PAM4 receiver including adaptive continuous-time linear equalizer and method of adaptively training the same using training data patterns

Abstract

A PAM4 receiver including an adaptive continuous-time linear equalizer and a method for training the same are disclosed. The PAM4 receiver and the method for training the same of the present invention employs a training pattern including a first training data pattern and second training data pattern to adaptively tune the PAM4 receiver to achieve accurate data reception and long-distance, high-speed communication.

Claims

1. A PAM4 (pulse amplitude modulation 4) receiver comprising: a CTLE (continuous-time linear equalizer) receiving a signal containing: (i) a first training data pattern containing data “00” and consecutively arranged first data “11” through m.sup.th data “11”; and (ii) a second training data pattern including one of data “01”, data “10” and combinations thereof, and equalizing the signal according to an equalization parameter of the CTLE including a high frequency amplification gain and a low frequency amplification gain, and outputting a signal CTLE_out containing equalized first training data pattern and equalized second training data pattern; a sampler sampling: (i) a difference dlev.sub.3HD; (ii) a difference dlev.sub.3LD; and (iii) a difference dlev.sub.1D or dlev.sub.2D, and outputting sampled differences as a signal SAMPLE_out, wherein the difference dlev.sub.3HD is a difference between: a first voltage level of the signal CTLE_out corresponding to the first data “11” of the equalized first training data pattern when a transition from the data “00” to the first data “11” occurs; and an upper limit dlev.sub.3H, the difference dlev.sub.3LD is a difference between: a second voltage level of the signal CTLE_out corresponding to one of second data “11” through the m.sup.th data “11” of the equalized first training data pattern; and a lower limit dlev.sub.3L, the difference dlev.sub.1D is a difference between: a third voltage level of the signal CTLE_out corresponding to the data “01” of the equalized second training data pattern; and the data level dlev.sub.1 corresponding to the data “01”, and the difference dlev.sub.2D is a difference between: a fourth voltage level of the signal CTLE_out corresponding to the data “10” of the equalized second training data pattern; and the data level dlev.sub.2 corresponding to data “10”; a DEMUX (demultiplexer) parallelizing the signal SAMPLE_out, and outputting parallelized signal SAMPLE_out as a signal DATA_out; a CDR (clock-and-data recovery) providing a clock signal for sampling to the sampler and the DEMUX; and a controller: (i) adaptively adjusting a high frequency amplification gain and a low frequency amplification gain of the CTLE by generating and providing a signal EQ_AC[N.sub.AC−1:0] and a signal EQ_DC[N.sub.DC−1:0] for adjusting the high frequency amplification gain and low frequency amplification gain based on the difference dlev.sub.3HD and the difference dlev.sub.3LD in the signal DATA_out, respectively; and (ii) providing the sampler with threshold voltages V.sub.TH01, V.sub.TH12 and V.sub.TH23, the data level dlev.sub.1 or dlev.sub.2, and the upper limit dlev.sub.3H and the lower limit dlev.sub.3L, wherein the threshold voltages V.sub.TH01, V.sub.TH12 and V.sub.TH23 are calculated from: a data level dlev.sub.0 corresponding to the data “00”; the data level dlev.sub.1 or dlev.sub.2; and a data level dlev.sub.3 corresponding to the data “11”, the data levels dlev.sub.1 and dlev.sub.2 are determined from the differences dlev.sub.1D and dlev.sub.2D, respectively; and the data level dlev.sub.3 is determined from the upper limit dlev.sub.3H and the lower limit dlev.sub.3L (where m is a natural number equal to or greater than 2, and N.sub.AC and N.sub.DC are natural numbers, respectively).

2. The PAM4 receiver of claim 1, wherein the CTLE comprises: a differential amplifier provided with transistors; N.sub.AC capacitors C.sub.unit connected between sources of the transistors; and N.sub.DC resistors R.sub.unit connected between the sources of the transistors, and the controller selectively turns on the N.sub.AC capacitors C.sub.unit according to the signal EQ_AC[N.sub.AC−1:0] to adaptively adjust the high frequency amplification gain, and selectively turns on the N.sub.DC resistor R.sub.unit according to the signal EQ_DC[N.sub.DC−1:0] to adaptively adjust the low frequency amplification gain.

3. The PAM4 receiver of claim 2, wherein the controller lowers the upper limit dlev.sub.3H and the lower limit dlev.sub.3L when the first voltage level of the signal CTLE_out is lower than the upper limit dlev.sub.3H even with the high frequency amplification gain at maximum by turning on an entirety of the N.sub.AC capacitors C.sub.unit.

4. The PAM4 receiver of claim 1, wherein the controller: determines the data level dlev.sub.1 or dlev.sub.2 based on a sign of the difference dlev.sub.1D or dlev.sub.2D; and provides the sampler with the threshold voltages V.sub.TH01, V.sub.TH12 and V.sub.TH23 thereof calculated according to equations ${\mathrm{dlev}}_3=\frac{dle{v}_{3H}+dle{v}_{3L}}{2},V_{\mathrm{TH}01}=\frac{dle{v}_0+dle{v}_1}{2},V_{\mathrm{TH}12}=\frac{dle{v}_1+dle{v}_2}{2}\mathrm{and}{V}_{\mathrm{TH}23}=\frac{dle{v}_2+dle{v}_3}{2}.$

5. A PAM4 receiver comprising: a CTLE (continuous-time linear equalizer) receiving a signal containing: (i) a first training data pattern containing data “11” and consecutively arranged first data “00” through m.sup.th data “00”; and (ii) a second training data pattern including one of data “01”, data “10” and combinations thereof, and equalizing the signal according to an equalization parameter of the CTLE including a high frequency amplification gain and a low frequency amplification gain, and outputting a signal CTLE_out containing equalized first training data pattern and equalized second training data pattern; a sampler sampling: (i) a difference dlev.sub.0LD; (ii) a difference dlev.sub.0HD; and (iii) a difference dlev.sub.1D or dlev.sub.2D, and outputting sampled differences as a signal SAMPLE_out, wherein the difference dlev.sub.0LD is a difference between: a first voltage level of the signal CTLE_out corresponding to the first data “00” of the equalized first training data pattern when a transition from the data “11” to the first data “00” occurs; and a lower limit dlev.sub.0L, the difference dlev.sub.0HD is a difference between: a second voltage level of the signal CTLE_out corresponding to one of second data “00” through the m.sup.th data “00” of the equalized first training data pattern; and an upper limit dlev.sub.0H, the difference dlev.sub.2D is a difference between: a third voltage level of the signal CTLE_out corresponding to the data “10” of the equalized second training data pattern; and the data level dlev.sub.2 corresponding to the data “10”, and the difference dlev.sub.1D is a difference between: a fourth voltage level of the signal CTLE_out corresponding to the data “01” of the equalized second training data pattern; and the data level dlev.sub.1 corresponding to data “01”; a DEMUX (demultiplexer) parallelizing the signal SAMPLE_out, and outputting parallelized signal SAMPLE_out as a signal DATA_out; a CDR (clock-and-data recovery) providing a clock signal for sampling to the sampler and the DEMUX; and a controller: (i) adaptively adjusting a high frequency amplification gain and a low frequency amplification gain of the CTLE by generating and providing a signal EQ_AC[N.sub.AC−1:0] and a signal EQ_DC[N.sub.DC−1:0] for adjusting the high frequency amplification gain and low frequency amplification gain based on the difference dlev.sub.0LD and the difference dlev.sub.0HD in the signal DATA_out, respectively; and (ii) providing the sampler with threshold voltages V.sub.TH01, V.sub.TH12 and V.sub.TH23, the data level dlev.sub.1 or dlev.sub.2, and the upper limit dlev.sub.0H and the lower limit dlev.sub.0L, wherein the threshold voltages V.sub.TH01, V.sub.TH12 and V.sub.TH23 are calculated from: a data level dlev.sub.0 corresponding to the data “00”; the data level dlev.sub.1 or dlev.sub.2; and a data level dlev.sub.3 corresponding to the data “11”, the data levels dlev.sub.1 and dlev.sub.2 are determined from the differences dlev.sub.1D and dlev.sub.2D, respectively; and the data level dlev.sub.0 is determined from the lower limit dlev.sub.0L and the upper limit dlev.sub.0H (where m is a natural number equal to or greater than 2, and N.sub.AC and N.sub.DC are natural numbers, respectively).

