Datasheet

LTC3115-2
26
31152f
For more information www.linear.com/LTC3115-2
applicaTions inForMaTion
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
= 4tan
–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:
G
CENTER
= 10log
2πf
P
2πf
Z
( )
3
R
TOP
C
FB
( )
2
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
dB
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
Figure 12. Converter Bode Plot, V
IN
= 3.5V, I
LOAD
= 500mA
FREQUENCY (Hz)
10
GAIN (dB)
PHASE (DEG)
0
10
20
10k
1M
31152 F12
–10
–20
–30
100 1k 100k
30
40
50
–200
–160
–120
–240
–280
–320
–80
–40
0
GAIN
PHASE
f
C