Texas Instruments | TPS53319 DCAP Mode with Ripple Injection Modeling Design Consideration | Application notes | Texas Instruments TPS53319 DCAP Mode with Ripple Injection Modeling Design Consideration Application notes

Texas Instruments TPS53319 DCAP Mode with Ripple Injection Modeling Design Consideration Application notes
Application Report
SLUA730 – October 2014
TPS53319 DCAP Mode With Ripple Injection Modeling Design
Consideration
Power Management/Field Applications
Tony Huang
ABSTRACT
TPS53319 is high-current buck converter with DCAP mode. To use all the ceramic output capacitors, the
DCAP mode buck converter can be configured with external ripple injection. This paper discusses a novel
small-signal model and loop frequency response analysis. An example is implemented to verify the
modeling and compensation.
Contents
1
TPS53319 Introduction ................................................................................................................ 1
2
DCAP Mode Small-Signal Circuitry ............................................................................................. 2
3
DCAP Model Buck Converter Modeling Analysis ...................................................................... 3
4
TPS53319 Design Example .......................................................................................................... 7
5
Conclusion ................................................................................................................................... 8
6
References.................................................................................................................................... 8
Figures
Figure 1.
TPS53319 Internal Block Diagram .................................................................................. 2
Figure 2.
Control Block Diagram for COT Mode Buck Converter ................................................ 3
Figure 3.
DCAP Mode Buck Converter .......................................................................................... 3
Figure 4.
Equivalent Control Circuitry ........................................................................................... 4
Figure 5.
Small-Signal Implementation From Control to Output.................................................. 6
Figure 6.
TPS53319 Buck Converter With 5.0-V, 10-A Output ...................................................... 7
Figure 7.
Simulation Results With the Bode Plot Based on the Modeling .................................. 8
1 TPS53319 Introduction
TPS53319 is a 14-A synchronous switcher with DCAP mode and integrated MOSFETs. The device is
designed for ease of use, low external component count, and space-conscious power systems. These
devices feature accurate 1%, 0.6-V reference, and integrated boost switch. A sample of competitive
features include: a conversion input voltage range of 1.5 V wide to 22 V wide, very low external component
count, DCAP mode control for superfast transient, auto-skip mode operation, internal soft-start control,
selectable frequency, and no need for compensation. The conversion input voltage range is 1.5 to 22 V,
the supply voltage range is 4.5 V to 25 V, and the output voltage range is 0.6 V to 5.5 V, as shown in
Figure.1.
1
SLUA730
Figure 1.
TPS53319 Internal Block Diagram
2 DCAP Mode Small-Signal Circuitry
For a Buck converter with constant on time control mode, a sampling function as below can be introduced
to describe the function of constant on time sampling-hold control.
1 − e − S ×ton
H e (s) =
≈
s × t on
1
1+
2
s
t on
+
s2
π2
t on2 ;
(1)
Define:
Ga ( s) =
2
( s 2 R1 R2 C1C 2 + sR1C1 + sR2 C 2 + 1)
1
; Gb ( s ) =
sR1C1
s 2 R1 R2 C1C 2
(2)
SLUA730
Figure 2.
3
Control Block Diagram for COT Mode Buck Converter
DCAP Model Buck Converter Modeling Analysis
Figure 3 shows circuitry for a DCAP mode converter. Figure 4 shows equivalent control circuitry.
Figure 3.
DCAP Mode Buck Converter
3
SLUA730
Figure 4.
G2 ( s) =
G1 ( s ) =
Equivalent Control Circuitry
R
R2
+ sR2 C 2 ) + sR1C 2 (1 + 2 )
R3
R3
sR2 C 2
(3)
s 2 R1 R2 C1C 2 + s ( R1C1 + R1C 2 ) + 1
R
R
(1 + sR1C1 )(1 + 2 + sR2 C 2 ) + sR1C 2 (1 + 2 )
R3
R3
(4)
(1 + sR1C1 )(1 +
Then:
< Vs > − < Vo > + < Vo > + < Vb > G1 ( s )G2 ( s )
=< V fb >
G2 ( s)
(5)
Considering:
< Vs > − < Vo >= sLs < i L > ,
(6)
Meanwhile, defining:
r=
Ls
R1C1
(7)
Then:
G1 ( s )G2 ( s ) 
r

 < i L > r + < Vo > sL + < Vb > sR C1 
1
s
 sR1C1 =< V fb >

G
s
(
)


