Systems and methods for tuning an impedance matching network in a step-wise fashion

1. A controller comprising:

a processor configured to:

obtain a first input parameter value associated with an output of a radio frequency (RF) generator when an impedance matching network operates at a first capacitance value;

initialize a model to have the first capacitance value;

propagate the first input parameter value via the model to output a first output parameter value when the model has the first capacitance value;

determine, using the first output parameter value and the model, an optimum capacitance value for which a reflection coefficient at an input of the model is at a minimum; and

control the impedance matching network to modify the first capacitance value to be closer to the optimum capacitance value; and

a memory device coupled to the processor.

2. The controller of claim 1 , wherein the first input parameter value is an impedance value, wherein the impedance value is generated from a reflection coefficient value measured at the output of the RF generator.

3. The controller of claim 1 , wherein the output of the RF generator is coupled to an input of the impedance matching network.

4. The controller of claim 1 , wherein the first capacitance value is a combined variable capacitance of two or more capacitors of the impedance matching network.

5. The controller of claim 1 , wherein the model is a computer-generated model, wherein the memory device is configured to store the computer-generated model.

6. The controller of claim 1 , wherein the processor is configured to determine a model parameter value based on the first capacitance value of the model, wherein to propagate the first input parameter value, the processor is configured to calculate a directional sum of the first input parameter value and the model parameter value to determine the first output parameter value.

7. The controller of claim 6 , wherein the processor is configured to:

back propagate the first output parameter value via the model parameter value to calculate a first reflection coefficient value at an input of the model;

back propagate the first output parameter value via another model parameter value to calculate a second reflection coefficient value at the input of the model, wherein the other model parameter value is associated with the optimum capacitance value of the model;

determining that the second reflection coefficient value is less than the first reflection coefficient value.

8. The controller of claim 1 , wherein the reflection coefficient is at the minimum when the reflection coefficient is zero.

9. A method comprising:

obtaining a first input parameter value associated with an output of a radio frequency (RF) generator when an impedance matching network operates at a first capacitance value;

initializing a model to have the first capacitance value;

propagating the first input parameter value via the model to output a first output parameter value when the model has the first capacitance value;

determining, using the first output parameter value and the model, an optimum capacitance value for which a reflection coefficient at an input of the model is at a minimum; and

controlling the impedance matching network to modify the first capacitance value to be closer to the optimum capacitance value.

10. The method of claim 9 , wherein the first input parameter value is an impedance value, wherein the impedance value is generated from a reflection coefficient value measured at the output of the RF generator.

11. The method of claim 9 , wherein the output of the RF generator is coupled to an input of the impedance matching network.

12. The method of claim 9 , wherein the first capacitance value is a combined variable capacitance of two or more capacitors of the impedance matching network.

13. The method of claim 9 , wherein the model is a computer-generated model, the method further comprising storing the computer-generated model in a memory device.

14. The method of claim 9 , further comprising determining a model parameter value based on the first capacitance value of the model, wherein said propagating comprises calculating a directional sum of the first input parameter value and the model parameter value to determine the first output parameter value.

15. The method of claim 14 , further comprising:

back propagating the first output parameter value via the model parameter value to calculate a first reflection coefficient value at an input of the model;

back propagating the first output parameter value via another model parameter value to calculate a second reflection coefficient value at the input of the model, wherein the other model parameter value is associated with the optimum capacitance value of the model; and

determining that the second reflection coefficient value is less than the first reflection coefficient value.

16. The method of claim 9 , wherein the reflection coefficient is at the minimum when the reflection coefficient is zero.

17. A plasma system comprising:

a radio frequency (RF) generator configured to generate an RF signal;

an impedance matching network coupled to the RF generator, wherein the impedance matching circuit is configured to receive the RF signal to output a modified RF signal;

a plasma chamber coupled to the impedance matching circuit to receive the modified RF signal; and

a host computer coupled to the RF generator, wherein the host computer is configured to:

obtain a first input parameter value associated with an output of the RF generator when the impedance matching network operates at a first capacitance value;

initialize a model to have the first capacitance value;

propagate the first input parameter value via the model to output a first output parameter value when the model has the first capacitance value;

determine, using the first output parameter value and the model, an optimum capacitance value for which a reflection coefficient at an input of the model is at a minimum; and

control the impedance matching network to modify the first capacitance value to be closer to the optimum capacitance value.

18. The plasma system of claim 17 , wherein the first input parameter value is an impedance value, wherein the impedance value is generated from a reflection coefficient value measured at the output of the RF generator.

19. The plasma system of claim 17 , wherein the host computer is configured to determine a model parameter value based on the first capacitance value of the model, wherein to propagate the first input parameter value, the host computer is configured to calculate a directional sum of the first input parameter value and the model parameter value to determine the first output parameter value.

20. The plasma system of claim 17 , wherein the first capacitance value is a combined variable capacitance of two or more capacitors of the impedance matching network.