Datasheet

100 1k 10k 100k 1M
FREQUENCY (Hz)
-10
0
10
20
30
40
50
ERROR AMP GAIN (dB)
100 1k 10k 100k 1M
FREQUENCY (Hz)
-180
-150
-120
-90
-60
-30
0
ERROR AMP PHASE (°)
G
EA
x OPG
G
EA-ACTUAL
=
1 + G
EA
+ OPG
OPG =
2S x 10 MHz
s +
2S x 10 MHz
g
m
x 72 M:
C
1
=
1
2S x R
1
x f
P
LM3495
www.ti.com SNVS410F –FEBRUARY 2006–REVISED APRIL 2013
The value, B, can be determined by evaluating the power stage transfer function at the desired cross-over
frequency, or by reading the value graphically from the power stage gain plot. Setting B equal to the inverse of
the linear gain will force the total loop gain to be 1 (0dB) at the cross-over frequency. For this example the
desired cross-over frequency is 1/10 of the switching frequency, or 50 kHz. At 50 kHz the value of G
PS
is
approximately -4dB, or 0.63V/V. This indicates a system where the f
Z
≥ f
SW
. The value B should then be set to
1.58V/V and increased by 0.1V/V steps until the phase margin is at 45°. For this example, phase is 45° when B
is 2.8V/V.
Once R
1
has been selected, C
1
is calculated based on the value of R
1
as shown in the following equation:
(32)
R
1
= 3.73 kΩ, and C1 = 15.7 nF. The closest 1% value should be used for R
1
and the closest 10% value used for
C
1
, which gives:
R
1
= 3.74 kΩ 1%
C
1
= 15 nF 10%
The error amplifier of the LM3495 has a unity-gain bandwidth of 10 MHz. In order to model the effect of this
limitation, the open-loop gain, OPG, can be calculated as:
(33)
The new error amplifier transfer function taking into account unity-gain bandwidth is:
(34)
The gain and phase of the error amplifier are shown in Figure 38.
Figure 38. Error Amplifier Gain and Phase
The total control loop transfer function, H, is equal to the power stage transfer function multiplied by the error
amplifier transfer function. The bandwidth and phase margin can be read graphically from Bode plots of H,
shown in Figure 39.
H = G
PS
x G
EA-ACTUAL
(35)
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