6. The PAM4 receiver of claim 5, wherein the CTLE comprises: a differential amplifier provided with transistors; N.sub.AC capacitors C.sub.unit connected between sources of the transistors; and N.sub.DC resistors R.sub.unit connected between the sources of the transistors, and the controller selectively turns on the N.sub.AC capacitors C.sub.unit according to the signal EQ_AC[N.sub.AC−1:0] to adaptively adjust the high frequency amplification gain, and selectively turns on the N.sub.DC resistor R.sub.unit according to the signal EQ_DC[N.sub.DC−1:0] to adaptively adjust the low frequency amplification gain.

7. The PAM4 receiver of claim 6, wherein the controller elevates the upper limit dlev.sub.0H and the lower limit dlev.sub.0L when the first voltage level of the signal CTLE_out is higher than the lower limit dlev.sub.0L even with the high frequency amplification gain at maximum by turning on an entirety of the N.sub.AC capacitors C.sub.unit.

8. The PAM4 receiver of claim 5, wherein the controller: determines the data level dlev.sub.1 or dlev.sub.2 based on a sign of the difference dlev.sub.1D or dlev.sub.2D; and provides the sampler with the threshold voltages V.sub.THoi, V.sub.TH12 and V.sub.TH23 thereof calculated according to equations $dle{v}_0=\frac{dle{v}_{0H}+dle{v}_{0L}}{2},V_{\mathrm{TH}01}=\frac{dle{v}_0+dle{v}_1}{2},V_{\mathrm{TH}12}=\frac{dle{v}_1+dle{v}_2}{2}\mathrm{and}{V}_{\mathrm{TH}23}=\frac{dle{v}_2+dle{v}_3}{2}.$

9. A method of training a PAM4 (pulse amplitude modulation 4) receiver comprising a linear equalizer, a sampler, a DEMUX (demultiplexer) and a controller, the method comprising: (a) receiving a signal containing: (i) a first training data pattern containing data “00” and consecutively arranged first data “11” through m.sup.th data “11”; and (ii) a second training data pattern including one of data “01”, data “10” and combinations thereof; (b) equalizing the signal received in step (a) according to an equalization parameter of the CTLE including a high frequency amplification gain and a low frequency amplification gain, and outputting a signal CTLE_out containing equalized first training data pattern and equalized second training data pattern; (c) sampling: (i) a difference dlev.sub.3HD; (ii) a difference dlev.sub.3LD; and (iii) a difference dlev.sub.1D or dlev.sub.2D according to a sampling parameter of the sampler, and outputting sampled differences as a signal SAMPLE_out, wherein the difference dlev.sub.3HD is a difference between: a first voltage level of the signal CTLE_out corresponding to the first data “11” of the equalized first training data pattern when a transition from the data “00” to the first data “11” occurs; and an upper limit dlev.sub.3H, the difference dlev.sub.3LD is a difference between: a second voltage level of the signal CTLE_out corresponding to one of second data “11” through the m.sup.th data “11” of the equalized first training data pattern; and a lower limit dlev.sub.3L, the difference dlev.sub.1D is a difference between: a third voltage level of the signal CTLE_out corresponding to the data “01” of the equalized second training data pattern; and the data level dlev.sub.1 corresponding to the data “01”, and the difference dlev.sub.2D is a difference between: a fourth voltage level of the signal CTLE_out corresponding to the data “10” of the equalized second training data pattern; and the data level dlev.sub.2 corresponding to data “10”; (d) parallelizing the signal SAMPLE_out, and outputting parallelized signal SAMPLE_out as a signal DATA_out; (e) generating a signal EQ_AC[N.sub.AC−1:0] and a signal EQ_DC[N.sub.DC−1:0] for adjusting the high frequency amplification gain and low frequency amplification gain based on the difference dlev.sub.3HD and the difference dlev.sub.3LD in the signal DATA_out, respectively; (f) generating threshold voltages V.sub.TH01, V.sub.TH12 and V.sub.TH23 of the sampler by calculating the threshold voltages V.sub.THoi, V.sub.TH12 and V.sub.TH23 from: a data level dlev.sub.0 corresponding to the data “00”; the data level dlev.sub.1 or dlev.sub.2; and a data level dlev.sub.3 corresponding to the data “11”, wherein the data level dlev.sub.1 or dlev.sub.2 is determined from the difference dlev.sub.1D or dlev.sub.2D, respectively, and the data level dlev.sub.3 is determined from the upper limit dlev.sub.3H and the lower limit dlev.sub.3L; (g) adaptively adjusting the equalization parameter including the high frequency amplification gain and low frequency amplification using the signal EQ_AC[N.sub.AC−1:0] and signal EQ_DC[N.sub.DC−1:0] generated in step (e); and (h) adaptively adjusting the sampling parameter of the sampler according to the threshold voltages V.sub.THol, V.sub.TH12 and V.sub.TH23, the data level dlev.sub.1 or dlev.sub.2, and the upper limit dlev.sub.3H and the lower limit dlev.sub.3L generated in step (f) (where m is a natural number equal to or greater than 2, and N.sub.AC and N.sub.DC are natural numbers, respectively).

10. The method of claim 9, further comprising: performing step (a) through step (d) after performing step (a) through step (h) based on the equalization parameter and the sampling parameter adaptively adjusted in step (g) and step (h), respectively.

