Development of a Fibonacci Switched-Capacitor DC-AC Inverter

In previous studies, we proposed the circuit topology of the Fibonacci SC DC-AC inverter and analyzed its characteristics theoretically. Unlike a common DC-AC inverter containing inductors or transformers, the SC inverter requires no magnetic components by using SC techniques. Furthermore, unlike conventional SC DC-AC inverters based on a series-parallel type converter, the proposed inverter can provide the staircase AC waveform by a smaller number of capacitors. In this paper, the experimental circuit of the Fibonacci SC DC-AC inverter is built with commercially available components and is evaluated its real behavior. In the experimental circuit, a bootstrap circuit is employed to drive bidirectional switches effectively. The effectiveness and feasibility of the proposed inverter are demonstrated through experiments.


Introduction
For cigarette socket in vehicles, DC-AC inverters have been marketed.The DC-AC inverter can generate AC waveform from the input DC voltage of a cigarette socket.However, the output waveform of the marketed DC-AC inverters is almost square wave which is far from a sine wave.Furthermore, the DC-AC inverters are heavy and balky due to magnetic components.Therefore, in recent years, a switched-capacitor (SC) DC-AC inverter has been proposed by many researchers.Unlike the common DC-AC inverter containing magnetic components, the SC DC-AC inverter can generate an AC voltage without the use of magnetic components.Therefore, the SC inverter can reduce not only circuit size but also effects of the electromagnetic inference (EMI).
In 1993, Ueno et al. suggested the voltage equation type SC DC-AC inverter (1) .Following this, Oota proposed a bidirectional SC DC-AC inverter (2) .By using a series-parallel type inverter (3) , these inverters can generate a staircase AC waveform.However, many circuit components are required in order to provide big number of steps of the staircase waveform.That is because the steps of the staircase waveform are proportional to the number of capacitors.To improve this drawback, Eguchi et al. suggested the DC-AC converter using ring-type converter (4) .The ring-type converter can provide flexible output voltages by changing connection-types of series capacitors.However, the ring-type converter cannot realize high voltage ratio unless many capacitors exist.To reduce the number of capacitors, Chang proposed the multistage switched-capacitor-voltage-multiplier (SCVM) DC-AC inverter (5) .The SCVM inverter can generate a staircase AC waveform by the small number of capacitors due to series-connected SC cells.However, all capacitor voltages of these conventional DC-AC inverters are the same.Therefore, in order to provide a staircase AC waveform formed by many steps, we proposed the circuit topology of the Fibonacci SC DC-AC inverter (6) and analyzed its characteristics theoretically.In the proposed inverter, the voltage ratio of capacitors is the ratio of the Fibonacci number.By combining some of these capacitors in series, the proposed inverter generates the staircase AC waveform by a small number of capacitors, because the voltage of the charged capacitors of the proposed inverter is higher than that of the conventional SC DC-AC inverter.
In this paper, the experimental circuit of the Fibonacci SC DC-AC inverter is built with commercially available components and is evaluated its behavior.In the experimental circuit, a bootstrap circuit is employed to drive bidirectional switches effectively.The effectiveness and feasibility of the proposed inverter are demonstrated through experiments.

Conventional Inverter
Figure 1 shows the conventional SC DC-AC inverter (2) .The conventional inverter is based on the series-parallel type converter.As figure 1 shows, there is no magnetic components.In the conventional inverter, all the capacitor voltages are Vin.To generate a staircase AC waveform, the bi-direction switches are controlled like a step-up DC-DC converter.The output voltage Vo of each step is expressed by In Eq. 1, N is the number of main capacitors.Concretely, the conventional inverter generates the staircase waveform formed by 8 ((3+1)×2) steps in the case of 3 stages.The staircase waveform Vout is obtain through the full bridge circuit.When bi-directional switches e are turned on, each capacitor of the sub circuit-1 are charged, and the sub circuit-2 generates stepped-up voltage.At that time, the output voltage is selected by controlling bi-directional switches en.On the other hand, when bi-directional switches o are turned on, each capacitor of the sub circuit-2 are charged, and the sub circuit-1 generates stepped-up voltage.At that time, the output voltage is selected by controlling bi-directional switchers on.In the conventional inverter, two capacitors and eight bi-directional switches are required for every additional one stage. 1

