SLVAFV2 Application note

SLVAFV2 June 2024 LMR51610 , TPS629210

2.1 Estimation of Voltage Drop in Buck Converter Working in CCM

In the buck converter, there are two main reasons causing the voltage drop: duty cycle and resistance. Equation 1 shows this relationship.

Equation 1.

V_{drop} =(V_{d u t y} + V_{R})

Where:

V_duty is the voltage drop caused by the duty cycle
V_R is the voltage drop caused by the resistance

The voltage drop caused by the duty cycle is easy to obtain, as shown in Equation 2.

Equation 2.

V_{duty} =[V_{i n} (1-D)]

V_in is the input voltage
D is the duty cycle

To further analyze the voltage drop caused by the MOSFET, Figure 2-1 shows the basic operating mode of buck converter.

Figure 2-1 Operating Mode

In mode 1, the high-side MOSFET is on, so the high-side MOSFET and inductor can be modeled as two resistors, R_mos1 and R_L. In mode 2, the high-side MOSFET is off but the low-side MOSFET is on, so there are still two resistors, R_mos2 and R_L.

Based on the operating mode, the battery only powers the system when the high-side MOSFET is on. Therefore, the basic concept involves the conservation of energy and power balancing. A few assumptions were made to simplify the calculations:

The capacitor is ideal which means no ripple in the output
The inductor average current is equal to the RMS value
Battery is a stable DC source

In one cycle, the power provided by the battery or the input power is only consumed by the resistor and then provided to the output. Although there is some switching loss, the loss is negligible compared with the conduction loss caused by the resistor. In addition, the SW voltage in the dropout zone is relatively low, which reduces the switching loss.

According to the previous analysis, we can obtain the power balanced equation.

Equation 3.

V_{in} I_{L} DT= {I_{L}}^{2} [{R_{L} T+R}_{mos1} DT+ {VR}_{mos2} (1-D)T+ V_{out} I_{out} T]

Where:

V_in, V_out are the input and output voltage
I_out, I_L are the output current and inductor average current
R_mos1 and R_mos2 are the on-state resistance of the high-side and low-side FETs.
T is the period
R_L is the DC resistance of the inductor used

Based on Equation 3, I_L is equal to I_out, which is similar to assumption 2, and we can obtain simplified Equation 4.

Equation 4.

V_{i n} D - I_{o u t} [{R_{L} T + R}_{m o s 1} D T + R_{m o s 2} (1 - D) T] = V_{o u t}

As we can see from the Equation 4, V_inD is the voltage drop caused by the duty cycle, the latter one is caused by the equivalent resistors.

Now, slightly transform the Equation 4 and we can obtain Equation 5.

Equation 5.

V_{d r o p =} V_{i n} (1 - D / P)

Equation 6.

P = [1 + {{(R}_{L} + R}_{m o s 1} D + R_{m o s 2} (1 - D)) / R_{o u t}]

Where:

P is a coefficient to simplify the equation

Equation 5 provides a convenient method to estimate the voltage drop in a buck converter. Some of TI buck converter have the 100% duty cycle function for the battery applications. In these products, the voltage drop can be easily obtained using Equation 7 because the drop is conducted directly.

Equation 7.

V_{d r o p =} I_{o u t} {{(R}_{L} + R}_{m o s 1})

In later chapter, we further discuss how to reduce the voltage drop to further use the battery.