LTC1703 Datasheet, PDF (29/36 Pages) Linear Technology – Dual 550kHz Synchronous 2-Phase Switching Regulator Controller with 5-Bit VID

LTC1703
APPLICATIO S I FOR ATIO
Very quickly, the feedback loop will realize that something
has changed and will move at the bandwidth allowed by
the external compensation network towards a new duty
cycle. If the bandwidth is set to 50kHz, the COMP pin will
get to 60% of the way to 90% duty cycle in 3µs. Now the
inductor is seeing 3.5V across itself for a large portion of
the cycle, and its current will increase from 1A at a rate set
by di/dt = V/L. If the inductor value is 0.5µH, the di/dt will
be 3.5V/0.5µH or 7A/µs. Sometime in the next few micro-
seconds after the switch cycle begins, the inductor current
will have risen to the 5A level of the load current and the
output capacitor will stop losing charge.
Note that the output voltage will stop dropping before the
inductor current reaches this new output current level.
Recall that any practical output capacitor looks like a pure
capacitance in series with some amount of ESR. When a
load transient hits, virtually all of the initial voltage drop at
the output is due to IR drop across the ESR. The output
capacitance begins to discharge at the same time and
continues until the inductor current rises to match the new
output current level.
The output voltage, however, will turn around and start
heading the right way before this happens. The next time
the top MOSFET turns on, the inductor current will begin
increasing linearly. This increasing current flows almost
entirely into the capacitor, going through the ESR as it
does so (Figure 16). Positive di/dt in the inductor causes
positive dv/dt in the ESR, regardless of what the “pure”
capacitance is doing. The output voltage will turn around
when the positive dv/dt across the ESR exceeds the
negative dv/dt across the pure capacitance. If the expected
load step (∆I) is known, an optimum inductor value can be
chosen:
( ) ^{L ≤}
V_IN – V_OUT
• C • ^ESR
∆I
Making L smaller than this optimum value yields little or no
improvement in transient response. As the output voltage
recovers, the inductor current will briefly rise above the
level of the output current to replenish the charge lost from
the output capacitor. With a properly compensated loop,
the entire recovery time will be inside of 10µs.
Most loads care only about the maximum deviation from
ideal, which occurs somewhere in the first two cycles after
the load step hits. During this time, the output capacitor
does all the work until the inductor and control loop regain
control. The initial drop (or rise if the load steps down) is
entirely controlled by the ESR of the capacitor and amounts
to most of the total voltage drop. To minimize this drop,
reduce the ESR as much as possible by choosing low ESR
I_L
I_L
I_OUT
I_L
V_SW
L
+
V_ESR
C_OUT
V_CAP
V_OUT
I_OUT
V_ESR
V_CAP
V_OUT
1703 F16a
Figure 16a. Capacitor Parasitics
Affecting Transient Recovery
I_OUT
V_ESR
V_CAP
V_OUT
V_OUT(NOMINAL)
TRANSIENT
HITS
V_OUT
TURNS
AROUND
I_L > I_OUT
TIME
Figure 16b. Transient Recovery Curves
1703 F16b
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