Texas Instruments TPS40090EVM-002 manual K N Ph, D +, Output Ripple Current Cancellation

SLUU195 − June 2004

where

•D is the duty cycle for a single phase

•NPH is the number of active phases

•K (NPH) is the intermediate function for calculation In this case, NPH=4 and Dmin=0.107 which yields k=0.573. The actual output ripple is calculated in equation (7)

IRIPPLE +	VOUT	K￿NPH, D￿ +	1.5 V	0.573	+ 3.41 A	(7)
	L f		0.6m H 420 kHz

	1.0
A
−				NPH = 4
RMS Input	0.8
− Normalized	0.6
				NPH = 3					NPH = 1
	0.4					NPH = 2
RMS Cout(nom)
	0.2
I
	0	NPH = 6
	0	10	20	30	40	50	60	70	80	90	100
						Duty Cycle − %

Figure 5. Output Ripple Current Cancellation

Selection of the output capacitor is based on many application variables, including function, cost, size, and availability. There are three ways to calculate the output capacitance.

1.The minimum allowable output capacitance is determined by the amount of inductor ripple current and the allowable output ripple, as given in equation (8).

COUT(min)	+	IRIPPLE	+	3.41 A		+ 101 mF	(8)
		8 f VRIPPLE		8 420 kHz	10 mV

In this design, COUT(min) is 101-∝F with VRIPPLE=10 mV. However, this affects only the capacitive component of the ripple voltage, and the final value of capacitance is generally

influenced by ESR and transient considerations.

2.ESR limitation. (To limit the ripple voltage to 10 mV, the capacitor ESR should be less than the value calculated in equation (9)).

RC t+	VRIPPLE	+	10 mV	+ 2.93 mW	(9)
	IRIPPLE		3.41 A

10TPS40090 Multi-Phase Buck Converter and TPS2834 Drivers Steps-Down from 12-V to 1.5-V at 100 A