
Application Information
FEEDBACK COMPENSATION
Open loop response of the regulator is defined as the product
of modulator transfer function and feedback transfer function.
When plotted on a dB scale, the open loop gain is shown as
the sum of modulator gain and feedback gain.
The modulator transfer function includes a power stage trans-
fer function with an embedded current loop and can be sim-
plified as one pole and one zero system as shown in equation
(15).
(15)
If the ESR of C
OUT (RESR) is very small, the modulator transfer
function can be further simplified to a one pole system and
the voltage loop can be closed with only two loop compensa-
tion components, R
COMP and CCOMP, leaving a single pole
response at the crossover frequency. A single pole response
at the crossover frequency yields a very stable loop with 90
degrees of phase margin.
The feedback transfer function includes the feedback resistor
divider and loop compensation of the error amplifier. R
COMP,
C
COMP and optional CHF configure the error amplifier gain and
phase characteristics and create a pole at origin, a low fre-
quency zero and a high frequency pole. This is shown math-
ematically in equation (16).
(16)
The pole at the origin minimizes output steady state error. The
low frequency zero should be placed to cancel the load pole
of the modulator. The high frequency pole can be used to
cancel the zero created by the output capacitor ESR or to
decrease noise susceptibility of the error amplifier. By placing
the low frequency zero an order of magnitude less than the
crossover frequency, the maximum amount of phase boost
can be achieved at the crossover frequency. The high fre-
quency pole should be placed well beyond the crossover
frequency since the addition of C
HF adds a pole in the feed-
back transfer function.
The crossover frequency (loop bandwidth) is usually selected
between one twentieth and one fifth of the f
SW. In a simplified
formula, the crossover frequency can be defined as:
(17)
For higher crossover frequency, R
COMP can be increased,
while proportionally decreasing C
COMP. Conversely, decreas-
ing R
COMP while proportionally increasing CCOMP, results in
lower bandwidth while keeping the same zero frequency in
the feedback transfer function.
The sampled gain inductor pole is inversely proportional to
the K factor, which is defined as:
(18)
The maximum achievable loop bandwidth, in fact, is limited
by this sampled gain inductor pole. In traditional current mode
control, the maximum achievable loop bandwidth varies with
input voltage. With the LM5117’s unique slope compensation
scheme, the sampled gain inductor pole is independent of
changes to the input voltage. This frees the user from addi-
tional concerns in wide varying input range applications and
is an advantage of the LM5117.
If the sampled gain inductor pole or the ESR zero is close to
the crossover frequency, it is recommended that the compre-
hensive formulas in
Table 1 be used and the stability should
be checked by a network analyzer. The modulator transfer
function can be measured and the feedback transfer function
can be configured for the desired open loop transfer function.
If a network analyzer is not available, step load transient tests
can be performed to verify acceptable performance. The step
load goal is minimum overshoot/undershoot with a damped
response.
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LM5117