2.2 The Push-Pull Topology
2.2.8 Coping with Flux Imbalance
Flux imbalance can become a major problem at high voltages and high powers. There are a number of ways to circumvent the problem, but most involve increased cost or component count. Some schemes to combat flux imbalance are described in the following subsections.
2.2.8.1 Gapping the Core
Flux imbalance becomes serious when the core moves out onto the curved part of the hysteresis loop (see Figure 2.3) and magnetizing current starts increasing exponentially as in Figure 2.4c.This effect can be reduced by moving the curved part of the hysteresis loop to a higher current by tilting the hysteresis loop. The core can then tolerate a larger DC current bias or volt-second product inequality.
An air gap introduced into the magnetic path of the core has the effect shown in Figure 2.5. It tilts the slope of the hysteresis loop.
An air gap of 2 to 4 mils (thousandths of an inch) brings the curved portion of the loop much further away from the origin so that the core can accept a reasonably large offset in H (current imbalance). This can help at higher power levels. It has the disadvantage of reducing the inductance so that the critical current must be larger to prevent discontinuous-mode operation.
FIGURE2.5 How a gap in the core reduces the slope of the hysteresis loop.
The air gap for a prototype EE or cup core is easily effected with plastic shims in the center and outer legs. Since the flux passes through the center leg and returns through the outer legs, the total gap is twice the shim thickness. In a production transformer, it is not very much more expensive to have the center leg ground down to twice the shim thickness. This will achieve pretty much the same effect as shims in the center and outer legs, but is preferable as the gap will not change with changes in the thickness of the plastic and results in less magnetic radiation and hence reduced RFI interference.
2.2.8.2 Adding Primary Resistance
It was pointed out in Section 2.2.6 that primary wiring resistance keeps the core from being driven rapidly into saturation if there is a volt- second inequality. If there is such an inequality, the half primary with the larger volt-second product draws a larger peak current. That larger current causes a larger voltage drop across the wiring resistance and robs volt-seconds from that half primary, restoring the current balance.
This effect can be augmented by adding additional resistance in series with both primary halves. The added resistors can be located in either the collectors or emitters of the power transistors. The value is best determined empirically by observing the current pulses in the transformer center tap. The required resistors are usually under 0.25. They will, of course, increase power loss and reduce efficiency.
2.2.8.3 Matching Power Transistors
Since volt-second inequality arises mainly from an inequality in stor- age time or voltage in the power transistors, if those parameters are
matched, it adds confidence that together with the earlier two “fixes”
there will be no problem with flux imbalance.
This is not a good solution and would be an expensive fix as it is quite expensive to match transistors in two parameters. To do such matching requires a specialized test setup that would not be available if field replacements become necessary.
It also must be ascertained that if the matching is done at certain load currents and temperature, the matching still holds when these vary. Further, a storage time match is difficult to make credible, as it depends strongly on forward and reverse base input currents in the bipolar transistors. Generally any matching is done by matchingVce
and Vbe (the “on” collector-to-emitter and base-to-emitter voltages) at the maximum operating current. Hence matching is not a viable solution for high-volume commercial supplies.
2.2.8.4 Using MOSFET Power Transistors
Since most of the volt-second inequality arises from storage time inequality between the two bipolar power transistors, the problem largely disappears if MOSFETs are used, because they have no stor- age time.
There is an added advantage, as the “on” voltage of a MOSFET tran- sistor increases with temperature. Thus if one half primary tends to take a large current, its transistor runs somewhat warmer and its “on”
voltage increases and steals voltage from the winding. This reduces the volt-second product on that side and tends to restore balance. This, of course, is qualitatively in the right direction, which is helpful but cannot be depended on to solve the flux-imbalance problem reliably at all power levels and with a worst-case combination.
However, with power MOSFETs at power levels under 100 W and low input voltages (as in most DC/DC converter applications), push- pull converters can be and are built with a high degree of confidence.
2.2.8.5 Using Current-Mode Topology
By far the best solution to the flux-imbalance problem is to use current- mode control. This completely and reliably solves the flux-imbalance problem; also it has significant additional advantages of its own.
In conventional push-pull, there is always a residual concern that despite all the fixes, a flux-imbalance problem will arise in some worst-case situation and a transistor will be destroyed. Current-mode topology solves this problem by monitoring the current in each of the push-pull transistors on a pulse-by-pulse basis. The control cir- cuit then forces alternate current pulses to have equal amplitude, maintaining the working point very near the center of the B/H loop.
Details of current-mode topology will be discussed in Chapter 5.