
Keywords: boost converter, step up converter, continuous conduction mode, CCM, discontinuous conduction mode, DCM, error amplifier compensation, PI controller
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Using a PeakCurrentMode Controller to Design a Boost Converter
By: 
Giridharan Shanmugavel 
© Oct 15, 2012, Maxim Integrated Products, Inc.


Abstract: This application note describes how to design boost converters using the the MAX17597 and MAX17498B/C peakcurrentmode controller. Boost converters can be operated in discontinuous conduction mode (DCM) or continuous conduction mode (CCM). The operating mode can affect the component choices, stress level in power devices, and controller design. Formulas for calculating component values and ratings are presented.
Boost Converter
A typical
boost converter circuit schematic, built around the
MAX17597 peakcurrentmode
controller, is shown in
Figure 1. Input capacitors C1 and C2, inductor L
_{IN},
MOSFET N1,
diode D1, and output capacitor C8 form the main components for power conversion. C3 decides the
softstart duration. C4 decouples V
_{DRV} output voltage (set to 4.9V by the MAX17597's internal
regulator). R1 programs the slope compensation, which is necessary to provide internal stability in peakcurrentcontrol scheme. R2 and R3 form the potential divider for output voltage feedback. The network R4, C5, C6 forms the closedloop compensation network. The resistor network R5, R6, R7 sets the input enable and overvoltage threshold levels. R8 sets the switching frequency. R
_{CS} senses the current in MOSFET N1, and filter components R7 and C7 provide leadingedge filtering of the sensed current signal.
Figure 1. Typical application circuit.
DCM Boost
In a DCM boost converter, the inductor current returns to zero in every switching cycle. Energy stored during the ON time of the main
switch, MOSFET N1, is entirely depleted within the switching cycle.
Inductor Selection
The design procedure starts with calculating the boost converter's input inductor (L_{IN} of Figure 1), such that it operates in DCM at all operating input voltage and load current conditions. The critical inductance required to maintain DCM operation is calculated as:
L_{IN} ≤ [((V_{OUT}  V_{INMIN}) × V_{INMIN}²) × 0.4]/(I_{OUT} × V_{OUT}² × F_{SW}) henry 
(Eq. 1) 
where V_{INMIN} is the minimum input voltage, V_{OUT} is the desired output voltage, I_{OUT} is the load current specification, and F_{SW} is the chosen switching frequency. Practical L_{INMIN} choice shall take into account tolerances and saturation effects.
Peak Current Limit
For the purposes of setting the current limit, the peak current in the inductor can be calculated as:
in amperes 
(Eq. 2) 
The value of current limit, in MOSFET N1, is set as:
I_{LIM} = I_{PK} × 1.2 in amperes 
(Eq. 3) 
The currentsense resistor (R
_{CS} in Figure 1), connected between the
source of the MOSFET N1 and PGND, sets the peak current limit. The currentlimit
comparator has a voltage trip level (V
_{CSPEAK}) of 300mV. Use the following equation to calculate the value of R
_{CS}:
R_{CS} = (300mV/I_{LIM})Ω
Output Capacitor Selection
The output
capacitance (C8 of Figure 1) can be calculated as follows:
C_{OUT} = (I_{STEP} × T_{RESPONSE})/ΔV_{OUT} in farads 
(Eq. 4) 
Where T
_{RESPONSE} = (0.33/F
_{C} + 1/F
_{SW}) is the
response time of the controller.
I
_{STEP} is the load step expected at the output of boost converter, ΔV
_{OUT} is the allowable output voltage deviation for the expected load step, and F
_{C} is the target closedloop
crossover frequency. F
_{C} is chosen to be 1/10 of the switching frequency F
_{SW}. For the boost converter, the output capacitor supplies the load current when the main switch is ON, and therefore the output voltage ripple is a function of duty cycle and load current. Use the following equation to calculate the steady state output voltage ripple:
ΔV_{COUT} = (I_{OUT} × L_{IN} × I_{PK})/(V_{INMIN} × C_{OUT}) in volts 
(Eq. 5) 
Input Capacitor Selection
The required input ceramic capacitor (C2 of Figure 1) can be calculated based on the ripple allowed on the input DC bus. The input capacitor should be sized based on the
RMS value of the AC current handled by it. The calculations are:
C_{IN} = [(3.75 × I_{OUT})/(V_{INMIN} × F_{SW} × (1  D_{MAX}))] 
(Eq. 6) 
The capacitor RMS current is calculated as:
I_{CINRMS} = I_{PK}/(2 × √3) 
(Eq. 7) 
Where I_{PK} is the peak inductor current.
In practice, an electrolytic capacitor (C1 of Figure 1) is provided to decouple any source inductance formed by the input cables. The electrolytic capacitor, C1, may also be used as an energy storage element, which can supply power when input power fails.
