Figure 11 shows a typical TLVR converter schematic, with important nodes, voltages and currents labeled. Figure 12 illustrates the steady-state operating waveforms of a TLVR converter, with four phases shown. In this example, the pulses from adjacent phases do not overlap in time. There is no maximum duty-cycle requirement for the TLVR topology. The same principles apply for higher-duty-cycle applications where pulses do overlap in time.

Figure 12 shows the voltage and current waveforms of the L_C of the secondary-side loop, switch nodes of all four phases, and the primary-side current of phase 4 (I_PRI4). For clarity, this figure includes labels for the three distinct states of operation.

The most important relationships are those of the L_C loop and its influence on I_PRI and I_SUM.

Four-phase example, no pulse overlap

Figure 11 Steady-state topology.

Four-phase, no pulse overlap

Figure 12 Steady-state waveforms.

The magnetizing voltage for each phase is similar to that of a buck converter. Equation 6 applies to phase on, and Equation 7 applies to phase off. The magnetizing inductance always follows the fundamental inductor relationship shown in Equation 8:

Equation 6. $\mathrm{\Delta }{\mathrm{V}}_{\mathrm{L}\mathrm{m},\mathrm{i}}={\mathrm{V}}_{\mathrm{I}\mathrm{N}}-{\mathrm{V}}_{\mathrm{O}\mathrm{U}\mathrm{T}}$

Equation 7. $\mathrm{\Delta }{\mathrm{V}}_{\mathrm{L}\mathrm{m},\mathrm{i}}=-{\mathrm{V}}_{\mathrm{O}\mathrm{U}\mathrm{T}}$

Equation 8. ${\mathrm{I}}_{\mathrm{L}\mathrm{M}}=\frac{\mathrm{\Delta }{\mathrm{V}}_{\mathrm{L}\mathrm{m}}}{{\mathrm{L}}_{\mathrm{m}}}$

The voltage across the L_C is always equal to the sum of the magnetizing voltages across all phases, as shown in Equation 9. L_C itself always follows the fundamental inductor relationship, expressed by Equation 10:

Equation 9. $\mathrm{\Delta }{\mathrm{V}}_{\mathrm{L}\mathrm{C}}={\mathrm{V}}_{\mathrm{L}\mathrm{m}1}+{\mathrm{V}}_{\mathrm{L}\mathrm{m}2}+\dots$

Equation 10. ${\mathrm{I}}_{\mathrm{L}\mathrm{C}}=\frac{\mathrm{\Delta }{\mathrm{V}}_{\mathrm{L}\mathrm{C}}}{{\mathrm{L}}_{\mathrm{C}}}$

The I_PRI for each phase is equal to the sum of its magnetizing current and I_LC, expressed in Equation 11. I_SUM is the sum of the primary currents from all phases, expressed by Equation 12:

Equation 11. ${\mathrm{I}}_{\mathrm{P}\mathrm{R}\mathrm{I},\mathrm{i}}={\mathrm{I}}_{\mathrm{L}\mathrm{m},\mathrm{i}}+{\mathrm{I}}_{\mathrm{L}\mathrm{C}}$

Equation 12. ${\mathrm{I}}_{\mathrm{S}\mathrm{U}\mathrm{M}}={\mathrm{I}}_{\mathrm{P}\mathrm{R}\mathrm{I}1}+{\mathrm{I}}_{\mathrm{P}\mathrm{R}\mathrm{I}2}+\dots$

Table 1 summarizes the state of each of the relevant voltages and currents shown in Figure 12, with respect to the derivation of I_PRI4 shown in the plot.

Table 1 Four-phase example, steady-state voltages and currents.

Parameter	State 1 Phase 4 on, phases 1, 2 and 3 off	State 2 All phases off	State 3 Phase 4 and two others off, one of the other phases is on
VSW1	0 V	0 V	One phase is equal to VIN and the other two are equal to 0 V.
VSW2	0 V	0 V
VSW3	0 V	0 V
VSW4	VIN	0 V	0V
ΔVLM1	–VOUT	–VOUT	One phase is equal to VIN – VOUT and the other two are equal to –VOUT
ΔVLM2	–VOUT	–VOUT
ΔVLM3	–VOUT	–VOUT
ΔVLm4	VIN – VOUT	–VOUT	–VOUT
ILm4	Increasing	Decreasing	Decreasing
ΔVLC	Sum of ΔVLM1–4	Sum of ΔVLM1–4	Sum of ΔVLM1–4
ILC	Increasing	Decreasing	Increasing
IPRI4	Increasing	Decreasing faster	Decreasing slower