T4
Transferring process Averaging process

Proposed Inverter
Figure 2 shows the proposed Fibonacci SC DC-AC inverter (6) .Unlike the conventional SC DC-AC inverter, the voltage ratio of capacitors becomes the ratio of a Fibonacci number.Concretely, the voltage of i-th (i = 1, 2, 3) capacitor is i×Vin in the case of 3 stages.In the proposed inverter, the output voltage Vo of each step is expressed as As Eq. 2 shows, the proposed inverter can generate the staircase waveform formed by 14 (=7×2) steps in the case of 3 stages.Therefore, the proposed inverter can provide the staircase AC waveform by a smaller number of capacitors.Table 1 shows the timing of the operation process.As table 1 shows, the proposed inverter has three processes: 1) charging process; 2) transferring process; and 3) averaging process.By repeating these three processes mutually, the voltage ratio of each capacitors becomes the ratio of a Fibonacci number.
As table 1 shows, by shifting the timing of each process of the inverter block-2 against that of the inverter block-1, the transferring process can be appeared at all timings.Table 2 shows an example of the timing of clock pulses in the case of the 7x step-up.As table 1 indicates, in the inverter block-1, T1 is the charging process, T2 and T4 are the transferring process, and T3 is the averaging process.On the other hand, in the inverter block-2, T2 is the charging process, T1 and T3 are the transferring process, and T4 is the averaging process.In the transferring process, the n (n = {1, 2, …, 7}) × stepped-up voltage is obtained by combing some of main capacitors in series.Concretely, to obtain the 7x stepped-up voltage, C1 j , C2 j , C3 j (j = 1, 2), and the input voltage are connected in series.In the proposed inverter, two capacitors, two diodes and six bi-directional switches are added to the proposed inverter for every additional one stage.
Table 3 shows comparison of the number of circuit components between the conventional inverter and the proposed inverter in the case of 7x step up.As table 3 shows, the conventional inverter needs 78 circuit components because the conventional inverter must be expanded to 7 stages to generate the 7 stepped-up voltage.On the other hand, the proposed inverter requires 38 circuit components.The number of the circuit components of the proposed the inverter is smaller than that of conventional

Experiment
To clarify the operation principle of the proposed inverter, experiments are performed.In the experiment, the number of stages of the proposed inverter was set to three stages.The experimental conditions of the proposed inverter with three stages are as follows: Vin= 12V and T= 2μs.Table 4 shows circuit components of the experimental inverter.As you can see from table 4, to control the bi-directional switches, an AVR micro controller ATMEGA 164P is used in the experimental inverter.However, the signals generated by the AVR micro controller cannot control the bi-directional switches because power of the AVR micro controller is too small.Therefore, to drive the bi-directional switches, bootstrap circuits are attached to each switch.The bootstrap circuit consists of high-low side driver ICs, diode switches and a pumping-up capacitors so it does not require magnetic component.The bootstrap circuit is controlled by the signal of the AVR micro controller and drives the gate terminal of the bi-directional switches by using a voltage of the pumping-up capacitor.
Figure 3 shows the experimental inverter.To charge the pumping-up capacitor of the bootstrap circuit, a charging time of the pumping-up capacitor is required.Therefore, the circuit for charging is added as shown in figure 3. To turn on the switch Sd during the charging process and the transferring process, the pumping-up capacitors of the bootstrap are charged.
Figure 4 shows the photograph of the experimental inverter.As table 4 shows, the experimental inverter of figure 4 was built with commercially available components on a print board.Figure 5 shows the measured output waveform of the proposed inverter.As figure 5 shows, the proposed inverter can generate a staircase AC waveform, where the maximum output voltage is 72.2 V. From this result, the experimental inverter can realize the high voltage ratio with the small number of capacitors because 72.2 V is about six times the input

Table 1 .
Operations during one cycle.

Table 2 .
Setting of clock pulses in the case of the 7x step-up.

Table 3 .
Comparison of the number of components.

Table 4 .
Circuit components of the experimental inverter.