2




(8)
With small-signal transaction, then:
^
^
r i L + Vo
4
^ G ( s )G ( s )
r
2
+ Vb 1
=0
sLs
sR1C1
(9)
SLUA730
And define:
Z o ( s) = Z c ( s) =
RL (1 + sEsrC o1 )
(1 + sRL (C o1 + C o 2 ) )
(10)
Considering the COT control with sampling-hold function He(s), the loop gain can be described as shown
in Equations 11 through 13.
G (s) = −
[G1 ( s)G2 ( s)]
H e (s)
Z o (s)
 H e (s) 
1 +

sLs 

H e( s )
RL (1 + sEsrC o1 )
s 2 R1 R2 C1C 2 + sR1 (C1 + C 2 ) + 1
=−
2
s R1 R2 C1C 2
 H e ( s )  r (1 + sR L (C o1 + C o 2 ) )
1 +

sLs 

srR1C1
(
)
 s2

s
 2 +

1
+
ω

Q
ω
H e( s )
RL (1 + sEsrC o1 )
a a

G (s) = −  a
2
s
 H e ( s )  r[1 + sR L (C o1 + C o 2 )]
2
1 +

ωa
sLs 

ωa =
1
R1 R2 C1C 2
; Qa =
(11)
(12)
R1 R2 C1C 2
R1 (C1 + C 2 )
(13)
From this previous analysis, it is critical that we can use the COT current mode to simulate the loop
function. We can define the following parameters:
La = L s ; C a =
2
t on
2L
; Ra = s
2
t on
π Ls
Lc = R1 R2 C 2 ; Rc = R1 (1 +
C2
)
C1
Gm = 1 ; Ga = Gc = Gv1 = 1
r
(14)
(15)
(16)
With the previous definition, Figure 5 shows a small-signal circuitry implementation:
5
SLUA730
Figure 5.
Small-Signal Implementation From Control to Output
For the COT mode with ripple injection, according to Routh Criterion, the related stability criteria as in
Equation 17:
L
T
R1 R2 C1C 2
> s C out > on
R1 (C1 + C 2 ) + R2 C 2 R1C1
2
(17)
The simplified criteria as in Equation 18:
C 2 < C1 ; R2 > R1 ; f sw >
1
2π Ls C out
>
LC
T
1
; s out > on
2πR2 C 2 R1C1
2
(18)
Defining the gain function of the ripple injection circuitry:
G R (s) = −
(s
2
)
s2
ω
R1 R2 C1C 2 + sR1 (C1 + C 2 ) + 1
=−
2
s R1 R2 C1C 2
2
a
+
s
+1
ω a Qa
s2
ω a2
Therefore, the closed-loop gain function as in Equation 20:
6
(19)
SLUA730
RL (1 + sEsrC o1 )
G ( s) = G R ( s)
 H e ( s )  r (1 + sR L (C o1 + C o 2 ) )
1 +

sLs 

H e( s )
(20)
The closed-loop gain and phase have the following additional impact:
G R ( j 2πf c ) ≈
ωa
ωa
PhaseDelay ≈ − A tan(
)
2πf c Qa
2πf c Qa ;
(21)
Then, without loading and ignoring the Esr resistor, the crossover frequency and phase margin can be
approximately deduced as follows:
ωa
fc ≈
rQa C out
2π
; PhaseM arg in ≈ 90 o − A tan(
ωa
)
2πf c Qa
(22)
4 TPS53319 Design Example
Based on the COT buck converter schematic design (see Figure 6), using the small-signal analysis, we
can get the overall simulation model according to Figure 5. Figure 7 shows the simulated Bode plot results.
C1
4.7u
C2
2.2u
R1
4.7
Enable
12
C5
22u
C6
22u
LL
LL
LL
C13
0.1u
L1
1uH
Output: 5.0V/10A
11
10
LL
C4
22u
GND
9
8
R5
0
C3
22u
VIN
13
VIN
14
VIN
15
VIN
16
VIN
17
VIN
LL
LL
7
18
VREG
ROVP
19
VDD
VBST
20
21
TRIP
PGOOD MODE
U1 TPS53319
6
5
4
3
1
EN
RF
R4
187k
VFB
R3
110k
2
R2
200k
22
VIN: 12V
R6
1.5k
C14
47n
C7
47u
C8
47u
C9
47u
C10
47u
C11
47u
C12
47u
R7
14.7k
R8
2k
R9
14.7k
R10
2k
C15
1n
Figure 6.
TPS53319 Buck Converter With 5.0-V, 10-A Output
The test results showed the crossover frequency, 41.3 kHz, and the phase margin, 63.1 degrees.
7
SLUA730
T 100.00
Gain (dB)
50.00
0.00
-50.00
-100.00
200.00
Phase [deg]
100.00
0.00
-100.00
10
100
1k
Figure 7.
10k
Frequency (Hz)
100k
1M
Simulation Results With the Bode Plot Based on the Modeling
5 Conclusion
The analysis has shown that novel modeling and analysis is effective and critical to the design of the
DCAP mode converter. In addition, this paper has provided the control block diagram and the simulation
circuitry.
6 References
8
10M
1.
Texas instruments, SLUSAY8B, TPS53319 data sheet.
2.
Texas instruments, SLVU728, TPS53319 EVM-136 User’s Guide
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