Methods and apparatus for a variable resistor configured to compensate for non-linearities in a heating element circuit

1. A vapor delivery system for dispensing a vaporized material having a controllable heating apparatus comprising:

a heating element;

a voltage source coupled to said heating element;

a variable resistor coupled to said heating element and said voltage source, said variable resistor including a fixed resistive element and a moveable element, said moveable element having a position and adjustably contacting said fixed resistive element at a contact point associated with said position;

said fixed resistive element having a length and comprising a first thin film resistor and a second thin film resistor substantially parallel to said first thin film resistor, said first and second thin film resistors having a width that varies non-linearly over said length

said variable resistor having a resistance that is at least partially non-linearly related to said position;

said heating element having a dissipated power that is at least partially linearly related to said position, said dissipated power at least partially linearly related to a temperature of said heating element.

2. The controllable heating apparatus of claim 1 , wherein said heating element comprises a thin-film resistor.

3. The controllable heating apparatus of claim 2 , wherein said heating element comprises a thin-film resistor having a serpentine pattern.

4. The controllable heating apparatus of claim 1 , wherein said voltage source comprises an AC power source.

5. The controllable heating apparatus of claim 1 , further including a vapor dispensing device thermally coupled to said heating element, said vapor dispensing device configured to release vapor into an environment at a rate that is a function of said dissipated power.

6. The controllable heating apparatus of claim 1 , wherein said moveable element comprises a component selected from the group consisting of a slider switch, a dial, a knob, a screw, and a thumbwheel.

7. The controllable heating apparatus of claim 1 , wherein said fixed resistive element comprises at least one thin film resistor.

8. The controllable heating apparatus of claim 7 , wherein said at least one thin film resistor has a first end, a second end, and an attribute that varies non-linearly between said first end and second end, said attribute selected from the group consisting of width, thickness, material, and sheet resistance.

9. The controllable heating apparatus of claim 1 , wherein said width varies continuously over said length in accordance with a geometric function selected from the group consisting of a square-root function, a logarithmic function, and a polynomial function.

10. The controllable heating apparatus of claim 1 , wherein said width varies in accordance with a period of discrete steps.

11. The controllable heating apparatus of claim 1 , wherein said moveable element has a high position, a low position, and at least one intermediate position between said high and low positions, and wherein said dissipated power at said high, low, and intermediate position define a substantially linear curve.

12. A variable resistor for controlling a heating element in a vapor delivery system for dispensing a vaporized material coupled in series with a voltage source V, the heating element being of the type characterized by a resistance RH and a dissipated power PH=IVH, wherein I is the current through the heating element and VH is the voltage across the heating clement, said variable resistor comprising:

a fixed resistive element having a length L;

a moveable element having a position x adjustably contacting said fixed resistive element at a contact point associated with said position x;

said fixed resistive element having a resistance RS(x);

wherein the dissipated power PH is related to RS(x) by the equation:

P

H

=

C

1

⁡

(

1

R

S

2

+

C

2

⁢

R

S

+

C

3

)

where C 1 =V 2 R H , C 2 =2R H , and C3=R H 2 ;

said dissipated power linearly related to a temperature of said heating element;

and wherein RS(x) is a non-linear function and PH(x) is at least partially linear.

13. The variable resistor of claim 12 , wherein R S (x)∝√{square root over (x/L)}.

14. The variable resistor of claim 12 , wherein said fixed resistive element comprises two substantially parallel thin film resistors having widths w which vary non-linearly as a function of x.

15. The variable resistor of claim 12 , wherein w(x)∝√{square root over (x/L)}.

16. The variable resistor of claim 12 , wherein said moveable element has a high position X high , a low position X low , and at least one intermediate position, wherein said dissipated power P H has a curve which substantially intersects a line defined by (X high , P H (X high )) and (X low , P H (X low )) at three points along said curve.