LTC3118_15 Datasheet, PDF (32/38 Pages) Linear Technology – 18V, 2A Buck-Boost DC/DC Converter with Low-Loss Dual Input PowerPath

LTC3118
Applications Information
this pole is close to DC, R_EA = Voltage Error Amp output
resistance, which is approximately 5MΩ. This pole is
mentioned for completeness, but has no effect on the
overall loop design:
V_A
Zero 1 =
1
2π R_Z
C_P1
this zero is placed below the crossover frequency to flatten
the V_A gain at the crossover to improve phase margin:
V_A
Pole 2 =
1
2π R_Z C_P2
This pole is placed above the crossover frequency to reduce
the gain to suppress noise and mitigate any RHPZ effects.
Referring to the power stage gain curves in Figure 9, the
loop gain needs to be reduced by 4dB to achieve a total
loop crossover frequency of 20kHz. Assuming Zero 1 is
placed well below the crossover frequency and Pole 2 is
placed well above the crossover frequency, the voltage
amplifiers gain at crossover is given by:
V_A gain at crossover:
20
log
⎛
⎜
V_FB
⎝
• g_m • R_Z
V_OUT
⎞
⎟
⎠
=
20 log
⎛
⎝⎜
1V
•
80µA / V
5V
•
40k
⎞
⎠⎟
=
−
4dB
Where g_m is the V_A transconductance, V_FB/ V_OUT is the
feedback divider gain, and R_Z is the external zero resistor.
As shown, a 40kΩ value for R_Z will provide –4db of gain
at crossover. With R_Z selected, C_P1’s value is determined
by setting the Zero 1 frequency at one-tenth the crossover
frequency, or 2kHz.
C_P1
=
2π
•
1
R_Z •
f _ZERO1
=
1
≅ 1.8nF
2π • 40kΩ • 2kHz
Finally, the high frequency Pole 2 is set at 10 times the
crossover frequency to provide a high frequency pole at
200kHz.
C_P2
=
2π
1
• R_Z •
f _POLE2
=
1
≅ 22pF
2π • 40kΩ • 200kHz
The second set of curves in Figure 9 show the resulting V_A
response to the selected values. Notice that the separation
between Zero 1 and Pole 2 provides 60 degrees phase
bump near the crossover frequency.
Combining the power stage and V_A frequency responses,
the measured overall loop gains are shown in the bottom set
of curves of Figure 9. As shown, the crossover frequency
was reduced to 20kHz in buck mode, 10kHz in boost. The
phase margin at crossover is around 70 degrees. The
V_A design provided the additional benefits of high gain
(>50dB) at DC and gain attenuation above the crossover
frequency to prevent RHPZ issues.
3118f
32
For more information www.linear.com/LTC3118