LTC3810-5
25
38105fd
degrees. Refer to your SPICE manual for details of how
to generate this plot.
*3810-5 modulator gain/phase
*2006 Linear Technology
*this file simulates a simplified model of
*the LTC3810-5 for generating a v(out)/
v(ith)
*bode plot
.param rdson=.0135 ;MOSFET rdson
.param Vrng=2 ;use 1.4 for INTVCC and
0.7 for ground
.param vsnsmax={0.173*Vrng-0.026}
.param Imax={vsnsmax/rdson}
.param DL=4 ;inductor ripple current
*inductor current
gl out 0 value={(v(ith)-1.2)*Imax/1.2+DL/2}
*output cap
cout out out2 270u ;capacitor value
resr out2 0 0.018 ;capacitor ESR
*load
Rout out 0 2 ; load resistor
vstim ith 0 0 ac 1 ;ac stimulus
.ac dec 100 100 10meg
.probe
.end
Mathematical software such as MATHCAD or MATLAB
can also be used to generate plots using the following
transfer function of the modulator:
H(s)
=
V
SENSE(MAX)
1.2 •R
DS(ON)
⎛
⎝
⎜
⎞
⎠
⎟
•
1
+
s •R
ESR
• C
OUT
1
+
s •R
L
• C
OUT
⎛
⎝⎜
⎞
⎠⎟
•R
L
s
=
j2
π
f
(2)
With the gain/phase plot in hand, a loop crossover fre-
quency can be chosen. Usually the curves look something
like Figure 13. Choose the crossover frequency about 25%
of the switching frequency for maximum bandwidth. Al-
though it may be tempting to go beyond f
SW
/4, remember
that significant phase shift occurs at half the switching
frequency that isn’t modeled in the above H(s) equation
and PSPICE code. Note the gain (GAIN, in dB) and phase
(PHASE, in degrees) at this point. The desired feedback
amplifier gain will be –GAIN to make the loop gain at 0dB
at this frequency. Now calculate the needed phase boost,
assuming 60° as a target phase margin:
BOOST = – (PHASE + 30°)
If the required BOOST is less than 60°, a Type 2 loop can
be used successfully, saving two external components.
BOOST values greater than 60° usually require Type 3
loops for satisfactory performance.
Finally, choose a convenient resistor value for R
FB1
(10k is
usually a good value). Now calculate the remaining values:
(K is a constant used in the calculations)
f = chosen crossover frequency
G = 10
(GAIN/20)
(this converts GAIN in dB to G in
absolute gain)
TYPE 2 Loop:
K
=
tan
BOOST
2
+
45
°
⎛
⎝⎜
⎞
⎠⎟
C2
=
1
2
π
• f • G •K •R
FB1
C1
=
C2 K
2
−
1
(
)
R2
=
K
2
π
• f • C1
R
FB2
=
V
REF
(R
FB1
)
V
OUT
−
V
REF
applicaTions inForMaTion
Figure 13. Transfer Function of Buck Modulator
FREQUENCY (Hz)
GAIN (dB)
PHASE (DEG)
38105 F13
0
0
–90
–180
GAIN
PHASE
