LTC3115-2_15 Datasheet, PDF (27/42 Pages) Linear Technology – 40V, 2A Synchronous Buck-Boost DC/DC Converter

LTC3115-2
Applications Information
50
0
40
GAIN
30
20
PHASE
–40
–80
–120
10
–160
0
–200
–10
–240
–20
–30
10
fC
100
1k
10k 100k
FREQUENCY (Hz)
–280
–320
1M
31152 F12
Figure 12. Converter Bode Plot, V_IN = 3.5V, I_LOAD = 500mA
At this point in the design process, there are three con-
straints that have been established for the compensation
network. It must have –19dB gain at f_C = 24kHz, a peak
phase boost of 60° and the phase boost must be centered
at f_C = 24kHz. One way to design a compensation network
to meet these targets is to simulate the compensated error
amplifier Bode plot in LTspice for the typical compensation
network shown on the front page of this data sheet. Then,
the gain, pole frequencies and zero frequencies can be
iteratively adjusted until the required constraints are met.
Alternatively, an analytical approach can be used to design
a compensation network with the desired phase boost,
center frequency and gain. In general, this procedure can
be cumbersome due to the large number of degrees of
freedom in a Type III compensation network. However the
design process can be simplified by assuming that both
compensation zeros occur at the same frequency, f_Z, and
both higher order poles (f_POLE2 and f_POLE3) occur at the
common frequency, f_P . In most cases this is a reasonable
assumption since the zeros are typically located between
1kHz and 10kHz and the poles are typically located near
each other at much higher frequencies. Given this as-
sumption, the maximum phase boost, f_MAX, provided by
the compensated error amplifier is determined simply by
the amount of separation between the poles and zeros as
shown by the following equation:
φ_MAX = 4 tan^{–1⎛⎝⎜}
f_P
f_Z
⎞
⎠⎟
–
270°
A reasonable choice is to pick the frequency of the poles,
f_P , to be about 50 times higher than the frequency of the
zeros, f_Z, which provides a peak phase boost of approxi-
mately φ_MAX = 60° as was assumed previously. Next, the
phase boost must be centered so that the peak phase
occurs at the target crossover frequency. The frequency
of the maximum phase boost, f_CENTER, is the geometric
mean of the pole and zero frequencies as:
f_CENTER = f_P • f_Z = 50 • f_Z ≅ 7 • f_Z
Therefore, in order to center the phase boost given a factor
of 50 separation between the pole and zero frequencies,
the zeros should be located at one seventh of the cross-
over frequency and the poles should be located at seven
times the crossover frequency as given by the following
equations:
f_Z
=
1
7
•
f_C
=
1
7
(24kHz
)
=
3.43kHz
f_P = 7 • f_C = 7(24kHz) = 168kHz
This placement of the poles and zeros will yield a peak phase
boost of 60° that is centered at the crossover frequency,
f_C. Next, in order to produce the desired target crossover
frequency, the gain of the compensation network at the
point of maximum phase boost, G_CENTER, must be set to
–19dB. The gain of the compensated error amplifier at the
point of maximum phase gain is given by:
( ) ^GCENTER
=
10
log
⎡
⎢
⎣⎢
(2π
f_Z
2π f_P
)³ R_TOP
C_FB
⎤
2
⎥
⎦⎥
dB
For more information www.linear.com/LTC3115-2
31152fa
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