MIC2111B Datasheet, PDF (25/35 Pages) Micrel Semiconductor – High-Performance, Multi-Mode, Step-Down Controller

Micrel, Inc.
MIC2111B
The feedback voltage-divider has a gain of A_FB = V_FB/V_OUT,
where V_FB is equal to 0.6V.The transconductance error
amplifier has a DC gain, A_EA(DC) = g_mEA × R_O, where g_mEA is
the error-amplifier transconductance, which is equal to
2ms, and R_O is the output resistance of the error amplifier,
which is 50MΩ. A dominant pole (ƒ_pdEA) is set by the
compensation capacitor (C_C), the amplifier output
resistance (R_O), and the compensation resistor (R_C); a
zero (ƒ_zEA) is set by the compensation resistor (R_C) and the
compensation capacitor (C_C). There is an optional pole
(ƒ_pEA) set by C_Cƒ and R_C to cancel the output capacitor
ESR zero if it occurs near the crossover frequency (ƒ_C):
ƒ_pdEA
=
2p ×
(R _O
1
+ R_C )× C_C
ƒ _zEA
=
2p
1
× R_C
× C_C
ƒ_pEA =
1
2p × R_C × C_Cƒ
ƒ_pdEA =
1
2π × (R_O + R_C ) × C_C
Eq. 11
A_MOD(ƒo) = A_MOD(DC) ×
ƒ _PO
ƒ_O
Eq. 15
Then R_C and C_C can be calculated as:
R_C
=
g_m
A_FB
× A_MOD(ƒO)
C_C
=
1
2π × R_C
× ƒ_PO
Eq. 16
Eq. 17
For high-current applications, it is recommended to place
C_Cƒ to cancel the effect of ESR zero:
C_Cƒ
=
1
2π × R_C
× ƒ_PO
Eq. 18
The crossover frequency, ƒ_O, should be much higher than
the power-modulator pole ƒ_PO. Also, ƒ_C should be less than
or equal to 1/5 the switching frequency:
ƒ_PO
<
<
ƒ_O
≤
ƒ _SW
5
Eq. 12
Choosing a lower cross-over frequency reduces the effects
of noise pickup into the feedback loop, such as jittery duty
cycle.
At the crossover frequency, the total loop gain must equal
1, and is expressed as:
A_MOD(ƒo) × A_EA(ƒo) × A_FB = 1
Eq. 13
Mid-band gain is decided by the g_m and R_C:
A_EA(ƒo) = g_m × R_C
Eq. 14
Where g_m = 2ms.
October 13, 2015
25
Revision 2.1