Datasheet


SLOS389A – NOVEMBER 2001– REVISED MAY 2002
www.ti.com
12
LC FILTER IN THE FREQUENCY DOMAIN
The transfer function for a 2
nd
order low-pass filter (Figures
17 and 18) is shown in equation (2):
H
LP
(jw) +
1
–
ǒ
w
w
0
Ǔ
2
)
1
Q
jw
w
0
) 1
w
0
+
1
LC
Ǹ
w + DRV591 switching frequency
Q + quality factor
For the DRV591, the differential output switching
frequency is typically selected to be 500 kHz. The resonant
frequency for the filter is typically chosen to be at least one
order of magnitude lower than the switching frequency.
Equation (2) may then be simplified to give the following
magnitude equation (3). These equations assume the use
of the filter in Figure 17.
Ť
H
LP
Ť
dB
+ –40 log
ǒ
f
s
f
o
Ǔ
f
o
+
1
2p LC
Ǹ
f
s
+ 500 kHz (DRV591 switching frequency)
If L=10 µH and C=10 µF, the cutoff frequency is 15.9 kHz,
which corresponds to –60 dB of attenuation at the 500 kHz
switching frequency. For VDD = 5 V, the amount of ripple
voltage at the TEC element is approximately 5 mV.
The average TEC element has a resistance of 1.5 Ω, so the
ripple current through the TEC is approximately 3.4 mA. At
the 3-A maximum output current of the DRV591, this 5.4
mA corresponds to 0.11% ripple current, causing less than
0.0001% reduction of the maximum temperature
differential of the TEC element (see equation 1).
LC FILTER IN THE TIME DOMAIN
The ripple current of an inductor may be calculated using
equation (4):
DI
L
+
ǒ
V
O
–V
TEC
Ǔ
DT
s
L
D + duty cycle (0.5 worst case)
T
s
+ 1ńf
s
+ 1ń500 kHz
For V
O
= 5 V, V
TEC
= 2.5 V, and L = 10 µH, the inductor
ripple current is 250 mA. To calculate how much of that
ripple current flows through the TEC element, however,
the properties of the filter capacitor must be considered.
For relatively small capacitors (less than 22 µF) with very
low equivalent series resistance (ESR, less than 10 mΩ),
such as ceramic capacitors, the following equation (5) may
be used to estimate the ripple voltage on the capacitor due
to the change in charge:
DV
C
+
p
2
2
ǒ
1–D
Ǔ
ǒ
f
o
f
s
Ǔ
2
V
TEC
f
o
+
1
2p LC
Ǹ
f
s
+ 500 kHz
D + duty cycle
For L = 10 µH and C = 10 µF, the cutoff frequency, f
o
, is 15.9
kHz. For worst case duty cycle of 0.5 and V
TEC
=2.5 V, the
ripple voltage on the capacitors is 6.2 mV. The ripple
current may be calculated by dividing the ripple voltage by
the TEC resistance of 1.5 Ω, resulting in a ripple current
through the TEC element of 4.1 mA. Note that this is
similar to the value calculated using the frequency domain
approach.
For larger capacitors (greater than 22 µF) with relatively
high ESR (greater than 100 mΩ), such as electrolytic
capacitors, the ESR dominates over the charging-
discharging of the capacitor. The following simple equation
(6) may be used to estimate the ripple voltage:
DV
C
+ D I
L
R
ESR
DI
L
+ inductor ripple current
R
ESR
+ filter capacitor ESR
For a 100 µF electrolytic capacitor, an ESR of 0.1 Ω is
common. If the 10 µH inductor is used, delivering 250 mA
of ripple current to the capacitor (as calculated above),
then the ripple voltage is 25 mV. This is over ten times that
of the 10 µF ceramic capacitor, as ceramic capacitors
typically have negligible ESR.
SWITCHING FREQUENCY CONFIGURATION:
OSCILLATOR COMPONENTS R
OSC
AND
C
OSC
AND FREQ OPERATION
The onboard ramp generator requires an external resistor
and capacitor to set the oscillation frequency. The
frequency may be either 500 kHz or 100 kHz by selecting
the proper capacitor value and by holding the FREQ pin
either low (500 kHz) or high (100 kHz). Table 1 shows the
values required and FREQ pin configuration for each
switching frequency.
Table 1. Frequency Configuration Options
SWITCHING
FREQUENCY
R
OSC
C
OSC
FREQ
500 kHz 120 kΩ 220 pF LOW (GND)
100 kHz 120 kΩ 1 nF HIGH (VDD)
(2)
(3)
(4)
(5)
(6)