Table 3. Application Example

Table 4. Application Example – Component Proposals

9.2.2.1 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 may become 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 because of 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 can become unstable.

Figure 23. Boost Compensation Components

This design assumes operation in continuous-conduction mode. During light load conditions, the boost converter operates in discontinuous mode without affecting stability. Hence, the assumptions here cover the worst case for stability.

9.2.2.2 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 the graphs in the Typical Characteristicssection.

Equation 5.

Therefore:

Equation 6.

9.2.2.3 Boost Inductor Selection, L

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

Equation 7.

Select a lower value of 4 µH 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 compensation is easier.

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.

9.2.2.4 Inductor Ripple Current, I_RIPPLE

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

9.2.2.5 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.

9.2.2.6 Right Half-Plane Zero RHP Frequency, f_RHP

Equation 10.

9.2.2.7 Output Capacitor, C_OUTx

To ensure stability, select the output capacitor, C_OUTx, such that Equation 11 is true.

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. Use Equation 12 to determine these frequencies.

Equation 12.

Equation 12 satisfies f_LC ≤ 0.1 f_RHP.

9.2.2.8 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:

9.2.2.9 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 may be tolerable in some cases. In such cases, select smaller components for the boost output.

9.2.2.10 Selection of Components for Type II Compensation

The required loop gain for unity-gain bandwidth (UGB) is calculated with Equation 14.

Equation 14.

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

Equation 15.

9.2.2.11 Input Capacitor, C_IN

The input ripple required is lower than 50 mV.

Equation 16.

Therefore, TI recommends 220 µF with 10-mΩ ESR.

9.2.2.12 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 should be higher than the maximum input voltage, and the component should have low reverse leakage current. Additionally, the peak forward current should be higher than the peak inductor current. The following calculation gives the power dissipation in the Schottky diode:

Equation 17.

9.2.2.13 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 TPS43330-Q1 device, TPS43332-Q1 device, and gate Miller capacitance of the MOSFET. The first term denotes the conduction losses, which the low on-resistance of the MOSFET minimizes. The second term denotes the transition losses which arise because of 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 (because of the large input peak current) and when the switching time is low.

9.2.2.14 BuckA Component Selection

9.2.2.14.1 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.

9.2.2.14.2 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, select a V_SENSE maximum of 50 mV.

Equation 20.

Select a value of 15 mΩ for R_SENSE.

9.2.2.15 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.

K_FLR = coil-selection constant = 200

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

9.2.2.16 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.

9.2.2.17 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.

9.2.2.18 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

9.2.2.19 Selection of Components for Type II Compensation

Figure 24. 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, is calculated with Equation 28.

Equation 28.

f_C is close to the target bandwidth of 50 kHz.

The resulting zero frequency, f_Z1, is calculated with Equation 29.

Equation 29.

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

The second pole frequency, f_P2, is calculated with Equation 30.

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.

9.2.2.20 Resistor Divider Selection for Setting V_OUTA Voltage

Equation 31.

Select the divider current through R1 and R2 to be 50 µA. Then use Equation 32 and Equation 33 to find the values of R1 and R2.

Equation 32.

Equation 33.

Therefore, R2 = 16 kΩ and R1 = 84 kΩ.

9.2.2.21 BuckB Component Selection

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

Equation 34.

This value 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, is calculated with Equation 43.

Equation 43.

f_Z1 is close to the f_C guideline of 5 kHz.

The second pole frequency, f_P2, is calculated with Equation 44.

Equation 44.

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

Therefore the design satisfies all requirements for a good loop.

9.2.2.22 Resistor Divider Selection for Setting V_OUT Voltage

Equation 45.

Select the divider current through R1 and R2 to be 50 µA. Then use Equation 46 and Equation 47 to calculate the values of R1 and R2.

Equation 46.

Equation 47.

Therefore, R2 = 16 kΩ and R1 = 50 kΩ.

9.2.2.23 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 TPS4333x-Q1 family of devices and to the gate Miller capacitance of the MOSFET. The first term denotes the conduction losses, which are minimal when the on-resistance of the MOSFET is low. The second term denotes the transition losses, which arise because of 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 the preceding equation denotes this. Using external Schottky diodes in parallel with the low-side MOSFETs of the buck converters helps to reduce this loss.