Small-signal modeling for design of robust variable-frequency flyback battery chargers for portable device applications

Small signal modeling of hysteretic current mode control using the PWM switch model

“…After the simplified state equation is manipulated in time domain, we add ESR zero individually in frequency domain [7]. The non-linear state equations and output equations are represented as follows: (7) Secondly, the on-time and off-time constraints that reflect the behavior of a converter in CRM are necessary to present the state-space equations as a function of the state variables, input variables, and the control variable [10].…”

“…The extended method replaces the duty cycle with other parameters, such as T S and T ON which are linear even in the variable switching frequencies [8]. This extended state-space averaging approach has already been proved by applying it to a few basic converters under hysteretic current CRM control [7]. However, the derivation procedures depending on the analytical calculation require very tedious and complicated steps, and the final equations are not simple and it is difficult to find the physical meaning.…”

“…In variable switching frequency converter modeling, however, there has been some limitations to apply the statespace averaging technique because the duty cycle is nonlinear to the control voltage (command). Recently, since some selfoscillating variable frequency topologies have emerged with very different system dynamics from the fixed frequency one, a new modeling method has been needed in order to describe the variable frequency action [6,7]. After this issue emerged, a new modeling approach was introduced by Suntio that extends the state-space averaging method from a fixed frequency to a variable frequency by taking additional conditions that explain the variable frequency effects.…”

Analysis and design of self-oscillating flyback converter

“…As can be seen, both the measured and calculated Bode plots show an excellent agreement up to one-tenth of the minimum switching frequency, i.e., up to 4 kHz, where the minimum switching frequency is equal to 40 kHz. Beyond one-tenth of the switching frequency, the compared phase plots are shown to diverge, possibly due to a right-half-plane RHP zero which is not described by either the small-signal model presented in Table 1, or by the small-signal model presented in [3].…”

“…However, the design optimization of the error amplifier compensation requires knowledge of the smallsignal transfer functions in the control loop. Since the selfoscillating flyback converter operates with a variable switching frequency, the small-signal block diagram model differs from that of the conventional, constant-frequency type PWM converter, as discussed in [3].…”