DRV593

DRV594

SLOS401A - SEPTEMBER 2002 REVISED - OCTOBER 2002

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15

LC FILTER IN THE FREQUENCY DOMAIN

The transfer function for a second-order low-pass filter (Figures 17 and 18) is shown in equation (5):

H

LP

(j

w) +

1

w

0

2

) 1

Q

j

w

w

0

) 1

w

0 +

1

LC

Q

+ quality factor

For the DRV593 and DRV594, 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 (5) may then be simplified to give the following magnitude equation (6). These

equations assume the use of the filter in Figure 22.

H

LP dB +

–40 log

fs

fo

fo +

1

2

p LC

fs + 500 kHz (DRV593 or DRV594 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 DRV593 and DRV594, 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 4).

LC FILTER IN THE TIME DOMAIN

The ripple current of an inductor may be calculated using equation (7):

DI

L +

V

O

–V

TEC

DTs

L

D

+ duty cycle (0.5 worst case)

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 m

Ω), such as ceramic capacitors, the following equation (8) may be used to estimate the ripple voltage on

the capacitor due to the change in charge:

DV

C +

2

1–D

fo

fs

2

V

TEC

fo +

1

2

p LC

fs + 500 kHz

D

+ duty cycle

(5)

(6)

(7)

(8)