11. The method of claim 9, wherein step (f) comprises: (f-1) determining the data level dlev.sub.1 or dlev.sub.2 based on a sign of the difference dlev.sub.1D or dlev.sub.2D; and (f-2) calculating the threshold voltages V.sub.THoi, V.sub.TH12 and V.sub.TH23 according to equations ${\mathrm{dlev}}_3=\frac{dle{v}_{3H}+dle{v}_{3L}}{2},V_{\mathrm{TH}01}=\frac{dle{v}_0+dle{v}_1}{2},V_{TH12}=\frac{dle{v}_1+dle{v}_2}{2}\mathrm{and}{V}_{\mathrm{TH}23}=\frac{dle{v}_2+{\mathrm{dlev}}_3}{2}.$

12. The method of claim 9, wherein step (g) comprises: (g-1) selectively turning on N.sub.AC capacitors C.sub.unit provided in the CTLE according to the signal EQ_AC[N.sub.AC−1:0] to adaptively adjust the high frequency amplification gain; and (g-2) selectively turning on N.sub.DC resistor R.sub.unit provided in the CTLE according to the signal EQ_DC[N.sub.DC−1:0] to adaptively adjust the low frequency amplification gain.

13. The method of claim 12, wherein step (g) further comprises: (g-3) lowering the upper limit dlev.sub.3H and the lower limit dlev.sub.3L when the first voltage level of the signal CTLE_out is lower than the upper limit dlev.sub.3H even with the high frequency amplification gain at maximum by turning on an entirety of the N.sub.AC capacitors C.sub.ut.

14. A method of training a PAM4 (pulse amplitude modulation 4) receiver comprising a CTLE (continuous-time linear equalizer), a sampler, a DEMUX and a controller, the method comprising: (a) receiving a signal containing: (i) a first training data pattern containing data “11” and consecutively arranged first data “00” through m.sup.th data “00”; and (ii) a second training data pattern including one of data “01”, data “10” and combinations thereof; (b) equalizing the signal received in step (a) according to an equalization parameter of the CTLE including a high frequency amplification gain and a low frequency amplification gain, and outputting a signal CTLE_out containing equalized first training data pattern and equalized second training data pattern; (c) sampling: (i) a difference dlev.sub.0LD; (ii) a difference dlev.sub.0HD; and (iii) a difference dlev.sub.1D or dlev.sub.2D according to a sampling parameter of the sampler, and outputting sampled differences as a signal SAMPLE_out, wherein the difference dlev.sub.0LD is a difference between: a first voltage level of the signal CTLE_out corresponding to the first data “00” of the equalized first training data pattern when a transition from the data “11” to the first data “00” occurs; and a lower limit dlev.sub.0L, the difference dlev.sub.0HD is a difference between: a second voltage level of the signal CTLE_out corresponding to one of second data “00” through the m.sup.th data “00” of the equalized first training data pattern; and an upper limit dlev.sub.0H, the difference dlev.sub.2D is a difference between: a third voltage level of the signal CTLE_out corresponding to the data “10” of the equalized second training data pattern; and the data level dlev.sub.2 corresponding to the data “10”, and the difference dlev.sub.1D is a difference between: a fourth voltage level of the signal CTLE_out corresponding to the data “01” of the equalized second training data pattern; and the data level dlev.sub.1 corresponding to data “01”; (d) parallelizing the signal SAMPLE_out, and outputting parallelized signal SAMPLE_out as a signal DATA_out; (e) generating a signal EQ_AC[N.sub.AC−1:0] and a signal EQ_DC[N.sub.DC−1:0] for adjusting the high frequency amplification gain and low frequency amplification gain based on the difference dlev.sub.0LD and the difference dlev.sub.0HD in the signal DATA_out, respectively; (f) generating threshold voltages V.sub.THoi, V.sub.TH12 and V.sub.TH23 of the sampler by calculating the threshold voltages V.sub.TH01, V.sub.TH12 and V.sub.TH23 from: a data level dlev.sub.0 corresponding to the data “00”; the data level dlev.sub.1 or dlev.sub.2; and a data level dlev.sub.3 corresponding to the data “11”, wherein the data level dlev.sub.1 or dlev.sub.2 is determined from the difference dlev.sub.1D or dlev.sub.2D, respectively, and the data level dlev.sub.0 is determined from the lower limit dlev.sub.0L and the upper limit dlev.sub.0H; (g) adaptively adjusting the equalization parameter including the high frequency amplification gain and low frequency amplification using the signal EQ_AC[N.sub.AC−1:0] and signal EQ_DC[N.sub.DC−1:0] generated in step (e); and (h) adaptively adjusting the sampling parameter of the sampler according to the threshold voltages V.sub.TH01, V.sub.TH12 and V.sub.TH23, the data level dlev.sub.1 or dlev.sub.2, and the lower limit dlev.sub.0L and the upper limit dlev.sub.0H generated in step (f) (where m is a natural number equal to or greater than 2, and N.sub.AC and N.sub.DC are natural numbers, respectively).

15. The method of claim 14, further comprising: performing step (a) through step (d) after performing step (a) through step (h) based on the equalization parameter and the sampling parameter adaptively adjusted in step (g) and step (h), respectively.

16. The method of claim 14, wherein step (f) comprises: (f-1) determining the data level dlev.sub.1 or dlev.sub.2 based on a sign of the difference dlev.sub.1D or dlev.sub.2D, respectively, and (f-2) calculating the threshold voltages V.sub.TH01, V.sub.TH12 and V.sub.TH23 according to equations $dle{v}_0=\frac{dle{v}_{0H}+dle{v}_{0L}}{2},V_{\mathrm{TH}01}=\frac{dle{v}_0+{\mathrm{dlev}}_1}{2},V_{\mathrm{TH}12}=\frac{dle{v}_1+dle{v}_2}{2}\mathrm{and}{V}_{\mathrm{TH23}}=\frac{dle{v}_2+{\mathrm{dlev}}_3}{2}.$

17. The method of claim 14, wherein step (g) comprises: (g-1) selectively turning on N.sub.AC capacitors C.sub.unit provided in the CTLE according to the signal EQ_AC[N.sub.AC−1:0] to adaptively adjust the high frequency amplification gain; and (g-2) selectively turning on N.sub.DC resistor R.sub.unit provided in the CTLE according to the signal EQ_DC[N.sub.DC−1:0] to adaptively adjust the low frequency amplification gain.

18. The method of claim 17, wherein step (g) further comprises: (g-3) elevating the lower limit dlev.sub.0L and the upper limit dlev.sub.0H when the first voltage level of the signal CTLE_out is higher than the lower limit dlev.sub.0L even with the high frequency amplification gain at maximum by turning on an entirety of the N.sub.AC capacitors C.sub.unit.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1A through FIG. 1C are diagrams illustrating binary PAM (PAM2), and multi-level PAM (PAM4, PAM8) signals, respectively.

(2) FIG. 2 is a block diagram illustrating a conventional PAM4 receiver.

(3) FIG. 3 is a circuit diagram illustrating, in detail, the CTLE 110 shown in FIG. 2.

(4) FIG. 4 is a diagram illustrating a waveform of a signal CTLE_out according to the capacitance of the capacitor C.sub.s and the resistance of the resistor R.sub.s.

