Datasheet

'I
n
=
S
f
- S
e
S
n
+ S
e
'I
n-1
V
C
V
SEN
S
n
PWM Comparator
Waveforms
Time
Voltage
S
f
S
e
'I
0
'I
1
'I
2
LM3478
LM3478-Q1
www.ti.com SNVS085V –JULY 2000–REVISED FEBRUARY 2013
Figure 26. Sub-Harmonic Oscillation for D>0.5 and Compensation Ramp to Avoid Sub-Harmonic
Oscillation
Sub-harmonic Oscillation can be easily understood as a geometric problem. If the control signal does not have
slope, the slope representing the inductor current ramps up until the control signal is reached and then slopes
down again. If the duty cycle is above 50%, any perturbation will not converge but diverge from cycle to cycle
and causes sub-harmonic oscillation.
It is apparent that the difference in the inductor current from one cycle to the next is a function of S
n
, S
f
and S
e
as
follows:
(1)
Hence, if the quantity (S
f
- S
e
)/(S
n
+ S
e
) is greater than 1, the inductor current diverges and subharmonic
oscillation results. This counts for all current mode topologies. The LM3478 has some internal slope
compensation V
SL
which is enough for many applications above 50% duty cycle to avoid subharmonic
oscillation .
For boost applications, the slopes S
e
, S
f
and S
n
can be calculated with the formulas below:
S
e
= V
SL
x f
s
(2)
S
f
= R
sen
x (V
OUT
- V
IN
)/L (3)
S
n
= V
IN
x R
sen
/L (4)
When S
e
increases then the factor which determines if subharmonic oscillation will occur decreases. When the
duty cycle is greater than 50%, and the inductance becomes less, the factor increases.
For more flexibility slope compensation can be increased by adding one external resistor, R
SL
, in the Isens path.
Figure 27 shows the setup. The externally generated slope compensation is then added to the internal slope
compensation of the LM3478. When using external slope compensation, the formula for S
e
becomes:
S
e
= (V
SL
+ (K x R
SL
)) x f
s
(5)
A typical value for factor K is 40 µA.
The factor changes with switching frequency. Figure 28 is used to determine the factor K for individual
applications and the formula below gives the factor K.
K = ΔV
SL
/ R
SL
(6)
It is a good design practice to only add as much slope compensation as needed to avoid subharmonic oscillation.
Additional slope compensation minimizes the influence of the sensed current in the control loop. With very large
slope compensation the control loop characteristics are similar to a voltage mode regulator which compares the
error voltage to a saw tooth waveform rather than the inductor current.
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