Equation 36 indicates that the power plant is basically a first-order system. A Type-II compensator
as shown in Figure 7-1 is adequate to stabilize the loop for both buck and boost mode operations.
Assuming the output impedance of the gm
amplifier is RGM, the current loop compensation gain is determined by :
Equation 37.
where
- ACS is the current sense
amplifier gain, that is 40;
- Gm is the trans-conductance of the gm error amplifier, which
is 100μA/V;
- ZCOMP(s) is the equivalent impedance of the compensation
network seen at the COMP pin (see Figure 7-1)
Equation 38.
Considering CHF <<
CCOMP, Equation 38 can be simplified to :
Equation 39.
Because RGM is > 5MegΩ, and
the frequency range for loop compensation is usually above a few kHz, the effects of
RGM on the loop gain in the interested frequency range becomes negligible.
Therefore, substituting Equation 39 into Equation 37, and neglecting RGM, one can get the following:
Equation 40.
From Figure 7-2, the open-loop gain of the inner current loop can be found as:
Equation 41.
where
Equation 42.
Equation 43.
- KFF is the ramp generator
coefficient. For LM5171, KFF=0.03125.
Substituting Equation 40 and Equation 36 into Equation 41, Ti(s) can be written as:
Equation 44.
The poles and zeros of the total loop
transfer function are determined by:
Equation 45.
Equation 46.
Equation 47.
To tailor the total inner current loop gain
to crossover at fCI, select the components of the compensation network according
to the following guidelines, then fine tune the network for optimal loop performance.
- The zero fz is placed at
around 1/5 of target crossover frequency fCI,
- The pole fp2 is placed at
approximately 1/2 of switching frequency fSW,
- The total open-loop gain is set to
unity at fCI, namely,
Equation 48.
Therefore, the compensation components can
be derived from the above equations, as shown in Equation 49.
Equation 49.