Capacitor values change with
temperature and applied voltage. Refer to capacitor data sheets to select capacitors that would guarantee the required C
_{IN} and C
_{OUT} values across the operating range. Use the worstcase derated value of capacitance, based on temperature range and applied voltage, for further calculations.
Error Amplifier Compensation Design
The DC gain of the power stage, GDC, is given as:

(Eq. 8) 
The loop compensation values for the error amplifier are calculated as (for R4, C5, and C6 of Figure 1):
f_{P} = ((2 × V_{OUT}  V_{INMIN}) × I_{OUT})/(2π × (V_{OUT}  V_{INMIN}) × V_{OUT} × C_{OUT}) 
(Eq. 9) 

(Eq. 10) 
where V_{INMIN} is the minimum operating input voltage, and I_{OUT} is the maximum load current, m_{S} is the programmed slope (with default minimum slope = 50mV/µs chosen for DCM operation), and m_{P} = V_{INMIN}/L × R_{CS}
C_{5} = 1/(2π × f_{P} × R_{4}) 
(Eq. 11) 
C_{6} = 1/(π × f_{SW} × R_{4}) 
(Eq. 12) 
Slope Compensation
In theory, a DCM boost converter does not require slope compensation for stable operation. In practice the converter needs a minimum amount of slope for good noise immunity at very light loads. The minimum slope is set for the MAX17597 by allowing the SLOPE pin to float. The minimum slope compensation ramp is set to 50mV/µs when the SLOPE pin is left to float.
Output Diode Selection
The voltage rating of the output diode (D1 of Figure 1) for a boost converter, ideally, equals the output voltage. In practice, parasitic inductances and capacitances in circuit layout and components interact to produce voltage overshoot during the turnoff transition of the diode, which occurs when the main switch Q1 turns ON. The diode voltage rating should, therefore, be selected with necessary margin to accommodate extra voltage stress. A voltage rating of 1.3 × V_{OUT} provides the necessary design margin in most cases.
The current rating of the output diode is chosen to minimize the power loss in the component. The average power loss is given by the product of forward voltage drop and average diode current. Minimizing the power loss in the diode at its peak current level (I
_{PK}) gives the least dissipation in the component. Choose a diode with minimum voltage drop at I
_{PK}. Select fast recovery diodes with a
recovery time of less than 50ns or Schottky diodes, with low junction capacitance.
MOSFET RMS Current Calculation
The voltage stress on the MOSFET N1 ideally equals the sum of the output voltage and the forward drop of the output diode. In practice, voltage overshoot and ringing occur due to action of circuit parasitic elements during the turn off of N1. The MOSFET voltage rating should be selected with necessary margin to accommodate this extra voltage stress. A voltage rating of 1.3 × V_{OUT} provides the necessary design margin in most practical cases. The RMS current in the MOSFET is useful in estimating the conduction loss, and is given as:

(Eq. 13) 
where I_{PK} is the peak current calculated at the lowest operating input voltage, V_{INMIN}.
CCM Boost
In a CCM boost converter, the inductor current does not
return to zero during a switching cycle. Since the MAX17597 implements a nonsynchronous boost converter, the inductor current will enter DCM operation at load currents below a critical value, equal to half of the peaktopeak ripple in the inductor current.
Inductor Selection
The design procedure for CCM boost starts with calculating the boost converter's input inductor at minimum input voltage. The inductor ripple current (LIR) can be chosen between 30% and 60% of the maximum input current.
L_{IN} = (V_{INMIN} × D_{MAX} × (1  D_{MAX}))/(LIR × I_{OUT} × F_{SW}) 
(Eq. 14) 
where LIR is the chosen inductor ripple ratio (expressed in per unit) and D_{MAX}, the duty cycle is calculated as:
D_{MAX} = (V_{OUT} + V_{D}  V_{INMIN})/(V_{OUT} + V_{D}) 
(Eq. 15) 
V_{D} is the voltage drop across the output diode of the boost converter at maximum output current.