(5) FIG. 5 is a block diagram illustrating a sampler used in a conventional PAM4 receiver.

(6) FIG. 6 is a waveform diagram illustrating signals in the conventional PAM4 receiver.

(7) FIG. 7 is a block diagram illustrating a PAM4 receiver according to the present invention.

(8) FIG. 8 is a circuit diagram illustrating, in detail, the CTLE of the PAM4 receiver shown in FIG. 7.

(9) FIG. 9A through FIG. 9D are diagrams illustrating in detail the sampler of the PAM4 receiver shown in FIG. 7.

(10) FIG. 10A and FIG. 10B are waveform diagrams for describing the operation of the PAM4 receivers according to first and second embodiments of the present invention, respectively.

(11) FIG. 11A and FIG. 11B are flow diagrams illustrating methods of training the PAM4 receivers according to the first and the second embodiments of the present invention, respectively.

(12) FIG. 12A and FIG. 12B are flow diagrams illustrating, in detail, step S150 and step S250 shown in FIG. 11A and FIG. 11B, respectively.

(13) FIG. 13A and FIG. 13B are flow diagrams illustrating, in detail, step S160 and step S260 shown in FIG. 11A and FIG. 11B, respectively.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

(14) Hereinafter, a PAM4 receiver including an adaptive continuous-time linear equalizer and a method for adaptively training the same using training patterns according to the present invention will be described in detail with reference to the accompanying drawings.

(15) FIG. 7 is a block diagram illustrating a PAM4 receiver according to the present invention.

(16) Referring to FIG. 7, a PAM4 receiver 1000 according to the present invention includes a continuous-time linear equalizer (CTLE) 1100, a sampler 1200, a DEMUX 1300, a clock-and-data recovery (CDR) 1400 and a controller 1500.

(17) CTLE 1100 equalizes a received signal and outputs an equalized signal CTLE_out.

(18) FIG. 8 is a circuit diagram illustrating, in detail, the CTLE of the PAM4 receiver 1000 shown in FIG. 7.

(19) Referring to FIG. 8, the CTLE 1100 is basically a differential amplifier circuit, and includes a plurality (N.sub.AC) of capacitors C.sub.unit and a plurality (N.sub.DC) of resistors R.sub.unit connected in parallel to the sources of the transistors (where N.sub.AC and N.sub.DC are natural numbers, respectively).

(20) The plurality of capacitors C.sub.unit are selectively turned on or off by a signal EQ_AC[N.sub.AC−1:0]. For example, when 8 capacitors C.sub.unit are provided and the signal EQ_AC[7:0] has a value of “00001111”, 4 capacitors C.sub.unit are turned on, and the remaining 4 capacitors C.sub.unit are turned off.

(21) The amplification gain of the high frequency component is determined according to the number of capacitors C.sub.unit turned on by the signal EQ_AC[N.sub.AC−1:0] among the plurality of capacitors C.sub.unit.

(22) A plurality of resistors R.sub.unit are selectively turned on or off by a signal EQ_DC[N.sub.DC−1:0]. For example, when 8 resistors R.sub.unit are provided and the signal EQ_DC[7:0] has a value of “00000111”, 3 resistors R.sub.unit are turned, and the remaining 5 resistors R.sub.unit are turned off.

(23) The amplification gain of the low frequency component is determined according to the number of resistors R.sub.unit turned on by the signal EQ_DC[N.sub.DC−1:0] among the plurality of resistors R.sub.unit.

(24) The signal EQ_AC[N.sub.AC−1:0] and the signal EQ_DC[N.sub.DC−1:0] are adaptively generated by the controller 1500.

(25) FIG. 9A through FIG. 9D are diagrams illustrating, in detail, the sampler 1200 of the PAM4 receiver shown in FIG. 7 wherein the sampler 1200 samples the signal CTLE_out and outputs a signal SAMPLE_out which basically corresponds to the sampled CTLE_out.

(26) FIG. 9A is a block diagram illustrating a sampler used in a training mode of the PAM4 receiver according to the present invention.

(27) Referring to FIG. 9A, a sampler 1200a for the training mode of the PAM4 receiver according to the present invention includes flip-flops 1210-1, 1210-2, 1220-1, 1220-2, 1220-3, 1220-4, 1230-1, 1230-2, 1240-1 and 1240-2 and adders 1250-1, 1250-2, 1250-3 and 1250-4.

(28) The signal CTLE_out of the CTLE 1100 is inputted to the four adders 1250-1, 1250-2, 1250-3 and 1250-4, respectively, and the adder 1250-1 outputs a difference dlev.sub.1D between the signal CTLE_out and a data level dlev.sub.1, the adder 1250-2 outputs a difference V.sub.TH12D between the signal CTLE_out and a threshold voltage V.sub.TH12, the adder 1250-3 outputs a difference dlev.sub.3LD between the signal CTLE_out and a data level dlev.sub.3L, and the adder 1250-4 outputs a difference dlev.sub.3HD between the signal CTLE_out and a data level dlev.sub.3H.

(29) The difference dlev.sub.1D between the signal CTLE_out and the data level dlev.sub.1 is inputted to the flip-flops 1210-1 and 1210-2, and is sampled at the rising edges of the clock signals DCK and DCKB and outputted as signals AEd.sub.1 and AOd.sub.1 by the flip-flops 1210-1 and 1210-2, respectively. The difference V.sub.TH12D between the signal CTLE_out and the threshold voltage V.sub.TH12 is inputted to the flip-flops 1220-1, 1220-2, 1220-3 and 1220-4, and is sampled at the rising edges of clock signals DCK, DCKB, XCK and XCKB and outputted as signals DET[1], DOT[1], XET[1] and XOT[1] by the flip-flops 1220-1, 1220-2, 1220-3 and 1220-4, respectively.

(30) In addition, the difference dlev.sub.3LD between the signal CTLE_out and the data level dlev.sub.3L is inputted to the flip-flops 1230-1 and 1230-2, and is sampled at the rising edges of the clock signals DCK and DCKB and outputted as signals AEd.sub.3L and AOd.sub.3L by the flip-flops 1230-1 and 1230-2, respectively. The difference dlev.sub.3HD between the signal CTLE_out and the data level dlev.sub.3H is inputted to the flip-flops 1240-1 and 1240-2, is sampled at the rising edges of the clock signals DCK and DCKB and outputted as signals AEd.sub.3H and AOd.sub.3H by the flip-flops 1240-1 and 1240-2, respectively.

(31) Here, the signals outputted by the flip-flops represent the sign of the signal inputted to the flip-flops. For example, when the value of the signal AEd.sub.3H obtained by sampling the difference dlev.sub.3HD is “1”, it indicates that the difference dlev.sub.3HD is a positive number. In other words, it indicates that the voltage level of the signal CTLE_out is higher than that of the data level dlev.sub.3H. Similarly, when the value of signal AEd.sub.3H is “0”, it indicates that the difference dlev.sub.3HD is a negative number. That is, it indicates that the voltage level of the signal CTLE_out is smaller than that of the data level dlev.sub.3H.

