Operation during T_closed (time when the switch is closed)

When the switch (transistor, vacuum tube) closes it places the source voltage V_b across the transformer primary. The magnetizing current I_m of the transformer^[2] is I_m = V_primary×t/L_p; here t (time) is a variable that starts at 0. This magnetizing current I_m will "ride upon" any reflected secondary current I_s that flows into a secondary load (e.g. into the control terminal of the switch; reflected secondary current in primary = I_s/N). The changing primary current causes a changing magnetic field ("flux") through the transformer's windings; this changing field induces a (relatively) steady secondary voltage V_s = N×V_b. In some designs (as shown in the diagrams) the secondary voltage V_s adds to the source voltage V_b; in this case because the voltage across the primary (during the time the switch is closed) is approximately V_b, V_s = (N+1)×V_b. Alternately the switch may get some of its control voltage or current directly from V_b and the rest from the induced V_s. Thus the switch-control voltage or current is "in phase" meaning that it keeps the switch closed, and it (via the switch) maintains the source voltage across the primary.

In the case when there is little or no primary resistance and little or no switch resistance, the increase of the magnetizing current I_m is a "linear ramp" defined by the formula in the first paragraph. In the case when there is significant primary resistance or switch resistance or both (total resistance R, e.g. primary-coil resistance plus a resistor in the emitter, FET channel resistance), the L_p/R time constant causes the magnetizing current to be a rising curve with continually decreasing slope. In either case the magnetizing current I_m will come to dominate the total primary (and switch) current I_p. Without a limiter it would increase forever. However, in the first case (low resistance), the switch will eventually be unable to "support" more current meaning that its effective resistance increases so much that the voltage drop across the switch equals the supply voltage; in this condition the switch is said to be "saturated" (e.g. this is determined by a transistor's gain h_fe or "beta"). In the second case (e.g. primary and/or emitter resistance dominant) the (decreasing) slope of the current decreases to a point such that the induced voltage into the secondary is no longer adequate to keep the switch closed. In a third case, the magnetic "core" material saturates, meaning it cannot support further increases in its magnetic field; in this condition induction from primary to secondary fails. In all cases, the rate of rise of the primary magnetizing current (and hence the flux), or the rate-of-rise of the flux directly in the case of saturated core material, drops to zero (or close to zero). In the first two cases, although primary current continues to flow, it approaches a steady value equal to the supply voltage V_b divided by the total resistance R in the primary circuit. In this current-limited condition the transformer's flux will be steady. Only changing flux causes induction of voltage into the secondary, so a steady flux represents a failure of induction. The secondary voltage drops to zero. The switch opens.

Operation during T_open (time when the switch is open)

Now that the switch has opened at T_open, the magnetizing current in the primary is I_peak,m = V_p×T_closed/L_p, and the energy U_p is stored in this "magnetizing" field as created by I_peak,m (energy U_m = 1/2×L_p×I_peak,m²). But now there is no primary voltage (V_b) to sustain further increases in the magnetic field, or even a steady-state field, the switch being opened and thereby removing the primary voltage. The magnetic field (flux) begins to collapse, and the collapse forces energy back into the circuit by inducing current and voltage into the primary turns, the secondary turns, or both. Induction into the primary will be via the primary turns through which all the flux passes (represented by primary inductance L_p); the collapsing flux creates primary voltage that forces current to continue to flow either out of the primary toward the (now-open) switch or into a primary load such as an LED or a Zener diode, etc. Induction into the secondary will be via the secondary turns through which the mutual (linked) flux passes; this induction causes voltage to appear at the secondary, and if this voltage is not blocked (e.g. by a diode or by the very high impedance of a FET gate), secondary current will flow into the secondary circuit (but in the opposite direction). In any case, if there are no components to absorb the current, the voltage at the switch rises very fast. Without a primary load or in the case of very limited secondary current the voltage will be limited only by the distributed capacitances of the windings (the so-called interwinding capacitance), and it can destroy the switch. When only interwinding capacitance and a tiny secondary load is present to absorb the energy, very high-frequency oscillations occur, and these "parasitic oscillations" represent a possible source of electromagnetic interference.

The potential of the secondary voltage now flips to negative in the following manner. The collapsing flux induces primary current to flow out of the primary toward the now-open switch i.e. to flow in the same direction it was flowing when the switch was closed. For current to flow out of the switch-end of the primary, the primary voltage at the switch end must be positive relative to its other end that is at the supply voltage V_b. But this represents a primary voltage opposite in polarity to what it was during the time when the switch was closed: during T_closed, the switch-end of the primary was approximately zero and therefore negative relative to the supply end; now during T_open it has become positive relative to V_b.

Because of the transformer's "winding sense" (direction of its windings), the voltage that appears at the secondary must now be negative. A negative control voltage will maintain the switch (e.g. NPN bipolar transistor or N-channel FET) open, and this situation will persist until the energy of the collapsing flux has been absorbed (by something). When the absorber is in the primary circuit, e.g. a Zener diode (or LED) with voltage V_z connected "backwards" across the primary windings, the current waveshape is a triangle with the time t_open determined by the formula I_p = I_peak,m - V_z×T_open/L_p, here I_peak,m being the primary current at the time the switch opens. When the absorber is a capacitor the voltage and current waveshapes are a 1/2 cycle sinewave, and if the absorber is a capacitor plus resistor the waveshapes are a 1/2 cycle damped sinewave.

When at last the energy discharge is complete, the control circuit becomes "unblocked". Control voltage (or current) to the switch is now free to "flow" into the control input and close the switch. This is easier to see when a capacitor "commutates" the control voltage or current; the ringing oscillation carries the control voltage or current from negative (switch open) through 0 to positive (switch closed).

Repetition rate 1/(T_closed + T_open)

In the simplest case, the duration of the total cycle (T_closed + T_open), and hence its repetition rate (the reciprocal of the cycle duration), is almost wholly dependent on the transformer's magnetizing inductance L_p, the supply voltage, and the load voltage V_z. When a capacitor and resistor are used to absorb the energy, the repetition rate is dependent on the R-C time-constant, or the L-C time constant when R is small or non-existent (L can be L_p, L_s or L_p,s).