ISL78223 Datasheet, PDF (14/20 Pages) Intersil Corporation – ZVS Full-Bridge PWM Controller with Adjustable Synchronous Rectifier Control

ISL78223
The criteria for determining the correct amount of external ramp
can be determined by appropriately setting the damping factor of
the double-pole located at half the oscillator frequency. The
double-pole will be critically damped if the Q-factor is set to 1,
and over-damped for Q > 1, and under-damped for Q < 1. An
under-damped condition can result in current loop instability.
Q = -_π---₍---_m-----_c---₍--₁-----–--¹---_D-----₎---–-----₀---_.--₅----₎
(EQ. 12)
where D is the percent of on time during a half cycle. Setting
Q = 1 and solving for S_e yields:
S_e
=
S_n
⎛⎛
⎝⎝
1_π--
+
0.5_⎠⎞
------¹-------
1–D
–
1_⎠⎞
(EQ. 13)
Since S_n and S_e are the on time slopes of the current ramp and
the external ramp, respectively, they can be multiplied by T_ON to
obtain the voltage change that occurs during T_ON.
V_e
=
V_n
⎛⎛
⎝⎝
1_π--
+
0.5_⎠⎞
------¹-------
1–D
–
1_⎠⎞
(EQ. 14)
where V_n is the change in the current feedback signal during the
on time and V_e is the voltage that must be added by the external
ramp.
V_n can be solved for in terms of input voltage, current transducer
components, and output inductance yielding:
V_e
=
T_{----S----W-------}⋅_---V_----O------⋅_---R_----C----S--
N_CT ⋅ L_O
⋅
N_-----S--
N_P
⎛
⎝
1_π--
+
D
–
0.5_⎠⎞
V
(EQ. 15)
where R_CS is the current sense burden resistor, N_CT is the current
transformer turns ratio, L_O is the output inductance, V_O is the
output voltage, and N_S and N_P are the secondary and primary
turns, respectively.
The inductor current, when reflected through the isolation
transformer and the current sense transformer to obtain the
current feedback signal at the sense resistor yields:
V_CS
=
N_{-N----SP-----}⋅⋅_---RN_{-----CC----ST--}
⎛
⎝⎜ ^{I O}
+
D_------⋅_---T_{----S----W---}
2L_O
⎛
⎝⎜ ^{V I N}
⋅
N_-----S--
N_P
–
⎞⎞
V_{O⎠⎟}
⎟
⎠
V
(EQ. 16)
where V_CS is the voltage across the current sense resistor and I_O
is the output current at current limit.
Since the peak current limit threshold is 1.00V, the total current
feedback signal plus the external ramp voltage must sum to this
value.
V_e + V_CS = 1
(EQ. 17)
Substituting Equations 15 and 16 into Equation 17 and solving
for R_CS yields:
R_CS
=
N_-----P-----⋅_---N_{-----C----T- ⋅ --------------------------1----------------------------}
N_S
I_O
+
V_-----O--
L_O
T_SW
⎛
⎝
1_-π-
+
D_{-2--⎠⎞}
Ω
(EQ. 18)
For simplicity, idealized components have been used for this
discussion, but the effect of magnetizing inductance must be
considered when determining the amount of external ramp to
add. Magnetizing inductance provides a degree of slope
compensation to the current feedback signal and reduces the
amount of external ramp required. The magnetizing inductance
adds primary current in excess of what is reflected from the
inductor current in the secondary.
ΔI_P
=
V_{-----I--N-----}⋅_---D_-----T_{----S----W---}
L_m
A
(EQ. 19)
where V_IN is the input voltage that corresponds to the duty cycle
D and L_m is the primary magnetizing inductance. The effect of
the magnetizing current at the current sense resistor, R_CS, is:
ΔV_CS
=
Δ_-----I_--P-----⋅_---R_----C----S--
N_CT
V
(EQ. 20)
If ΔV_CS is greater than or equal to V_e, then no additional slope
compensation is needed and R_CS becomes:
R_CS
=
--------------------------------------------------------------^N----^C----^T---------------------------------------------------------------
N_-----S--
N_P
⋅
⎛
⎝⎜ ^{I O}
+
D_-----T_{----S----W---}
2L_O
⋅
⎛
⎜
⎝
V_I
N
⋅
N_-----S--
N_P
–
⎞⎞
V_{O⎠⎟}
⎟
⎠
+
-^V----^I--^N-----^â‹---^D-----^T----^S----^W---
L_m
(EQ. 21)
If ΔV_CS is less than Ve, then Equation 16 is still valid for the value
of R_CS, but the amount of slope compensation added by the
external ramp must be reduced by ΔV_CS.
Adding slope compensation may be accomplished in the
ISL78223 using the CTBUF signal. CTBUF is an amplified
representation of the sawtooth signal that appears on the CT pin.
It is offset from ground by 0.4V and is 2x the peak-to-peak
amplitude of CT (0.4V to 4.4V). A typical application sums this
signal with the current sense feedback and applies the result to
the CS pin as shown in Figure 12.
R9
R6
RCS
1
20
2
19
3 CTBUF
18
4
17
5
16
6
ISL78223 ₁₅
7
14
8 RAMP
13
9 CS
12
10
GND 11
C4
FIGURE 12. ADDING SLOPE COMPENSATION
Assuming the designer has selected values for the RC filter
placed on the CS pin, the value of R9 required to add the
appropriate external ramp can be found by superposition.
V_e – ΔV_CS
=
-⁽--^D-----⁽--^V----^C-----^T---^B----^U----^F-----–----⁰----^.-⁴----⁾----+-----⁰---^.--⁴---⁾----^â‹---^R-----⁶-
R6 + R9
V
(EQ. 22)
14
FN7936.1
January 2, 2013