Eye opening measurement circuit calculating difference between sigma levels, receiver including the same, and method for measuring eye opening

1. A receiver comprising:

a sampler that samples first voltage levels corresponding to a first logical value of data and second voltage levels corresponding to a second logical value of the data, based on a sampling clock;

an equalizer that receives and adjusts the first and second voltage levels;

a clock and data recovery circuit that recovers the sampling clock, based on the first and second voltage levels received from the equalizer; and

an eye opening measurement circuit that:

tracks a first sigma level by a first step unit depending on upper voltage levels, which are greater than a first reference voltage level, from among the first voltage levels,

tracks a second sigma level by a second step unit depending on lower voltage levels, which are less than a second reference voltage level, from among the second voltage levels, and

calculates a difference between the first sigma level and the second sigma level.

2. The receiver of claim 1 , wherein:

the first reference voltage level is a center level of the first voltage levels, and

the second reference voltage level is a center level of the second voltage levels.

3. The receiver of claim 1 , wherein:

the first sigma level, when converged by the eye opening measurement circuit, is greater than the first reference voltage level and is less than a maximum level of the upper voltage levels, and

the second sigma level, when converged by the eye opening measurement circuit, is less than the second reference voltage level and is greater than a minimum level of the lower voltage levels.

4. The receiver of claim 3 , wherein:

the first sigma level, when converged by the eye opening measurement circuit, is an average level of the upper voltage levels, and

the second sigma level, when converged by the eye opening measurement circuit, is an average level of the lower voltage levels.

5. The receiver of claim 1 , wherein the eye opening measurement circuit:

increases or decreases the first sigma level by as much as the first step unit based on results of comparing the upper voltage levels with the first sigma level; and

increases or decreases the second sigma level by as much as the second step unit based on results of comparing the lower voltage levels with the second sigma level.

6. The receiver of claim 1 , wherein the eye opening measurement circuit:

further tracks first sigma levels by the first step unit depending on the upper voltage levels;

further tracks second sigma levels by the second step unit depending on the lower voltage levels;

further calculates differences between the first sigma levels and the second sigma levels; and

calculates an average of the differences.

7. The receiver of claim 6 , further comprising a logic circuit that adjusts the equalizer and the clock and data recovery circuit based on the average.

8. The receiver of claim 1 , wherein the eye opening measurement circuit operates, to receive the data, after the equalizer and the clock and data recovery circuit are locked.

9. The receiver of claim 1 , wherein the first step unit is identical to the second step unit.

10. An eye opening measurement circuit comprising:

a demultiplexer that:

tracks first sigma levels by a first step unit depending on upper voltage levels, which are greater than a first reference voltage level, from among first voltage levels corresponding to a first logical value of data, and

tracks second sigma levels by a second step unit depending on lower voltage levels, which are less than a second reference voltage level, from among second voltage levels corresponding to a second logical value of the data;

a difference calculator that calculates differences between the first sigma levels and the second sigma levels; and

an average calculator that calculates an average of the differences.

11. The eye opening measurement circuit of claim 10 , wherein:

the first sigma levels, when converged by the demultiplexer, are greater than the first reference voltage level and are less than a maximum level of the upper voltage levels, and

the second sigma levels, when converged by the demultiplexer, are less than the second reference voltage level and are greater than a minimum level of the lower voltage levels.

12. The eye opening measurement circuit of claim 10 , wherein the demultiplexer:

increases or decreases the first sigma levels by as much as the first step unit based on results of comparing the upper voltage levels with the first sigma levels; and

increases or decreases the second sigma levels by as much as the second step unit based on results of comparing the lower voltage levels with the second sigma levels.

13. The eye opening measurement circuit of claim 10 , wherein the demultiplexer:

receives the first voltage levels corresponding to the first logical value of the data, the second voltage levels corresponding to the second logical value of the data, third voltage levels corresponding to a third logical value of the data, and fourth voltage levels corresponding to a fourth logical value of the data;

further tracks third sigma levels by a third step unit depending on upper voltage levels, which are greater than the second reference voltage level, from among the second voltage levels;

further tracks fourth sigma levels by a fourth step unit depending on lower voltage levels, which are less than a third reference voltage level, from among the third voltage levels;

further tracks fifth sigma levels by a fifth step unit depending on upper voltage levels, which are greater than the third reference voltage level, from among the third voltage levels; and

further tracks sixth sigma levels by a sixth step unit depending on lower voltage levels, which are less than a fourth reference voltage level, from among the fourth voltage levels.

14. The eye opening measurement circuit of claim 13 , wherein:

the differences are first differences and the average is a first average,

the difference calculator:

further calculates second differences between the third sigma levels and the fourth sigma levels; and

further calculates third differences between the fifth sigma levels and the sixth sigma levels, and

the average calculator:

further calculates a second average of the second differences; and

further calculates a third average of the third differences.

15. The eye opening measurement circuit of claim 14 , further comprising a determination circuit that determines a minimum average of the first to third averages.

16. An eye opening measurement method of a receiver which receives data through a channel, the method comprising:

receiving first voltage levels corresponding to a first logical value of the data and second voltage levels corresponding to a second logical value of the data;

comparing a first reference voltage level, which is a center level of the first voltage levels, with the first voltage levels and comparing a second reference voltage level, which is a center level of the second voltage levels, with the second voltage levels;

adjusting a first sigma level by comparing the first sigma level with upper voltage levels, which are greater than the first reference voltage level, from among the first voltage levels, and adjusting a second sigma level by comparing the second sigma level with lower voltage levels, which are less than the second reference voltage level, from among the second voltage levels; and

calculating a difference between the first sigma level and the second sigma level, wherein:

the first sigma level is greater than the first reference voltage level and is less than a maximum level of the upper voltage levels, and

the second sigma level is less than the second reference voltage level and is greater than a minimum level of the lower voltage levels.

17. The method of claim 16 , wherein the adjusting the first sigma level and the adjusting the second sigma level includes:

increasing or decreasing the first sigma level by as much as a first step unit based on results of comparing the upper voltage levels with the first sigma level; and

increasing or decreasing the second sigma level by as much as a second step unit based on results of comparing the lower voltage levels with the second sigma level.

18. The method of claim 17 , wherein the increasing or decreasing the first sigma level by as much as the first step unit includes:

increasing the first sigma level by as much as the first step unit in response to determining the first sigma level is less than one of the upper voltage levels; and

decreasing the first sigma level by as much as the first step unit in response to determining the first sigma level is greater than another of the upper voltage levels, wherein:

the increasing or decreasing the second sigma level by as much as the second step unit includes:

increasing the second sigma level by as much as the second step unit in response to determining the second sigma level is less than one of the lower voltage levels; and

decreasing the second sigma level as much as the second step unit in response to determining the second sigma level is greater than another of the lower voltage levels.

19. The method of claim 17 , wherein:

the first step unit is identical to the second step unit, and

a difference between the first reference voltage level and the first sigma level is identical to a difference between the second reference voltage level and the second sigma level.

20. The method of claim 16 , further comprising:

calculating differences between first sigma levels and second sigma levels by repeatedly performing:

the receiving the first voltage levels and the second voltage levels,

the adjusting the first sigma level and the second sigma level, and

the calculating the difference; and

calculating an average of the differences.