Datasheet

TPS5103
MULTIPLE MODE SYNCHRONOUS DC/DC CONTROLLER
SLVS240A – SEPTEMBER 1999 – REVISED MAY 2001
22
POST OFFICE BOX 655303 • DALLAS, TEXAS 75265
APPLICATION INFORMATION
switching frequency
With hysteretic control, the switching frequency is a function of the following:
input voltage
output voltage
hysteresis window
delay of the hysteresis comparator and the driver
output inductance
resistance in the output inductor
output capacitance
ESR and ESL in the output capacitor
output current
turnon resistance of the high-side and the low-side MOSFET
This is a very complex equation if everything is included. To make it more useful to the designers, a simplified
equation only considers the most influential factors. The tolerance of this equation is about 30%.
ƒs
V
O
(V
I
V
O
) (ESR (10 10
7
Td) C
O
)
V
I
(V
I
ESR (10 10
7
Td) 0.0097 L
(O)
ESL V
I
)
Where fs is the switching frequency (Hz), V
O
is the output voltage, V
I
is the input voltage, C
O
is the output
capacitance, ESR is the equivalent series resistance in the output capacitor (Ω), ESL is the equivalent series
inductance in the output capacitor (H), L
(O)
is the output inductance (H), and Td is the output feedback RC filter
time constant (s).
For example: V
I
= 5 V, V
O
= 1.8 V, C
O
= 680 µF; ESR = 40 mΩ; ESL = 3 nH; L
(O)
= 6 µH; Td = 0.5 µs.
Then, the frequency (fs) = 122 kHz.
output inductor ripple current
The output inductor current ripple can affect not only the efficiency and the inductor saturation, but also the
output voltage capacitor selection. The equation is exhibited as below:
I
(ripple)
V
I
V
O
I
O
r
ds(on)
RL
L
O
D Ts
Where I
(ripple)
is the peak-to-peak ripple current (A) through inductor; V
I
is the input voltage, V
O
is the output
voltage, I
O
is the output current, r
ds(on)
is the on-time resistance of MOSFET (Ω), D is the duty cycle, and Ts
is the switching cycle (S). From the equation, it can be seen that the current ripple can be adjusted by changing
the output inductor value.
Example:
V
I
= 5 V, V
O
= 1.8 V, I
O
= 5 A, r
ds(on)
= 10 mΩ, RL = 5 mΩ, D = 0.36, Ts = 10 µs, L
(O)
= 6 µH
Then, the
I
(ripple)
= 2 A.
output capacitor RMS current
Assuming the inductor ripple current totally goes through the output capacitor to the ground, the RMS current
in the output capacitor can be calculated as:
I
O(rms)
I
12