(32) FIG. 9B is a block diagram illustrating a sampler which is a combination of the samplers shown in FIG. 9A and FIG. 5.

(33) Referring to FIG. 9B, a sampler 1200b of the PAM4 receiver according to the present invention differs from the sampler 120 shown in FIG. 5 in that the sampler 1200b further includes the flip-flops 1240-1 and 1240-2 and the adder 1250-4 of the sampler 1200a shown in FIG. 9A added to the sampler 120 shown in FIG. 5.

(34) Additional difference between the sampler 1200b shown in FIG. 9B and the sampler 120 shown in FIG. 5 is as follows.

(35) First, the sampler 1200b differs from the sampler 120 shown in FIG. 5 in that, in the training mode, the adder 1250-1 outputs the difference dlev.sub.1D between the signal CTLE_out and the data level dlev.sub.1, and the difference dlev.sub.1D is sampled at the rising edges of the clock signals DCK, DCKB, XCK and XCKB and outputted as the signals AEd.sub.1, AOd.sub.1, XEd.sub.1 and XOd.sub.1 by the flip-flops 1210-1, 1210-2, 1210-3 and 1210-4, respectively. In addition, the sampler 1200b differs from the sampler 120 shown in FIG. 5 in that, when the sampler 1200b is actually in use after exiting the training mode, the adder 1250-1 outputs the difference V.sub.TH01D between the signal CTLE_out and a threshold voltage V.sub.TH01, and the difference V.sub.TH01D is sampled at the rising edges of clock signals DCK, DCKB, XCK and XCKB, and is outputted as the signals DET[0], DOT[0], XET[0] and XOT[0] by the flip-flops 1210-1, 1210-2, 1210-3 and 1210-4, respectively.

(36) Similarly, the sampler 1200b differs from the sampler 120 shown in FIG. 5 in that the adder 1250-3 and the flip-flops 1230-1, 1230-2, 1230-3 and 1230-4, as well as the adder 1250-1 and the flip-flops 1210-1, 1210-2, 1210-3 and 1210-4, sample and output the corresponding signal.

(37) FIG. 9C is a block diagram illustrating another example of the sampler used in the training mode of the PAM4 receiver according to the present invention.

(38) Referring to FIG. 9C, a sampler 1200c used in the training mode of the PAM4 receiver according to the present invention includes flip-flops 1210-1, 1210-2, 1220-1, 1220-2, 1220-3, 1220-4, 1230-1, 1230-2, 1240-1 and 1240-2 and adders 1250-1, 1250-2, 1250-3 and 1250-4.

(39) The sampler 1200c shown in FIG. 9C has the same configuration as the sampler 1200a shown in FIG. 9A. However, the signals inputted to the sampler 1200c differ from those inputted to the sampler 1200a.

(40) Specifically, the sampler 1200c differs from the sampler 1200a in that data level dlev.sub.2 is inputted to the adder 1250-1 instead of the data level dlev.sub.1, and data levels dlev.sub.0H and dlev.sub.0L are inputted to the adder 1250-3 and 1250-4 instead of data levels dlev.sub.3L and dlev.sub.3H, respectively. However, the sampler 1200c is the same as the sampler 1200a in that the outputs of the adders 1250-1, 1250-3 and 1250-4 are sampled at the rising edge of the corresponding clock, and the sampled data are outputted.

(41) FIG. 9D is a block diagram illustrating a sampler which is a combination of the samplers shown in FIG. 9C and FIG. 5.

(42) Referring to FIG. 9D, the sampler 1200d of the PAM4 receiver according to the present invention is the same as the sampler 1200b shown in FIG. 9B except the difference between the sampler 1200c shown in FIG. 9C and the sampler 1200a shown in FIG. 9A. Therefore, a detailed description thereof is omitted.

(43) Referring back to FIG. 7, the DEMUX 1300 parallelizes the signal SAMPLE_out from the sampler 1200 and outputs the signal DATA_out.

(44) Specifically, the DEMUX 1300 parallelizes, according to a predetermined clock, the signals DET[0], DOT[0], XET[0], XOT[0], DET[1], DOT[1], XET[1], XOT[1], DET[2], DOT[2], XET[2] and XOT[2] contained in the signal SAMPLE_out, and outputs the parallelized signals DET[2:0], DOT[2:0], XET[2:0] and XOT[2:0] as the signal DATA_out. More specifically, since the signals DET[0], DOT[0], XET[0], XOT[0], DET[1], DOT[1], XET[1], XOT[1], DET[2], DOT[2], XET[2] and XOT[2] contained in the signal SAMPLE_out are not simultaneously outputted, the signals DET[0], DOT[0], XET[0], XOT[0], DET[1], DOT[1], XET[1], XOT[1], DET[2], DOT[2], XET[2] and XOT[2] contained in the signal SAMPLE_out are parallelized (synchronized) according to a predetermined clock and outputted as the signal DATA_out. Similarly, the DEMUX 1300 may parallelize other signals outputted from the sampler 1200.

(45) In addition, the DEMUX 1300 provides the signal DATA_out to the CDR 1400 and the controller 1500.

(46) The CDR (Clock-and-Data Recovery) 1400 provides the sampling clock signals DCK, XCK, DCKB and XCKB to the sampler 1200 and the controller 1500.

(47) Specifically, the CDR 1400 adjusts the timings or the phases of the sampling clock signals DCK, XCK, DCKB and XCKB based on the signal DET[2:0], DOT[2:0], XET[2:0], XOT[2:0]. Here, the sampling clock signal DCK, XCK, DCKB and XCKB are the same as those shown in FIG. 6.

(48) More specifically, the CDR 1400 adjusts the phases of the sampling clock signal DCK, XCK, DCKB and XCKB according to the time point at which the signal CTLE_out passes the threshold voltage V.sub.TH12, that is, the time point at which a transition section of the signal CTLE_out and the threshold voltage V.sub.TH12 meet. For example, since the transition section of signal CTLE_out is sampled according to the clock signals XCK and XCKB, CDR 1400 determines the time point at which the signal CTLE_out passes the threshold voltage V.sub.TH12 at the rising edges of the clock signals XCK and XCKB, and adjusts the phases of the sampling clock signals DCK and DCKB such that the signal CTLE_out is sampled at the center of the symbol according to the clock signals DCK and DCKB.

(49) The controller 1500 feeds a threshold voltage V.sub.TH01, V.sub.TH12, V.sub.TH23 and the data levels dlev.sub.3H, dlev.sub.3L, dlev.sub.1 and dlev.sub.2 to the sampler 1200, and generates signals EQ_AC[N.sub.AC−1:0] and EQ_DC[N.sub.DC−1:0] for selectively turning on or off a plurality of capacitors C.sub.unit and a plurality of resistors R.sub.unit included in the CTLE 1100, respectively in order to control high frequency amplification characteristics and low frequency amplification characteristics of the CTLE 1100.