Peak/RMS Current Calculation
For the purposes of setting current limit, the peak current in the inductor and MOSFET can be calculated as follows:
I_{PK} = [(V_{OUT} × D_{MAX} × (1  D_{MAX}))/(L_{IN} × F_{SW}) + (I_{OUT}/(1  D_{MAX}))] for D_{MAX} < 0.5 
(Eq. 16) 
for D_{MAX} ≥ 0.5 
(Eq. 17) 
The value of current limit, in MOSFET N1, is set as:
I_{LIM} = I_{PK} × 1.2 
(Eq. 18) 
The currentsense resistor (R_{CS} in Figure 1), connected between the source of the MOSFET N1 and PGND, sets the peak current limit. The currentlimit comparator has a voltage trip level (V_{CSPEAK}) of 300mV. Use the following equation to calculate the value of R_{CS}:
R_{CS} = (300mV/I_{LIM})Ω 
(Eq. 19) 
Output Capacitor Selection
The output capacitance may be calculated as follows:
C_{OUT} = I_{STEP} × T_{RESPONSE}/ΔV_{OUT} 
(Eq. 20) 
T_{RESPONSE} (0.33/F_{C}) + (1/F_{SW}) 
(Eq. 21) 
where I_{STEP} is the load step, T_{RESPONSE} is the response time of the controller, ΔV_{OUT} is the allowable output voltage deviation, and F_{C} is the target closedloop crossover frequency. F_{C} is chosen to be 1/10 of the switching frequency F_{SW}. For a boost converter, the output capacitor supplies the load current when the main switch is ON, and therefore the output voltage ripple is a function of duty cycle and load current. Use the following equation to calculate the output capacitor steadystate ripple voltage:
ΔV_{COUT} = (I_{OUT} × D_{MAX})/(C_{OUT} × F_{SW}) 
(Eq. 22) 
Input Capacitor Selection
The required input ceramic capacitor (C2 of Figure 1) can be calculated based on the ripple allowed on the input DC bus. The input capacitor should be sized based on the RMS value of the AC current handled by it. The calculations are:
C_{IN} = [(3.75 × I_{OUT})/(V_{INMIN} × F_{SW} × (1  D_{MAX}))] 
(Eq. 23) 
The input capacitor RMS current can be calculated as:
I_{CIN_RMS} = (ΔI_{LIN})/(2 × √3) 
(Eq. 24) 
where
for D_{MAX} < 0.5 
(Eq. 25) 
for D_{MAX} ≥ 0.5 
(Eq. 26) 
In practice, an electrolytic capacitor (C1 of Figure 1) is provided to decouple any source inductance formed by the input cables. The electrolytic capacitor, C1, may also be used as an energy storage element, which can supply power when input power fails.
Capacitor values change with temperature and applied voltage. Refer to capacitor data sheets to select capacitors that would guarantee the required C_{IN} and C_{OUT} values across the operating range. Use the worst case derated value of capacitance, based on temperature range and applied voltage, for further calculations.
Error Amplifier Compensation Design
The loop compensation values for the error amplifier may now be calculated as (for R4, C5, and C6 of Figure 1):
R_{4} = (182 × V_{OUT}² × C_{OUT} × (1  D_{MIN}) × R_{CS})/(I_{OUT} × L_{IN}) 
(Eq. 27) 
where D_{MIN} is the duty cycle at the highest operating input voltage, given by the following expression.
D_{MIN} = (V_{OUT} + V_{D}  V_{INMAX})/(V_{OUT} + V_{D}) 
(Eq. 28) 
C_{5} = (V_{OUT} × C_{OUT})/(2 × I_{OUT} × R_{4}) 
(Eq. 29) 
C_{6} = 1/(π × F_{SW} × R_{4}) 
(Eq. 30) 
Slope Compensation Ramp
The slope required to stabilize the converter at duty
cycles greater than 50% can be calculated as follows:
m_{S} = ((0.82 × (V_{OUT}  V_{INMIN}) × R_{CS})/L_{IN})V/µs 
(Eq. 31) 
where L
_{IN} is in µH. Refer to the
MAX17597 data sheet to set the R1 value for the required slope m
_{S}.
Output Diodes Selection
The design procedure for outputdiode selection is identical to that outlined in the
DCM Boost section.
MOSFET RMS Current Calculation
The voltage stress on the MOSFET ideally equals the sum of the output voltage and the forward drop of the output diode. In practice, voltage overshoot and ringing occur due to action of circuit parasitic elements during the turnoff transition. The MOSFET voltage rating should be selected with the necessary margin to accommodate this extra voltage stress. A voltage rating of 1.3 × V_{OUT} provides the necessary design margin in most cases. The RMS current in the MOSFET is useful in estimating the conduction loss, and is given as:
I_{MOSFETRMS} = (I_{OUT} × √D_{MAX})/(1  D_{MAX}) 
(Eq. 32) 
where D_{MAX} is the duty cycle at the lowest operating input voltage, and I_{OUT} is the maximum load current.
Feedback Potential Divider (Common Method for DCM and CCM Designs)
R2 and R3 of Figure 1 form the output voltage feedback network. Choose R2 = 10kΩ. Based on R2, calculate R3 as:
R_{3} = R_{2} × (V_{OUT}/1.21  1)kΩ 
(Eq. 33) 
Refer to the
MAX17597 data sheet to program the softstart duration, EN/UVLO, and OVI potential divider and switching frequency.
Typical Operating Circuit
Figure 2. MAX17597 typical application circuit—CCM boost design.
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APP 5503: Oct 15, 2012
APPLICATION NOTE 5503,
AN5503,
AN 5503,
APP5503,
Appnote5503,
Appnote 5503
