Page 24 - PEN Ebook March 2021

Design
Figure 1: PCM Buck Regulator Schematic and Bode Plot.
PEAK CURRENT MODE BUCK
REGULATORS
Peak current mode (PCM) control is widely used as
the control method for buck regulators. The bene-
fits associated with PCM control over voltage mode
(VM) control have already been well established.
Figure 1 shows the application schematic and typi-
cal bode diagram for a PCM buck regulator.
The two power-stage pole frequencies in Figure 1
can be calculated with Equation (1) and Equation
(2), respectively:
(1)
(2)
Where R can be calculated with Equation (3):
i
(3)
And K can be calculated with Equation (4), when
m
D = 0.5 (D represents the duty cycle):
(4)
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The ESR zero frequency in PCM-controlled buck
regulators (ω ) can be calculated with Equation (5):
Z
(5)
TYPICAL TYPE II COMPENSATION
NETWORK
Figure 2 shows a typical Type II compensation
network. A Type II compensation adds one zero
(COMP-Z) and one pole (COMP-P) to a system.
The frequency of COMP-Z and COMP-P can be
calculated based on the passive components
of the system (see Figure 2, Equation (6), and
Figure 2: Type II Compensation Network and Zero/Pole
Locations.
Equation (7)). Note that both the angle/phase and
the slope/magnitude due to a pole/zero will start
changing at 10% of the pole/zero frequency and
will reach their maximum value at 10 times the
frequency of the pole/zero.
The frequency of COMP-Z can be calculated with
Equation (6):
(6)
The frequency of COMP-P can be calculated with
Equation (7):
(7)
There are two criteria when it comes to the
transient performance of buck regulators. One
is the system bandwidth (BW), and the second
is the system phase margin (PM). The higher the
BW, the faster the transient response. The higher
the PM, the quieter and more stable the system.
Unfortunately, in practice, increasing the BW
decreases the PM, and vice versa. This means
there is a tradeoff between BW and PM. To have
a proper BW along with an acceptable PM and
acceptable noise level in a buck regulator, a BW
equal to 10% of the switching frequency (f ) is
SW
reasonable.
GUIDELINES TO EVALUATE
INTERNAL COMPENSATION
NETWORKS
Based on the discussion in the previous section,
let’s assume that the target BW can be calculat-
ed with Equation (8):
(8)
For a maximum PM, the compensation network
zero (COMP-Z) needs to provide its maximum
Design
phase boost at the BW frequency. In theory, the
positive phase due to a zero reaches its maxi-
mum value at 10 times its frequency. Therefore,
set COMP-Z between 10% and 20% of the BW
frequency. The range accounts for any additional
parasitic effects in the system. Therefore, the
relation between the COMP-Z frequency and the
BW frequency can be calculated with Equation (9):
(9)
For proper noise attenuation at higher frequen-
cies, the pole by the compensator (COMP-P)
must be approximately equal to f / 2, assum-
SW
ing that the switching frequency is <1MHz. If the
switching frequency is >1MHz, then COMP-P must
be near the lower value between f / 2 and the
SW
output capacitor ESR zero, estimated with Equa-
tion (5).
An important practical tip to consider is that,
unless C OUT is electrolytic with high ESR, f / 2
SW
has a dominant effect, and COMP-P is dependent
on that value. This allows COMP-P to be estimat-
ed with Equation (10):
(10)
Since COMP-Z and COMP-P are both defined
based on the switching frequency, one can use
the two equations to come up with the third
requirement, which is the relationship between
C COMP and C , and can be calculated with Equa-
HF
tion (11):
(11)
With these three basic requirements, one can
evaluate the performance of the internal com-
pensation networks based on the switching fre-
quency of the application.
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