II. BEHAVIOR OF NOVEL FLYBACK CONVERTER
　Figure 1 shows two types of a novel flyback converter, where an active current-clamp circuit is added to the conventional flyback converter. Figure 2 shows the time sequence of gate drive voltages for two switches Q1 and Q2, the magnetizing current Im of transformer, the secondary current through diode D2, and the transformer voltage.
We explain the operation of the circuit shown in Fig.1 (a) as a example of the proposed novel flyback converter.

　The difference between this new topology and the conventional flyback converter is to insert an energy storage time of (1-D-K)T and to fix the energy discharge time of KT.
As the result, the input-to-output voltage conversion ratio M becomes proportional to duty ratio D similarly to the forward converter. This relationship is easily derived from replacing the term of 1-D in the voltage conversion ratio D/(1-D) of the conventional flyback converter with the constant value of K

III. ANALYSIS OF DYNAMIC CHARACTERISTICS
A.. Conventional flyback converter
　As seen in many literatures, the conventional flyback converter shown in Fig.3 has a 2nd-order transfer function with a right-half-plane zero (RHPZ). Furthermore, a so-called jumping phenomenon appears when the duty ratio becomes larger[2]. When the load current becomes heavier and the output voltage decreases, the duty ratio is made larger for the output voltage regulation. However, the duty ratio becomes close to the unity, the output voltage jumps down to a low voltage outside the regulation range as shown in Fig.4.

Fig 3. Conventional Flyback converter	Fig 4. Control characteristics of conventional flyback converter

　This topology has three states during one switching period as shown in Fig.5. Their durations are D for state1, (1-D-K)T for state2, and KT for state3, respectively.
　The state-space equations are obtained as shown below, regarding two state variables of the magnetizing current im and the equivalent output voltage vo referred to the primary side. Here, these two state variables are combined as the following vector x:

State3

　By applying the state-space averaging method to these three states, the following differential equation is derived:

　The steady-state characteristics are obtained by substituting in the above equation as follows:

and the linear approximation around the operating point, an equation representing the small-signal model is derived as follows:

where

　Therefore the voltage conversion ratio Mn and the control- to-output voltage transfer function Fn(s) are obtained as follows:

　As seen from (17), the voltage conversion ratio Mn is proportional to the duty ratio because K is chosen as a constant, and then the cause of the jumping phenomenon disappeared. The control-to-output transfer function Fn(s) expressed by (18) has no RHPZ the same as the forward converter. As a result, the stability and the dynamic response can be much improved when compared with the conventional flyback converter.

IV. EXPERIMENTAL RESULT
A. Key waveforms of experimental circuit
　The experimental circuit is shown Fig.1(b). This circuit operates the same as the circuit shown in Fig.1(a). The experimental waveforms of the circuit are shown in Fig.6, where gate signals of Q1 and Q2, transformer voltage, primary and secondary currents are shown respectively. The waveforms of primary and secondary currents differ from the ideal ones shown in Fig.2 due to the leakage inductance of transformer. This leakage inductance causes the reduction of transfer energy from primary to secondary, and as the result the DC gain in the control-to-output transfer function decreases as seen from the comparison of Fig.7(experiment) and Fig.8(theory). The ringing waveform means the resonance of the leakage inductance of transformer and the parasitic capacitances in the primary side.

B. Converter efficiency for different core size
　We used three kinds of core size to implement a low- profile transformer in the power converter module. Three kinds of core size, PCC13, PCC19 and PCC29, were selected from the power capacity. As seen from Table I, the converter efficiency using these cores are around 80%. The switching frequency was set at 300kHz

V. APPLICATION OF PROPOSED FLYBACK CONVERTER
　Recently, the power supply with low-voltage and high-current output has been required in many electronic equipments using LSIs. In this case, the parallel connection of the proposed flyback converter is effective. We have investigated the interleaved topology of the proposed converters by connecting two converters in parallel and driving them in the two-phase mode alternately. Its circuit configuration is shown in Fig.11, where the topology shown in Fig.1(b) is utilized. The merit of this configuration is that

Fig.21. Interleaved system with proposed flyback Converter.


Fig.13. Efficiency characteristics for load variation.
the frequency of input and output current variation is twice of the switching frequency and therefore the voltage ripples are made smaller than a single-converter configuration. The experimental results of the converter system with the output condition of 3.3V and 50A are mentioned below.

A. Efficiency
　Figure 12 shows the efficiency characteristics of the interleaved system using the proposed flyback converters with PCC29 cores.

B. Output voltage ripple
　In the conventional flyback converter, the output voltage ripple is expressed as

where Ts is switching period.
　The output voltage ripple is largest when D=0.5 (for the case of K=0.5). Substituting practical parameter values to (19), an output ripple value is obtained as
Let D=0.5, Ts=3.3μs, R=3.3/50Ω, C=72μF
1.15 V
　On the other hand, as seen from the measured waveform shown in Fig.13, the output voltage ripple of the proposed flyback converter is reduced half of the conventional one because of the interleaved configuration.

Fig.14. Output voltage ripple waveform.

C. Frequency response of transfer function
　The frequency response of control-to-output transfer function of the single proposed flyback converter is shown in Fig.14, where some parameters values are a little different from ones used previously. The frequency response of the transfer function for the interleaved system shown in Fig.11 is shown in Fig.15. Comparing these frequency responses, it is evident that the frequency response is shifted to higher frequency region because the equivalent magnetizing inductance becomes half due to the parallel connection.
　Figure 16 shows the frequency response of the open-loop transfer function including PWM and PI compensator used as a feedback controller. As seen from this result, the phase margin of 60 degrees and the gain margin of 10dB were obtained, and the stable operation was confirmed.

VI. CONCLUSION
　A novel flyback converter and its control scheme have been proposed. By adding only one auxiliary switch to the conventional flyback converter and fixing the discharging interval of the energy stored in the transformer, the input-to-output voltage conversion ratio becomes proportional to the duty ratio, and the RHPZ disappears from the control-to-output transfer function. Consequently, the dynamic characteristics can be much improved.
　The analysis and the experimental confirmation have clarified the improvement of the stability and dynamic response of this modified flyback converter.
Furthermore, the extension of this proposed converter to the interleaved system has been confirmed.


REFERENCES
[1] T.Ninomiya, M.Nakahara, T.Higashi, K.Harada: "A Unified Analysis of Resonant Converters," IEEE Trans. on Power Electronics, Vol.PE-6, No.2, April 1991, pp. 260-270.
[2] T.Ninomiya, K.Harada, M.Nakahara "Stability Analysis of Boost and Buck-Boost Converters," The Trans. of IEIEC, Vol.J66-C, No.1, Jan. 1983, pp.1-8.