(50) Hereinafter, a method of training a PAM4 receiver according to the present invention will be described in detail.

(51) The PAM4 receiver according to the present invention receives actual data after being tuned or trained by a training pattern. Specifically, the PAM4 receiver is used for actual communication after various parameters such as the threshold voltages V.sub.TH01, V.sub.TH12 and V.sub.TH23 are tuned using the training pattern.

(52) The training pattern was created considering DC balance, timing of transitions, and facilitation of data level measurement. For DC balance, it is desirable to create the training pattern including combinations of “00” and “11” wherein the number of “00” and “11” are the same, and the number of “01” and “10” are the same. For the timing of the transition, it is desirable to select data in the training pattern such that the signal CTLE_out passes the threshold voltage V.sub.TH12 only when the transitions “00”.fwdarw.“11”, “11”.fwdarw.“00”, “01”.fwdarw.“10” and “10”.fwdarw.“01” occur. For facilitation of data level measurement, it is desirable to select data in the training pattern such that the number of each of “00”, “01”, “10” and “11” is equal to or more than two.

(53) FIG. 10A and FIG. 10B are waveform diagrams of for describing the operation of the PAM4 receivers according to first and second embodiments of the present invention, respectively, wherein training patterns are shown.

(54) The training pattern illustrated in FIG. 10A includes a first training data pattern and a second training data pattern. The training pattern includes four counts of data “00” and four counts of data “11”, and two counts of data “01” and two counts of data “10” in overall. Specifically, the first training data pattern includes one data “00” and consecutive first data “11” through fourth data “11” in order, and the second training data pattern includes combinations of “00” and “11” having two counts of data “00”, one count of data “01”, two counts of data “10”, one count of data “01” and two counts of data “00”. However, as described above, different combinations of “00”, “01”, “10” and “11” are possible by considering DC balance, timing of transitions, and ease of data level measurement. For example, the first training data pattern may include consecutive first data “11” through m.sup.th data “11” in order where m is a natural number equal to or greater than 2.

(55) The training pattern illustrated in FIG. 10B includes a first training data pattern and a second training data pattern. The training pattern includes four counts of data “00” and four counts of data “11”, and two counts of data “01” and two counts of data “10” in overall. Specifically, the first training data pattern includes one data “11” and consecutive first data “00” to fourth data “00” in order, and the second training data pattern includes combinations of “00” and “11” having two counts of data “11”, one count of data “10”, two counts of data “01”, one count of data “10” and two counts of data “11”. However, as described above, different combinations of “00”, “01”, “10” and “11” are possible by considering DC balance, timing of transitions, and ease of data level measurement. For example, the first training data pattern may include consecutive first data “00” through m.sup.th data “00” in order where m is a natural number equal to or greater than 2.

(56) Hereinafter, the method of training the PAM4 receiver according to the first embodiment and the second embodiment of the present invention will be described in detail with reference to FIGS. 10A, 10B, 11A and 11B.

(57) FIG. 11A is a flow diagrams illustrating a method of training the PAM4 receivers according to the first embodiment of the present invention. It is preferable to use the sampler shown in FIG. 9A when training the PAM4 receiver according to the present invention using the training pattern exemplified in FIG. 10A. However, the present invention is not limited thereto.

(58) First, for convenience of describing the present invention, equations

(59) $V_{TH01}=\frac{dle{v}_0+dle{v}_1}{2}{V}_{TH12}=\frac{dle{v}_1+dle{v}_2}{2},\mathrm{and}$$V_{TH23}=\frac{dle{v}_2+{\mathrm{dlev}}_3}{2}$
are assumed. That is, the threshold voltages V.sub.TH01, V.sub.TH12 and V.sub.TH23 are calculated by the controller 1500 according to the equations and provided to the sampler 1200. In addition, predetermined initial values of the data levels dlev.sub.3H and dlev.sub.3L are stored in the controller 1500 in advance, and equation

(60) $dle{v}_3=\frac{dle{v}_{3H}+dle{v}_{3L}}{2}$
is assumed.

(61) Referring to FIG. 11A, the CTLE 1100 of the PAM4 receiver according to the present invention receives a signal containing the training pattern shown in FIG. 10A (S100). Specifically, the CTLE 1100 shown in FIG. 7 receives the training pattern including the first training data pattern and the second training data pattern.

(62) Thereafter, the CTLE 1100 equalizes the signal received in the step S100 based on the initial equalization parameter, and outputs the signal CTLE_out shown in FIG. 10A (S110). Here, the equalization parameter includes a high frequency amplification gain and a low frequency amplification gain of a linear equalizer.

(63) Specifically, CTLE 1100 equalizes the received signal containing the training pattern according to the initial equalization parameter, and outputs the signal CTLE_out containing equalized first training data pattern and equalized second training data pattern.

(64) Thereafter, the sampler 1200a samples the signal CTLE_out at the rising edge of the clock signals DCK and DCKB to generate a signal SAMPLE_out (S120).

(65) Specifically, The sampler 1200a shown in FIG. 9A samples the difference dlev.sub.3HD which is a difference between: the voltage level of the signal CTLE_out immediately after the transition from the data “00” to the first data “11” of the first training data pattern (i.e. a first voltage level of the signal CTLE_out (denoted by .diamond-solid. in FIG. 10A) corresponding to the first data “11” of the equalized first training data pattern when a transition from the data “00” to the first data “11” occurs); and a predetermined upper limit dlev.sub.3H. The sampled difference dlev.sub.3HD is then outputted as the signal SAMPLE_out by the sampler 1200a.

(66) Here, the difference dlev.sub.3HD is sampled by the flip-flops 1240-1 and 1240-2 shown in FIG. 9A at the rising edges of the clock signals DCK and DCKB, respectively, and outputted as signals AEd.sub.3H and AOd.sub.3H, respectively. Each of the signals AEd.sub.3H and AOd.sub.3H may have value of “1” or “0” (representing whether the difference dlev.sub.3HD is a positive number or a negative number) depending on the first voltage level (magnitude) of the signal CTLE_out.

(67) In addition, the sampler 1200a shown in FIG. 9A samples the difference dlev.sub.3LD which is a difference between: a second voltage level of the signal CTLE_out (denoted by □ in FIG. 10A) corresponding to one of the data after the first data “11” of the first training data pattern (i.e. any one of the second data “11” through the min data “11” of the equalized first training data pattern, where m is a natural number equal to or greater than 2, and an example wherein m=4 is shown in FIG. 10A); and a predetermined lower limit dlev.sub.3L. The sampled difference dlev.sub.3LD is then outputted as the signal SAMPLE_out by the sampler 1200a.

(68) Here, the difference dlev.sub.3LD is sampled by the flip-flops 1230-1 and 1230-2 shown in FIG. 9A at the rising edges of the clock signals DCK and DCKB, respectively, and outputted as signals AEd.sub.3L and AOd.sub.3L, respectively. Each of the signals AEd.sub.3L and AOd.sub.3L may have value of “1” or “0” (representing whether the difference dlev.sub.3LD is a positive number or a negative number) depending on the voltage level (magnitude) of the signal CTLE_out.

