SLVAFU9 Application note

SLVAFU9 January 2025 TPS62840 , TPS62843

1.2 Output Current Calculations

The average inductor current is also affected in this topology. In the buck configuration, the average inductor current is equal to the average output current because the inductor always supplies current to the load during both the on and off times of the control MOSFET. However, in the inverting buck-boost configuration, the load is supplied with current only from the output capacitor and is completely disconnected from the inductor during the on time of the control MOSFET. During the off time, the inductor connects to both the output capacitor and the load (see Figure 1-5). Knowing that the off time is (1 – D) of the switching period, Equation 1 can be used to calculate the average inductor current:

Equation 1.

I_{L (A v g)} = \frac{I_{O U T}}{(1 - D)}

The operating duty cycle for an inverting buck-boost converter can be found with Equation 2:

Equation 2.

D = \frac{V_{O U T}}{(V_{O U T} - V_{I N}) \times η}

Rather than V_OUT/V_IN for a buck converter. The efficiency term in Equation 2 adjusts the equations in this section for power conversion losses and yields a more accurate maximum output current result. The peak-to-peak inductor ripple current is given by Equation 3:

Equation 3.

Δ I_{L} = \frac{V_{I N} \times D}{f_{S} \times L}

where:

ΔI_L (A): the peak-to-peak inductor ripple current
D: duty cycle
η: efficiency
f_S (MHz): switching frequency
L (μH): inductor value
V_IN (V): the input voltage with respect to ground, not with respect to the device ground or V_OUT

Equation 4 calculates the maximum inductor current:

Equation 4.

I_{L} = I_{L (a v g)} + \frac{Δ I_{L}}{2}

For example, for an output voltage of –1.8V, 2.2μH inductor, and input voltage of 3.3V, the following calculations produce the maximum allowable output current that can be achieved based on the TPS62840 minimum current limit value of 1A. The efficiency term is estimated at 80 %.

Equation 5.

D = \frac{V_{O U T}}{(V_{O U T} - V_{I N}) \times η} = \frac{- 1.8 V}{(- 1.8 V - 3.3 V) \times 0.8} = 0.441

Equation 6.

Δ I_{L} = \frac{V_{I N} \times D}{f_{S} \times L} = \frac{3.3 V \times 0.441}{1.8 M H z \times 2.2 μ H} = 368 m A

Rearranging Equation 4 and setting I_L(max) equal to the minimum value of I_LIMF, as specified in the data sheet, gives:

Equation 7.

I_{L (a v g)} = I_{L (m a x)} - \frac{Δ I_{L}}{2} = 1000 m A - \frac{368 m A}{2} = 816 m A

This result is then used in Equation 1 to calculate the maximum achievable output current:

Equation 8.

I_{O U T} = I_{L (a v g)} \times (1 - D) = 816 m A \times (1 - 0.441) = 456 m A

Table 1-1 provides several examples of the calculated maximum output currents for different output voltages (–1.8V, –1.5V and –1.2V) based on an inductor value and switching frequency of 2.2μH and 1.8MHz, respectively. Increasing the inductance and/or input voltage allows higher output currents in the inverting buck-boost configuration. The maximum output currents for the TPS62840 in the inverting buck-boost topology are frequently lower than 750mA due to the fact that the average inductor current is higher than that of a typical buck. The output current for the same three output voltages and different input voltages is displayed in Figure 1-6.

Table 1-1 Maximum Output Current Calculation for Different Values of V_OUT

Parameter	VOUT = -1.8V	VOUT = -1.5V	VOUT = -1.2V
V_IN (V)	3.3	3.3	3.3
η	0.8	0.8	0.8
f_s (MHz)	1.8	1.8	1.8
L (μH)	2.2	2.2	2.2
I_L(max) (mA)	1000	1000	1000
D	0.441	0.391	0.333
ΔI_L (mA)	368	326	278
I_L(avg) (mA)	816	837	861
I_OUT (mA)	456	510	574

Figure 1-6 Maximum Output Current versus V_IN