We investigated how differences among inductors affect the power conversion efficiency of Bluetooth^{®} Low Energy applications.
Here, attention is paid to the DC losses and the AC losses that exist in inductors. DC losses are losses that are attributable to the DC component of the current flowing in the inductor, and are expressed below using the DC resistance (Rdc) and the DC component of the current (Idc).
On the other hand, AC losses are losses that are attributable to mainly the AC component of the current flowing in the inductor, and are expressed below using the AC resistance (Rac), which is the apparent resistance due to the winding resistance plus the core losses, and the AC component of the current (Irms).
The AC component (Irms) expresses the size of the current amplitude, and this value can be reduced by increasing the switching frequency or increasing the inductance of the power inductor.
As of 2020 the switching frequencies of most DC-DC converters incorporated into Bluetooth^{®} Low Energy ICs were either around 1 MHz or 4 MHz. We ran a simulation to determine the ratio of DC loss and AC loss when using inductors with rated inductances of 1.5 µH and 10 µH at each frequency (Figure 1).
Although the frequency conditions and other factors also have an influence, Rac increases more than Rdc in the power inductor. For this reason, in the small area in which the load current (equal to Idc) is 50 mA or less as shown in Figure 1, we see that the DC loss becomes very small and the AC loss occupies a large portion.
From these results, in order to reduce the inductor loss in Bluetooth^{®} Low Energy applications, the inductance, which affects AC loss, and the Rac become important parameters.
At low Rac it is ideal to obtain high inductance; however, in trying to obtain inductance the winding resistance and core losses will be increased. For this reason, the balance between inductance and Rac becomes important.
In regard to Rdc, in the Bluetooth^{®} Low Energy environment where there is a small proportion of DC loss, the degree of influence may be considered to be low. However, when Rdc becomes overly large it cannot be ignored and attention must be paid to this.
As causes of DC-DC converter power losses, in addition to inductor losses, other losses that can be considered include switching losses of the IC, and IC continuity losses.
Concerning power inductors intended for Bluetooth^{®} Low Energy, since the size of the inductance may influence the switching loss, this point must also be considered in the selection.
Figure 2 is a simulation of the current waveforms that flow in the inductor.
To boost power conversion efficiency when operating under the light loads that characterize Bluetooth^{®} Low Energy applications, a control mode called pulse frequency modulation (PFM) control is typically used. PFM control increases power conversion efficiency by reducing the number of times switching occurs by not performing switching continuously. The left chart of Figure 2 shows the current waveform when the inductance has been changed at the same frequency.
Larger inductance will keep down the size of the current amplitude; however, the number of triangular waves generated will increase to adjust the total current amount. This signifies an increase in the number of switching cycles, and there will be an increase of the switching loss. Similarly, the right chart of Figure 2 shows the current waveform when the frequency has been changed with the same inductance. Higher frequencies will keep down the size of the current amplitude; however, it is understood that the number of switching cycles will increase.
In this way, in PFM control, by increasing the inductance or the frequency and making the current amplitude smaller, on one hand the AC losses can be reduced, but there is also the aspect of increasing the switching losses.
Well then, how much inductance would be good to use?
Figure 3 shows the results of a simulation of the DC-DC converter loss when the inductance value is changed, at switching frequencies of 1 MHz and 4 MHz. Using the characteristics of the LQM21P-GH series as the basis, we calculated the change in Rac as well when the inductance value changes.
The graphs show the total loss of the DC-DC converter and the loss for the inductor alone.
In the case of the low 1 MHz switching frequency, it can be seen that as the inductance became larger the inductor loss dropped, and accompanying this the total losses also dropped.
On the other hand, in the case of 4 MHz, as the inductance became larger the inductor loss dropped, but the result was that the total losses increased. The reason for this is that as the inductance became larger, the switching losses increased as a result.
In the case of 4 MHz compared to 1 MHz, because the number of switching cycles is large, the proportion of switching loss is large, and so it can be said that the increase of switching loss appeared remarkable due to the change of the inductance.
Based on these results, we determined that the appropriate inductance value for reducing total loss is around 10 µH at 1 MHz and 0.47 µH to 1.0 µH at 4 MHz.