Table 4. Application Example

8.2.2.1 Boost Component Selection

A boost converter operating in continuous-conduction mode (CCM) has a right-half-plane (RHP) zero in its transfer function. The RHP zero relates inversely to the load current and inductor value and directly to the input voltage. The RHP zero limits the maximum bandwidth achievable for the boost regulator. If the bandwidth is too close to the RHP zero frequency, the regulator becomes unstable.

Thus, for high-power systems with low input voltages, choose a low inductor value. A low value increases the amplitude of the ripple currents in the N-channel MOSFET, the inductor, and the capacitors for the boost regulator. Select these components with the ripple-to-RHP zero trade-off in mind and considering the power dissipation effects in the components due to parasitic series resistance.

A boost converter that operates always in the discontinuous mode does not contain the RHP zero in the transfer function. However, designing for the discontinuous mode demands an even lower inductor value that has high ripple currents. Also, ensure that the regulator never enters the continuous-conduction mode; otherwise, it becomes unstable.

Figure 25. Boost Compensation Components

8.2.2.2 Boost Maximum Input Current I_{IN_MAX}

The maximum input current flows at the minimum input voltage and maximum load. The efficiency for V_BAT = 5 V at 2.5 A is 80%, based on Figure 7.

Equation 5.

Hence,

Equation 6.

8.2.2.3 Boost Inductor Selection, L

Allow input ripple current of 40% of I_{IN max} at V_BAT = 5 V.

Equation 7.

Choose a lower value of 4 µH in order to ensure a high RHP-zero frequency while making a compromise that expects a high current ripple. This inductor selection also makes the boost converter operate in discontinuous conduction mode, where it is easier to compensate.

The inductor-saturation current must be higher than the peak-inductor current and some percentage higher than the maximum current-limit value set by the external resistive-sensing element.

Determine the saturation rating at the minimum input voltage, maximum output current, and maximum core temperature for the application.

8.2.2.4 Inductor Ripple Current, I_RIPPLE

Based on an inductor value of 4 µH, the ripple current is approximately 3.1 A.

8.2.2.5 Peak Current in Low-Side FET, I_PEAK

Equation 8.

Based on this peak current value, calculate the external current-sense resistor R_SENSE.

Equation 9.

Select 20 mΩ, allowing for tolerance.

The filter component values R_IFLT and C_IFLT for current sense are 1.5 kΩ and 1 nF, respectively, which allows for good noise immunity.

8.2.2.6 Right Half-Plane Zero RHP Frequency, f_RHP

Equation 10.

8.2.2.7 Output Capacitor, C_OUTx

To ensure stability, choose output capacitor C_OUTx such that

Equation 11.

Select C_OUTx = 680 µF.

This capacitor is usually aluminum electrolytic with ESR in the tens-of-milliohms. ESR in this range is good for loop stability, because it provides a phase boost. The output filter components, L and C, create a double pole (180-degree phase shift) at a frequency f_LC and the ESR of the output capacitor R_ESR creates a zero for the modulator at frequency f_ESR. One can determine these frequencies by Equation 12.

Equation 12.

This satisfies f_LC ≤ 0.1 f_RHP.

Potentially use a parallel configuration of smaller values to achieve this R_ESR or recalculate with the correct value.

8.2.2.8 Bandwidth of Boost Converter, f_C

Use the following guidelines to set the frequency poles, zeroes, and crossover values for the trade-off between stability and transient response:

f_LC < f_ESR< f_C< f_{RHP Zero}

f_C < f_{RHP Zero} / 3

f_C < f_SW / 6

f_LC < f_C / 3

8.2.2.9 Output Ripple Voltage Due to Load Transients, ?V_OUTx

Assume a bandwidth of f_C = 10 kHz.

Equation 13.

Because the boost converter is active only during brief events such as a cranking pulse, and the buck converters are high-voltage tolerant, a higher excursion on the boost output is tolerable in some cases. In such cases, choose smaller components for the boost output.

8.2.2.10 Selection of Components for Type II Compensation

The required loop gain for unity-gain bandwidth (UGB) is

Equation 14.

The boost-converter error amplifier (OTA) has a Gm that is proportional to the V_BAT voltage, which allows a constant loop response across the input-voltage range and makes compensation easier by removing the dependency on V_BAT.

Equation 15.

8.2.2.11 Input Capacitor, C_IN

The input ripple required is lower than 50 mV.

Equation 16.

Therefore, TI recommends 220 µF with 10-mΩ ESR or a parallel configuration of several capacitors to achieve such ESR-levels.

8.2.2.12 Output Schottky Diode D1 Selection

Maximizing efficiency requires a Schottky diode with low forward-conducting voltage (V_F) over temperature and fast switching characteristics. The reverse breakdown voltage must be higher than the maximum input voltage, and the component must have low reverse leakage current. Additionally, the peak forward current must be higher than the peak inductor current. Equation 17 gives the power dissipation in the Schottky diode:

Equation 17.

8.2.2.13 Low-Side MOSFET (BOT_SW3)

Equation 18.

The times t_r and t_f denote the rising and falling times of the switching node and relate to the gate-driver strength of the TPS43330A-Q1 and gate Miller capacitance of the MOSFET. The first term, t_r, denotes the conduction losses, which the low ON-resistance of the MOSFET minimizes. The second term, t_f, denotes the transition losses which arise due to the full application of the input voltage across the drain-source of the MOSFET as it turns on or off. Transition losses are higher at high output currents and low input voltages (due to the large input peak current), and when the switching time is low.

8.2.2.14 BuckA Component Selection

8.2.2.14.1 BuckA Component Selection

Equation 19.

t_{ON min} is higher than the minimum duty cycle specified (100 ns typical). Hence, the minimum duty cycle is achievable at this frequency.

