Zachary Mink December 7 th 2013 ZETA Converter Inductor Analysis In the following plots, the current through the input side inductor is analyzed as a function of the duty cycle of the ZETA converter. The purpose of this analysis is to explore the effect of reducing the size of the coupled inductor. This analysis is important for the following reasons. As the size of the inductor increases, the electromagnetic interference created by the inductor increases. Since EMI will have no significant impact on the function of our design, this aspect of inductor sizing is not critical. With an increase of the coupled inductor size, typically the parasitic resistance of the device increases linearly, resulting in a linear increase in power dissipation. Because of this, the smallest possible inductor would be desired. Decreasing the inductance of the coupled inductor also has the advantage of increasing the maximum allowable current through the inductor. The main disadvantage of decreasing the inductor size is that the ripple current of the system increases and therefore the stability of the converter will decrease. The analysis and discussion below seek to pick the optimal inductor size based on these parameters. The following graphs begin with the current response of the input side inductor with the inductor sized such that the ripple current is ~.3 of the input side current. This should ensure the desired characteristics and a stable system. These circuits were tested with a duty cycle range between.1 and.9 in steps of.1. Figure 1: 200uH Coupled Inductor Duty Cycle Response
The important aspect of Figure 1 to notice is that at steady state, all currents show that the inductor is constantly on or out of discontinuous current mode. Unfortunately, at the present time, a coupled inductor with inductance of 200uH cannot handle currents within the 3A range. The first inductor size that can handle over 3A that was found was 120uH. The plot of its response is shown in Figure 2. Figure 2: 120uH Coupled Inductor Duty Cycle Response As can be seen in Figure 2, the inductor remains safely in continuous conduction mode with marginally low current ripple. The typical equivalent series resistance for an inductor of this size is ~150mOhms.
Figure 3: 60uH Coupled Inductor Duty Cycle Response In Figure 3, the duty cycle response can be seen to deviate from the response in Figures 2 and 3. Typical equivalent resistances for this inductor size are ~60mOhms. Because of this, the power dissipation is approximately halved. To investigate the trend, the duty cycle response of a 30uH coupled inductor is shown in Figure 4.
Figure 4: 30uH Coupled Inductor Duty Cycle Response In duty cycle response shown in Figure 4 begins to show that in steady state, the ripple current may exceed the DC component of the inductor current. Also, response resembles the response predicted by Figure 1 much less and the inductor is very nearly pushed into discontinuous current mode. The typical max dc resistance of this inductor size has again decreased by a factor of 2 to ~23mOhms.
Figure 5: 15uH Coupled Inductor Duty Cycle Response The response shown in Figure 5 shows that an inductance of 15uH for our design is much too low. The AC ripple current is much greater than the DC component which has been damped to an approximate value of 0. The inductor is clearly turning on and off at steady state for almost every value of duty cycle. Because of this, the 15uH coupled inductor cannot be used for our design. Based on the study shown above, a coupled inductor value of ~60uH should be optimal for our converter design. It may be possible to use a ~30uH inductor and as such, we may decide to purchase coupled inductors of each value with the same PCB footprint such that the both may be tested and the smaller inductor utilized if the efficiency is increased and system response not adversely affected.
After this analysis, it was determined that the ATtiny can achieve much higher PWM frequencies using an asynchronous clock mode. Based on this increased frequency, the size of the required capacitors and inductors could be greatly reduced. The frequency that we used for a new evaluation of our circuit was 400kHz. A quick reevaluation of the above effects for higher frequencies was performed. The minimum calculated inductor size for the new PWM frequency was determined to be 15uH. The duty cycle response is given in Figure 6. Figure 6: 15uH Coupled Inductor @400 khz As shown in this figure, the inductor remains clearly in CCM and the ripple current is minimal. By decreasing the inductance below 15uH, the equivalent DC resistance does not drop significantly while the conduction mode approaches discontinuity. Based on this result, a 15uH coupled inductor was chose for the modified 400kHz design.