(69) Thereafter, the signal SAMPLE_out outputted by the sampler 1200a is parallelized and the parallelized signal SAMPLE_out is outputted as the signal DATA_out (S130). Specifically, the DEMUX 1300 generates the signal DATA_out by parallelizing the signal SAMPLE_out. Here, since the signal DATA_out is obtained by parallelizing signal SAMPLE_out, the signal DATA_out contains the signals included in the signal SAMPLE_out of the sampler 1200 such as the differences dlev.sub.3HD and dlev.sub.3LD.

(70) Thereafter, the signals EQ_AC[N.sub.AC−1:0] and EQ_DC[N.sub.DC−1:0] for adjusting the high and the low frequency amplification gains of the CTLE 1100, respectively, are generated from the signal DATA_out (S140).

(71) Specifically, the signals EQ_AC[N.sub.AC−1:0] and EQ_DC[N.sub.DC−1:0] are generated based on the first training data pattern which is used for adjusting the high and the low frequency amplification gains of the CTLE 1100.

(72) Hereinafter, a method of generating the signal EQ_AC[N.sub.AC−1:0] will be described in detail, and a method of generating the signal EQ_DC[N.sub.DC−1:0] will be described in detail thereafter.

(73) The signal EQ_AC[N.sub.AC−1:0] is generated based on the difference dlev.sub.3HD contained in the signal DATA_out.

(74) Specifically, as described above, the difference dlev.sub.3HD is the difference between: the first voltage level of the signal CTLE_out (denoted by .diamond-solid. in FIG. 10A); and the upper limit dlev.sub.3H. The reason for generating the signal EQ_AC[N.sub.AC−1:0] and using the same to adjust the high frequency amplification gain of CTLE 1100 is to make the first voltage level of the signal CTLE_out equal to the upper limit dlev.sub.3H.

(75) In the case of the example shown in FIG. 10A, the difference dlev.sub.3HD has a negative value since the first voltage level of the signal CTLE_out is lower than the upper limit dlev.sub.3H.

(76) As a result, the first voltage level of the signal CTLE_out should be increased in the example shown in FIG. 10A since the goal is to make the first voltage level of the signal CTLE_out equal to the upper limit dlev.sub.3H.

(77) However, when the transition from the data “00” to the first data “11” of the first training data pattern occurs, the first voltage level of the signal CTLE_out corresponding to the first data “11” varies depending on the high frequency amplification gain of CTLE 1100. Therefore, in order to increase the first voltage level of the signal CTLE_out, the controller 1500 generates the signal EQ_AC[N.sub.AC−1:0] that increases the high frequency amplification gain of the CTLE 1100 and provides the same to the CTLE 1100. For example, the controller 1500 generates the signal EQ_AC[N.sub.AC−1:0] with increased number of value “1” contained therein and provides the same to the CTLE 1100 such that the number of capacitors C.sub.unit turned on by the signal EQ_AC[N.sub.AC−1:0] increases.

(78) On the other hand, when the first voltage level of the signal CTLE_out is higher than the upper limit dlev.sub.3H, the difference dlev.sub.3HD has a positive value.

(79) Similarly, the first voltage level of the signal CTLE_out should be decreased since the goal is to make the first voltage level of the signal CTLE_out equal to the upper limit dlev.sub.3H,

(80) However, when the transition from the data “00” to the first data “11” of the first training data pattern occurs, the first voltage level of the signal CTLE_out corresponding to the first data “11” varies depending on the high frequency amplification gain of CTLE 1100. Therefore, in order to decrease the first voltage level of the signal CTLE_out, the controller 1500 generates the signal EQ_AC[N.sub.AC−1:0] that decreases the high frequency amplification gain of the CTLE 1100 and provides the same to the CTLE 1100. For example, the controller 1500 the signal EQ_AC[N.sub.AC−1:0] with increased number of value “0” contained therein and provides the same to the CTLE 1100 such that the number of capacitors C.sub.unit turned on by the signal EQ_AC[N.sub.AC−1:0] decreases.

(81) The signal EQ_DC[N.sub.DC−1:0] is generated based on the difference dlev.sub.3LD contained in the signal DATA_out.

(82) Specifically, as described above, the difference dlev.sub.3LD is the difference between: the second voltage level of the signal CTLE_out (denoted by □ in FIG. 10A); and the lower limit dlev.sub.3L. The reason for generating the signal EQ_DC[N.sub.DC−1:0] and using the same to adjust the low frequency amplification gain of CTLE 1100 is to make the second voltage level of the signal CTLE_out equal to the lower limit dlev.sub.3L.

(83) In the case of the example shown in FIG. 10A, the difference dlev.sub.3LD has a positive value since the second voltage level of the signal CTLE_out is higher than the lower limit dlev.sub.3L.

(84) As a result, the second voltage level of the signal CTLE_out should be decreased in the example shown in FIG. 10A since the goal is to make the second voltage level of the signal CTLE_out equal to the lower limit dlev.sub.3L.

(85) However, the second voltage level of the signal CTLE_out corresponding to any one of the second data “11” through the min data “11” of the equalized first training data pattern varies depending on the low frequency amplification gain of CTLE 1100. Therefore, in order to decrease the second voltage level of the signal CTLE_out, the controller 1500 generates the signal EQ_DC[N.sub.DC−1:0] that decreases the low frequency amplification gain of the CTLE 1100 and provides the same to the CTLE 1100. For example, the controller 1500 generates the signal EQ_DC[N.sub.DC−1:0] with increased number of value “0” contained therein and provides the same to the CTLE 1100 such that the number of resistors R.sub.unit turned on by the signal EQ_DC[N.sub.DC−1:0] decreases.

(86) On the other hand, when the second voltage level of the signal CTLE_out is lower than the lower limit dlev.sub.3L, the difference dlev.sub.3LD has a negative value.

(87) Similarly, the second voltage level of the signal CTLE_out should be increased since the goal is to make the second voltage level of the signal CTLE_out equal to the lower limit dlev.sub.3L,

(88) However, the second voltage level of the signal CTLE_out corresponding to any one of the second data “11” through the m.sup.th data “11” of the equalized first training data pattern varies depending on the low frequency amplification gain of CTLE 1100. Therefore, in order to increase the second voltage level of the signal CTLE_out, the controller 1500 generates the signal EQ_DC[N.sub.DC−1:0] that increases the low frequency amplification gain of the CTLE 1100 and provides the same to the CTLE 1100. For example, the controller 1500 generates the signal EQ_DC[N.sub.DC−1:0] with increased number of value “1” contained therein and provides the same to the CTLE 1100 such that the number of resistors R.sub.u, turned on by the signal EQ_DC[N.sub.DC−1:0] increases.

