Start-Up Supplies
Before a switching power supply can supply power, it must itself be powered. Start-up supplies provide power for converter control circuits, but are usually not themselves converters and are inefficient. To minimize start-up supply power loss, they are usually turned off after the main supply is running, which then supplies the control power instead.
The main supply, once running, provides control power through an auxiliary output on the primary side of the converter transformer. This auxiliary supply usually parallels the start-up supply output. Passive start-up supplies are on all the time and can eliminate the need for an auxiliary supply. Active start-up supplies, however, turn off after start-up, allowing the efficient auxiliary supply to operate solely, thereby significantly increasing overall efficiency in all but large-power supplies.
Passive Start-Up
The simplest but crudest approach to a start-up supply design is to hang a resistor from the raw dc input to a Zener diode. The maximum control-circuit current for start-up must be supplied at minimum operating input voltage. The minimum power rating of the resistor must be calculated based on the maximum input voltage. Resistors must be sized for power and multiple resistors used in series, if necessary, to satisfy the resistor voltage rating.
The big disadvantage of this oft-used scheme is that the start-up resistor continues to dissipate power after the main supply is running. In a low-power supply, this can appreciably degrade efficiency. A better approach is to turn off the inefficient start-up supply when the main supply can provide power instead.
Active Start-Up: the Supertex LR745
The Supertex LR745 is a low-cost, 3-terminal TO-92- or TO-243-packaged start-up IC capable of working from 25 V up to 450 V. It consists of a high-voltage MOSFET in series with a 2 to 4 mA current regulator that turns on at power-on and turns off when its output exceeds an internally set threshold value of nominally 13.5 V. If the output voltage drops beneath 7 V, it turns back on. The series MOSFET gate drive is provided by a very large pull-up resistor with a 23 V Zener diode to ground, to protect the MOSFET gate. The output voltage compliance is nominally about 21.5 V. This single-part solution (with output capacitor, of course) connects to the output of the auxiliary supply that takes over later. Intersil also has variations on this start-up IC theme, but in larger packages.
Start-Up Problems
Active start-up supplies go away once the auxiliary supply of the main converter kicks in. One common problem is that the start-up supply does not stay on long enough, failing to overlap in operation with the main supply until it sources the required current. What can happen is that the start-up voltage rises until the control IC turns on, loading the start-up supply excessively. The control voltage decreases below the undervoltage lockout threshold, turning off the control IC. On-off oscillation of the control IC then occurs. A larger supply capacitor is the simplest remedy, though if the start-up supply current is inadequate, the control IC might never stay on. Some control ICs, especially those operating at low switching frequencies, can take a relatively long time to bring up the converter and its auxiliary supply. There is no need to skimp on start-up power for active start-up supplies since their power loss is short-lived and thereby insignificant. However, parts cost and space might be adversely affected.
The control loop of the supply typically has compensation capacitors which can be substantial in value - enough to keep them from adequately charging from the start-up supply. Consequently, the high duty-ratio needed at start-up does not occur, and the converter auxiliary supply fails to deliver.
Another somewhat different kind of start-up problem is that the supply input voltage stays low too long, causing excessive input current from the power line, which blows the fuse.
PFC Start-Up
A PFC start-up supply is complicated by the sine-magnitude (rectified sine) input instead of a raw dc input. A dc input with large ripple can be improvised using a small (low loss) series resistor and small high-voltage filter capacitor, placed before the start-up circuit input. This keeps the instantaneous voltage to the start-up supply above its minimum operating voltage. However, voltage ripple can cause the following problem.
As the LR745 output voltage increases at power-on, it crosses and trips the 13.5 V comparator. Because this threshold has no hysteresis, the LR745 turns off. This is shown in the oscillograph below.

Trace 1 is the sine-magnitude input. The resulting output voltage ripple is evident on trace 2. The upper voltage cursor, set at 12.9 V, is crossed and the LR745 shuts off, as evidenced by the subsequently decreasing output voltage.
On a slower time scale, the start-up voltage continues to decrease until it crosses the 7 V threshold which turns the LR745 on again. The result is a start-up voltage oscillation, as shown in the oscillograph below.

As a result of this behavior, the start-up voltage never reaches the power-on voltage (undervoltage-lockout hysteresis upper-level) threshold of the converter controller.
For controllers with a lower start-up threshold, but with their lower turn-off (UVLO) threshold above 7 V, an on-off oscillation of the converter itself might ensue. With enough cycles, it might provide enough drive to the controller supply to keep it running. This form of start-up, though unusual, might have the advantage of providing a soft-start capability. This soft-start technique may not appeal to your aesthetic sense of design, but if you can't "fix" it, you can still feature it. For PFCs, however, it is likely to cause more trouble than it alleviates. At the least, such a PFC start-up will be non-linear and very complicated to analyze in detail, best suited for a master's-degree thesis.
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Dennis L. Feucht, 2001