ER3125QI Datasheet, PDF (24/30 Pages) Altera Corporation – MOSFET for Synchronous Buck or Boost Buck Converter

Page 24
Current Sampling Transfer Function H_e(S)
In current loop, the current signal is sampled every switching cycle. It has the following transfer function in Equation
22:
H_e(S)= -S_ω---_n22- + _ω----_n-S--Q----_n- + 1
where, Q_n and ω_n are given by
Q_n = –_π-2-, ω_n= πf_SW
(EQ. 22)
Power Stage Transfer Functions
Transfer function F₁(S) from control to output voltage is:
F₁(S)
=
v-ˆ---o-
dˆ
=
V_in --S_ω------_o22-----1₊-----⁺_-ω-------_o---^ω_S------Q---^{eS--------sp------r}--₊-----1-
(EQ. 23)
Where,
ω_esr = -R---_c-1--C----_o- ,Q_p ≈
R_o
C-L---_Po-
,ω_o=
--------1--------
L_PC_o
Transfer function F₂(S) from control to inductor current is given by Equation 24:
F₂(S)
=
ˆI--_o-
dˆ
= _R----Vo----^P₊---^V--R-^I--^N-_L---_P--
-S-_ω------_o22-----₊---1---_ω---⁺_{----o--S----Q}^{ω---S-------z}_--p-----+-----1-
(EQ. 24)
where ^ωz ⁼ _R----o^--1-C----_o^- .
Current loop gain T_i(S) is expressed as Equation 25:
T_i(S) = R_tF_mF₂(S)H_e(S)
(EQ. 25)
The voltage loop gain with open current loop is expressed in Equation 26:
T_v(S) = KF_mF₁(S)A_v(S)
(EQ. 26)
The Voltage loop gain with current loop closed is given by Equation 27:
L_v(S) = -1----T₊---^v--T-⁽--S_i--₍--⁾_S----)
(EQ. 27)
If T_i(S)>>1, then Equation 27 can be simplified as Equation 28:
L_v(S)= -R---^o-----⁺_R----t^R----L---^P-- -1--1--⁺--₊----^ω-----_ω--^e_--SS------ps^-------r _H-A---^ve---⁽⁽--S-S---⁾⁾- , ω_p ≈ _R----o--1-C----_o-
(EQ. 28)
Enpirion Power Datasheet ER3125QI 2.5A Regulator with Integrated High-Side MOSFET for
Synchronous Buck or Boost Buck Converter
10040
May 28, 2014
May 2014 Altera Corporation
Rev A