LM4961LQBD/NOPB National Semiconductor, LM4961LQBD/NOPB Datasheet - Page 11

• Manufacturer Part Number: LM4961LQBD/NOPB
• Manufacturer: National Semiconductor

Specifications of LM4961LQBD/NOPB

• Lead Free Status / Rohs Status: Compliant

DUTY CYCLE
The maximum duty cycle of the boost converter determines
the maximum boost ratio of output-to-input voltage that the
converter can attain in continuous mode of operation. The
duty cycle for a given boost application is defined as:
This applies for continuous mode operation.
INDUCTANCE VALUE
The first question we are usually asked is: “How small can I
make the inductor.” (because they are the largest sized com-
ponent and usually the most costly). The answer is not simple
and involves trade-offs in performance. Larger inductors
mean less inductor ripple current, which typically means less
output voltage ripple (for a given size of output capacitor).
Larger inductors also mean more load power can be delivered
because the energy stored during each switching cycle is:
Where “lp” is the peak inductor current. An important point to
observe is that the LM4961 will limit its switch current based
on peak current. This means that since lp(max) is fixed, in-
creasing L will increase the maximum amount of power avail-
able to the load. Conversely, using too little inductance may
limit the amount of load current which can be drawn from the
output.
Best performance is usually obtained when the converter is
operated in “continuous” mode at the load current range of
interest, typically giving better load regulation and less output
ripple. Continuous operation is defined as not allowing the in-
ductor current to drop to zero during the cycle. It should be
noted that all boost converters shift over to discontinuous op-
eration as the output load is reduced far enough, but a larger
inductor stays “continuous” over a wider load current range.
To better understand these trade-offs, a typical application
circuit (5V to 12V boost with a 10µH inductor) will be analyzed.
We will assume:
Since the frequency is 1.6MHz (nominal), the period is ap-
proximately 0.625µs. The duty cycle will be 62.5%, which
means the ON-time of the switch is 0.390µs. It should be not-
ed that when the switch is ON, the voltage across the inductor
is approximately 4.5V. Using the equation:
We can then calculate the di/dt rate of the inductor which is
found to be 0.45 A/µs during the ON-time. Using these facts,
we can then show what the inductor current will look like dur-
ing operation:
Duty Cycle = V
V
IN
= 5V, V
OUT
OUT
= 12V, V
+ V
E = L/2 x (lp)2
V = L (di/dt)
DIODE
DIODE
- V
IN
= 0.5V, V
/ V
OUT
+ V
SW
DIODE
= 0.5V
- V
SW
11
During the 0.390µs ON-time, the inductor current ramps up
0.176A and ramps down an equal amount during the OFF-
time. This is defined as the inductor “ripple current”. It can also
be seen that if the load current drops to about 33mA, the in-
ductor current will begin touching the zero axis which means
it will be in discontinuous mode. A similar analysis can be
performed on any boost converter, to make sure the ripple
current is reasonable and continuous operation will be main-
tained at the typical load current values. Taiyo-Yudens
NR4012 inductor series is recommended.
MAXIMUM SWITCH CURRENT
The maximum FET switch current available before the current
limiter cuts in is dependent on duty cycle of the application.
This is illustrated in a graph in the typical performance char-
acterization section which shows typical values of switch
current as a function of effective (actual) duty cycle.
CALCULATING OUTPUT CURRENT OF BOOST
CONVERTER (I
As shown in Figure 2 which depicts inductor current, the load
current is related to the average inductor current by the rela-
tion:
Where "DC" is the duty cycle of the application. The switch
current can be found by:
Inductor ripple current is dependent on inductance, duty cy-
cle, input voltage and frequency:
combining all terms, we can develop an expression which al-
lows the maximum available load current to be calculated:
The equation shown to calculate maximum load current takes
into account the losses in the inductor or turn-OFF switching
losses of the FET and diode.
DESIGN PARAMETERS V
The value of the FET "ON" voltage (referred to as V
equations 7 thru 10) is dependent on load current. A good
I
LOAD
(max) = (1–DC)x(I
I
RIPPLE
I
FIGURE 3. 10μH Inductor Current
SW
I
LOAD
AMP
= I
5V - 12V Boost (LM4961X)
= DC x (V
IND
= I
)
IND
(AVG) + 1/2 (I
(AVG) x (1 - DC)
SW
SW
(max)–DC(V
IN
-V
AND I
SW
) / (f x L)
RIPPLE
SW
IN
)
-V
SW
))/2FL
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20094099
SW
(10)
(7)
(8)
(9)
in