shows the capacitor current waveform.
Minimum output capacitance9
Q = ½ (T/2)(∆iL/2) = ∆iL/8F = [(Vo/L)(1-D)T] / 8F = (1-D)Vo/8LF2 Q= C*∆Vo
C= Q/∆Vo = [(1-D) Vo]/∆Vo 8LF2 =
(3.14) Vo/∆Vo =
(3.15)
∆Vo = ripple Voltage
∆Vo/Vo = percentage Ripple
T/2 +Q
T
-Q Ic
t
31 3.3 Open Loop Buck Converter Design
In the buck converter been designed, the circuit has the following specification:
Specification Value
Input Voltage (Vin) 32 – 64 V
Power Output (Po) 10 – 50 W
Switching Frequency (F) 20 kHz
Loading (R) 3 – 14 (Ω)
Output Voltage (Vout) 12 V
Time period of operation = T= Ton + Toff T= 1/F = 1/20000 = 50 us
The Duty Cycle D is ;
Dmin = Vo/Vin(max) = 12/64 = 0.19 Dmax = Vo/Vin(min) = 12/32 = 0.375
3.3.1 Inductance
The minimum required inductance is LC = (1-DMAX) RMAX / 2F
LC = (1-0.375)*14 / 2* 20000 LC = 2.1875 x 10-4 Henry
The Basic Buck circuit is simulated using the Portunus software using a period T = 50us and pulse-width Duty Cycle of 0.19 (Fig 3.7). During Ton, the switch S1 drops to 0.01 Ω connecting 64V (VIN) to L2. During Toff , the switch S1 pops open to 1 MΩ effectively disconnecting voltage input from the inductor L2. R represents the load powered by the Buck Converter.
With an inductance L equal to 0.3mH, the resulting inductor wave form is as shown in Fig 3.8.
32 Fig 3.7 buck converter
t/s
50 u 100 u 150 u 200 u 250 u 300 u 350 u 400 u 450 u 500 u 550 u 600 u 650 u 700 u 750 u 800 u 850 u 900 u 950 u 0
500 m 1 1.5 2
L2.I
Fig 3.8 Inductor Current at L= 0.3mh
t/s
50 u 100 u 150 u 200 u 250 u 300 u 350 u 400 u 450 u 500 u 550 u 600 u 650 u 700 u 750 u 800 u 850 u 900 u 950 u 0
500 m 1
L2.I
Fig 3.9 Inductor Current at L= 0.7mh
The resulting critical inductance is 0.3mH. For the actual Buck Converter, an inductor of size 0.7mH was selected, easily guaranteeing enough inductance to sustain continuous current operation as shown in Fig 3.9. With the inductor size taken into consideration, the 0.7mH inductor was designed with the following parameters:
Peak winding current Imax (A) 5
Inductance L (H) 0.0007
33
AL is equal to the inductance, in mH, obtained with a winding of 1000 turns.
AL = 10 B2max Ae2
Using Equations 3.15 – 3.18, the following results were obtained(16,17,18,19)
.
Using the ETD 39, the following parameters were obtained using
34 Aw= Kµ WA / N (3.20) Where Aw = Bare copper Area
A wire with bare copper area AW less than or equal to this value is selected using the metric Wire Gauge table is included in Appendix D.
R= ρN(MLT)/ Aww
Where Aww = bare copper area of actual copper used Ρ = resistivity of copper = 1.724 * 10-6 Ω-cm
The resulting Inductor Design Parameter is shown in Table 3.2.
Type of Core ETD 39
Number of Turns(n) 64
Air Gap 1mm
Wire Bare Area (metric format) 0.91186 mm
Wire Bare Area (Aww) 6.5 x 10 -3cm2
Winding resistance R(Ω) 0.102
Table 3.2 Inductor Design parameters
3.3.2 Capacitance
The key factor in determining the size of the capacitor is the amount of ripple voltage desired. Specifically, it is preferable to minimize ripple voltage. A larger capacitor leads to smaller ripple voltage. It was decided for this thesis that the ripple voltage, defined as ΔVo /Vo is about 0.1%
Solving for the capacitor size using equation 3.14 yields
C= = = 362 microfarad
A Portunus Model is simulated using an inductance of 0.7mH and capacitance of 362uF as shown in Fig 3.10
35
Fig 3.10 Output voltage and inductor current at L= 0.7mH and C= 362µF
t/s
Fig 3.11 Output voltage (R1.V) and inductor current (L2.I)at L= 0.7mH and C=
1000µF
The actual capacitor chosen for this thesis was 1000uF as shown in Fig 3.11. When substituted into equation 3.15 this value yields a peak-to-peak ripple voltage of 0.036 %.