SLVAFC5 Application note

SLVAFC5 March 2022 TPS629210 , TPS629210-Q1

1.2 Output Current Calculations

The average inductor current is affected in this topology. In the buck configuration, the average inductor current equals 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 1-3). Knowing that the off time is 1-D of the switching period, then the average inductor current is:

Equation 1.

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

The duty cycle for the typical buck converter is simply V_OUT / V_IN but the duty cycle for an inverting buck - boost converter becomes:

Equation 2.

D = \frac{V_{O U T}}{V_{O U T} - V_{I N}} x \frac{1}{ƞ}

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. Where V_OUT is a negative value. The peak to peak inductor ripple current is calculated as:

Equation 3.

∆ I_{L} = \frac{V_{I N} x D}{f_{s} x L}

Where,

∆I_L (A): Peak to peak inductor ripple current

D: Duty cycle

η: Efficiency

f_S (MHz): Switching frequency

L (µH): Inductance

V_IN (V): Input voltage with respect to ground, instead of IC ground or -V_OUT.

Finally, the maximum inductor current becomes:

Equation 4.

I_{L (m a x)} = I_{L (avg)} + \frac{∆ I_{L}}{2}

For an output voltage of –3.3 V, 2.5 MHz switching frequency, 2.2 µH inductor, and an input voltage of 12 V, the following calculations produce the maximum allowable output current that can be delivered based on the 1.3 A minimum current limit (I_LIM) of TPS629210-Q1. The efficiency term is estimated at 85%.

Equation 5.

D = \frac{V_{O U T}}{V_{O U T} - V_{I N}} x \frac{1}{ƞ} = \frac{- 3.3}{- 3.3 - 12} x \frac{1}{0.85} = 0.254

Equation 6.

∆ I_{L} = \frac{V_{I N} x D}{f_{s} x L} = \frac{12 x 0.254}{2.5 M H z x 2.2 μ H} = 0.554 A

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

Equation 7.

I_{L (a v g)} = I_{L (\max)} - \frac{∆ I_{L}}{2} = 1.3 - \frac{0.554}{2} = 1.023 A

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

Equation 8.

I_{O U T} = I_{L (avg)} x (1 - D) = 1.023 x (1 - 0.254) = 0.763 A

Table 1-1 provides several examples of the calculated maximum output current for different output voltages (–5 V, –3.3 V and –1.2 V) based on an inductor value of 2.2 μH and 3.3 µH with 2.5 MHz switching frequency, respectively. Increasing the inductance and/or input voltage allows higher output current in the inverting buck - boost topology. The maximum output current for the TPS629210-Q1 in the inverting buck - boost topology are frequently lower than 1 A 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 are displayed in Figure 1-4.

Table 1-1 Maximum Output Current Calculation for Different Values of V_IN, V_OUT and Inductance

V_IN (V)	12	12	12	12	12	12	5	5	5	5	5	5
V_OUT (V)	–5	-3.3	–1.2	-5	–3.3	-1.2	-5	-3.3	-1.2	-5	-3.3	-1.2
L(µH)	2.2	2.2	2.2	3.3	3.3	3.3	2.2	2.2	2.2	3.3	3.3	3.3
f_S (MHz)	2.5	2.5	2.5	2.5	2.5	2.5	2.5	2.5	2.5	2.5	2.5	2.5
η (%)	86	85	80	86	85	80	86	85	80	86	85	80
I_LIM(A)	1.3	1.3	1.3	1.3	1.3	1.3	1.3	1.3	1.3	1.3	1.3	1.3
D	0.342	0.254	0.114	0.342	0.254	0.114	0.581	0.468	0.242	0.581	0.468	0.242
∆I_L (A)	0.746	0.554	0.248	0.497	0.369	0.165	0.529	0.425	0.22	0.352	0.283	0.147
I_L(avg) (A)	0.927	1.023	1.176	1.051	1.115	1.217	1.036	1.087	1.19	1.124	1.158	1.227
I_OUT (A)	0.610	0.763	1.0	0.692	0.832	1.0	0.434	0.579	0.902	0.470	0.616	0.93

Figure 1-4 Maximum Output Current vs Input Voltage