8.2.2.14.2 Current-Sense Resistor R_SENSE

Based on the typical characteristics for the V_SENSE limit with V_IN versus duty cycle, the sense limit is approximately 65 mV (at V_IN = 12 V and duty cycle of 5 V / 12 V = 0.416). Allowing for tolerances and ripple currents, choose a V_SENSE maximum of 50 mV.

Equation 20.

Select 15 mΩ.

8.2.2.15 Inductor Selection L

As explained in the description of the buck controllers, for optimal slope compensation and loop response, choose the inductor such that:

Equation 21.

where

• K_FLR = coil-selection constant = 200

Choose a standard value of 8.2 µH. For the buck converter, choose the inductor saturation currents and core to sustain the maximum currents.

8.2.2.16 Inductor Ripple Current I_RIPPLE

At the nominal input voltage of 12 V, this inductor value causes a ripple current of 30% of I_{OUT max} ≈ 1 A.

8.2.2.17 Output Capacitor C_OUTA

Select an output capacitance C_OUTA of 100 µF with low ESR in the range of 10 mΩ, giving ?V_OUT(Ripple) ≈ 15 mV and a ?V drop of ≈ 180 mV during a load step, which does not trigger the power-good comparator and is within the required limits.

Equation 22.

Equation 23.

Equation 24.

8.2.2.18 Bandwidth of Buck Converter f_C

Use the following guidelines to set frequency poles, zeroes, and crossover values for the trade-off between stability and transient response.

• Crossover frequency f_C between f_SW / 6 and f_SW / 10. Assume f_C = 50 kHz.
• Select the zero f_z ≈ f_C / 10
• Make the second pole f_P2 ≈ f_SW / 2

8.2.2.19 Selection of Components for Type II Compensation

Figure 26. Buck Compensation Components

Equation 25.

where

• V_OUT = 5 V
• C_OUT = 100 µF
• Gm_BUCK = 1 mS
• V_REF = 0.8 V
• K_CFB = 0.125 / R_SENSE = 8.33 S (0.125 is an internal constant)

Use the standard value of R3 = 24 kΩ.

Equation 26.

Use the standard value of 1.5 nF.

Equation 27.

The resulting bandwidth of buck converter f_C

Equation 28.

f_C is close to the target bandwidth of 50 kHz.

The resulting zero frequency f_Z1

Equation 29.

f_Z1 is close to the f_C / 10 guideline of 5 kHz.

The second pole frequency f_P2

Equation 30.

f_P2 is close to the f_SW / 2 guideline of 200 kHz. Hence, the design satisfies all requirements for a good loop.

8.2.2.20 Resistor Divider Selection for Setting V_OUTA Voltage

Equation 31.

Choose the divider current through R1 and R2 to be 50 µA. Then

Equation 32.

and

Equation 33.

Therefore, R2 = 16 kΩ and R1 = 84 kΩ.

8.2.2.21 BuckB Component Selection

Using the same method as for V_BuckA produces the following parameters and components.

Equation 34.

This result is higher than the minimum duty cycle specified (100 ns typical).

Equation 35.

?I_ripple current ≈ 0.4 A (approximately 20% of I_{OUT max})

Select an output capacitance C_OUTB of 100 µF with low ESR in the range of 10 mΩ.

Assume f_C = 50 kHz.

Equation 36.

Equation 37.

Equation 38.

Equation 39.

Use the standard value of R3 = 30 kΩ.

Equation 40.

Equation 41.

Equation 42.

f_C is close to the target bandwidth of 50 kHz.

The resulting zero frequency f_Z1

Equation 43.

f_Z1 is close to the f_C guideline of 5 kHz.

The second pole frequency f_P2

Equation 44.

f_P2 is close to the f_SW / 2 guideline of 200 kHz.

Hence, the design satisfies all requirements for a good loop.

8.2.2.22 Resistor Divider Selection for Setting V_OUT Voltage

Equation 45.

Choose the divider current through R1 and R2 to be 50 µA. Then

Equation 46.

and

Equation 47.

Therefore, R2 = 16 kΩ and R1 = 50 kΩ.

8.2.2.23 BuckX High-Side and Low-Side N-Channel MOSFETs

An internal supply, which is 5.8 V typical under normal operating conditions, provides the gate-drive supply for these MOSFETs. The output is a totem pole, allowing full-voltage drive of V_REG to the gate with peak output current of 1.5 A. The reference for the high-side MOSFET is a floating node at the phase terminal (PHx), and the reference for the low-side MOSFET is the power-ground (PGNDx) terminal. For a particular application, select these MOSFETs with consideration for the following parameters: r_DS(on), gate charge Qg, drain-to-source breakdown voltage BVDSS, maximum DC current IDC(max), and thermal resistance for the package.

The times t_r and t_f denote the rising and falling times of the switching node and have a relationship to the gate-driver strength of the TPS43330A-Q1 and to the gate Miller capacitance of the MOSFET. The first term, t_r, denotes the conduction losses, which are minimimal when the ON-resistance of the MOSFET is low. The second term, t_f, denotes the transition losses, which arise due to the full application of the input voltage across the drain-source of the MOSFET as it turns on or off. Transition losses are lower at low currents and when the switching time is low.

Equation 48.

Equation 49.

In addition, during the dead time (t_d) when both the MOSFETs are off, the body diode of the low-side MOSFET conducts, increasing the losses. The second term in Equation 49 denotes this dead time. Using external Schottky diodes in parallel with the low-side MOSFETs of the buck converters helps to reduce this loss.

Table 5. Application Example 1

Table 6. Application Example 1 – Component Proposals

Table 7. Application Example 2

Table 8. Application Example 2 – Component Proposals