"tail" of its exponential curve by the time it reaches Vb, so the frequency will depend sensitively on the breakdown threshold and supply voltage levels, causing variations in frequency. Therefore, the supply voltage is usually made significantly higher than the bulb firing voltage. This also makes the charging more linear, and the sawtooth wave more triangular. The resistor R must also be within a certain range of values for the circuit to oscillate. This is illustrated by the load line (blue) on the IV graph. The slope of the load line is equal to R. The possible DC operating points of the circuit are at the intersection of the load line and the neon lamp's IV curve (black) In order for the circuit to be unstable and oscillate, the load line must intersect the IV curve in its negative resistance region, between b and d, where the voltage declines with increasing current. This is defined by the shaded region on the diagram. If the load line crosses the IV curve where it has positive resistance, outside the shaded region, this represents a stable operating point, so the circuit will not oscillate: If R is too large, of the same order as the "off" leakage resistance of the bulb, the load line will cross the IV curve between the origin and b. In this region, the current through R from the supply is so low that the leakage current through the bulb bleeds it off, so the capacitor voltage never reaches Vb and the bulb never fires. The leakage resistance of most neon bulbs is greater than 100MΩ, so this is not a serious limitation. If R is too small, the load line will cross the IV curve between c and d. In this region the current through R is too large; once the bulb has turned on, the current through R will be large enough to keep it conducting without current from the capacitor, and the voltage across the bulb will never fall to Ve so the bulb will never turn off. Small neon bulbs will typically oscillate with values of R between 500kΩ and 20MΩ. If C is not small, it may be necessary to add a resistor in series with the neon bulb, to limit current through it to prevent damage when the capacitor discharges. This will increase the discharge time and decrease the frequency slightly, but its