(89) Thereafter, the threshold voltages V.sub.TH01, V.sub.TH12 and V.sub.TH23 of the sampler 1200a (or the sampler 1200b) are generated from the data level dlev.sub.1 or dlev.sub.2 (S150).

(90) Specifically, the data level dlev.sub.1 or dlev.sub.2 is generated from the difference dlev.sub.1D or dlev.sub.2D, respectively, and the threshold voltages V.sub.TH01, V.sub.TH12 and V.sub.TH23 of the sampler 1200a (or the sampler 1200b) are generated from the upper limit dlev.sub.3H, the lower limit dlev.sub.3L and the data levels dlev.sub.0, dlev.sub.1, dlev.sub.2 and dlev.sub.3.

(91) The step S150 includes a step S150a and a step S150b shown in FIG. 12A. Hereinafter, the step S150 will be described in detail with reference to FIG. 12A.

(92) Referring to FIG. 12A, the data levels dlev.sub.1 and dlev.sub.2 are determined according to the signs of the differences dlev.sub.1D and dlev.sub.2D, respectively (S150a).

(93) Specifically, the data levels dlev.sub.1 and dlev.sub.2 are determined using the second training data pattern.

(94) As shown in FIG. 9A, the sampler 1200a samples the difference dlev.sub.1D which is a difference between: a third voltage level (denoted by .circle-solid. in FIG. 10A) of the signal CTLE_out corresponding to the data “01” of the second training data pattern at the rising edge of the clock signals DCK and DCKB; and the data level dlev.sub.1. Here, the data level dlev.sub.1 has an initial value, and the controller 1500 then adjusts the data level dlev.sub.1 according to the sign of the difference dlev.sub.1D. That is, depending on which one of the third voltage level of the signal CTLE_out and the data level dlev.sub.1 is higher, the data level dlev.sub.1 is increased or decreased by a predetermined value.

(95) While the sampler 1200a samples the difference dlev.sub.1D in FIG. 9A, the difference dlev.sub.2D, which is a difference between: a fourth voltage level (denoted by .box-tangle-solidup. in FIG. 10A) of the signal CTLE_out corresponding to the data “10” of the second training data pattern at the rising edge of the clock signals DCK and DCKB; and the data level dlev.sub.2, may also be sampled. In particular, when the data levels dlev.sub.1 and dlev.sub.2 have the same magnitude and opposite signs (i.e., dlev.sub.2=-dlev.sub.1), it is sufficient when only one of the data levels dlev.sub.1 and dlev.sub.2 is determined since the other can be automatically determined. However, when the data levels dlev.sub.1 and dlev.sub.2 have different magnitudes or have the same sign, both of the differences dlev.sub.1D and dlev.sub.2D may be sampled to adjust both of the data levels dlev.sub.1 and dlev.sub.2.

(96) Thereafter, the threshold voltages V.sub.TH01, V.sub.TH12 and V.sub.TH23 of the sampler 1200a (or the sampler 1200b) are calculated from the upper limit dlev.sub.3H, the lower limit dlev.sub.3L and the data levels dlev.sub.0, dlev.sub.1, dlev.sub.2 and dlev.sub.3 according to the equation 1 below (S150b).

(97) $\begin{array}{cc}{\mathrm{dlev}}_3=\frac{dle{v}_{3H}+dle{v}_{3L}}{2},V_{TH01}=\frac{dle{v}_0+dle{v}_1}{2},V_{TH12}=\frac{dle{v}_1+dle{v}_2}{2},V_{TH23}=\frac{dle{v}_2+{\mathrm{dlev}}_3}{2}& \left[\mathrm{Equation}1\right]\end{array}$

(98) Thereafter, as shown in FIG. 11A, the equalization parameter is adaptively adjusted according to the signals EQ_AC[N.sub.AC−1:0] and EQ_DC[N.sub.DC−1:0] generated in the step S140 (S160).

(99) The step S160 will be described in detail with reference to FIG. 13A,

(100) Referring to FIG. 13A, the plurality of capacitors C.sub.unit included in the CTLE 1100 are selectively turned on using the signal EQ_AC[N.sub.AC−1:0] generated in the step S140 to adjust the high frequency amplification gain of the CTLE 1100 (S160a).

(101) Thereafter, the plurality of resistors R.sub.unit included in the CTLE 1100 are selectively turn on using the signal EQ_DC[N.sub.DC−1:0] generated in step S140 to adjust the low frequency amplification gain of the CTLE 1100 (S160b).

(102) Thereafter, it is determined whether the high frequency amplification gain of the CTLE 1100 is at its maximum (S160c). The reason for determining whether the high frequency amplification gain is at its maximum is to determine whether the upper limit dlev.sub.3H is excessively high. For example, when the first voltage level of the signal CTLE_out is lower than the upper limit dlev.sub.3H even with the high frequency amplification gain at its maximum by turning on entirety of N.sub.AC capacitors C.sub.unit, the upper limit dlev.sub.3H must be lowered as the high frequency amplification gain cannot be increased any further. Therefore, it is necessary to determine whether the high frequency amplification gain is at its maximum.

(103) When the high frequency amplification gain is not at its maximum (“N” in step S160c), the step S160 ends since the high frequency amplification gain can be further increased if necessary.

(104) On the other hand, when the high frequency amplification gain is at its maximum (“Y” in step S160c), it is determined that which one of the first voltage level of the signal CTLE_out and the upper limit dlev.sub.3H is higher (S160d).

(105) When the first voltage level of the signal CTLE_out is lower than the upper limit dlev.sub.3H even with the high frequency amplification gain at its maximum (“Y” in step S160d), the upper limit dlev.sub.3H and the lower limit dlev.sub.3L are lowered as the high frequency amplification gain cannot be increased any further (S160e).

(106) When the first voltage level of the signal CTLE_out is higher than or equal to the upper limit dlev.sub.3H (“N” in step S160d), the step S160 ends.

(107) The steps S160c through S160e for lowering the upper limit dlev.sub.3H and the lower limit dlev.sub.3L may be performed when the steps S100 through S170 shown in FIG. 11A are repeatedly performed.

(108) For example, when the first voltage level of the signal CTLE_out obtained from the (k+1).sup.th first training data pattern (where k is a natural number equal to or greater than 2) is not as high as the upper limit dlev.sub.3H although the high frequency amplification gain was adjusted to its maximum due to the insufficient first voltage level of the signal CTLE_out obtained from the k.sup.th first training data pattern, the controller 1500 may lower both of the upper limit dlev.sub.3H and the lower limit dlev.sub.3L instead of adjusting the high frequency amplification gain. That is, after lowering the upper limit dlev.sub.3H and the lower limit dlev.sub.3L until the first voltage level of the signal CTLE_out is between the upper limit dlev.sub.3H and lower limit dlev.sub.3L, the high frequency amplification gain may then be tuned.

(109) Thereafter, as shown in FIG. 11A, the sampling parameter of the sampler is adaptively adjusted according to the data levels dlev.sub.1 and dlev.sub.2, the upper limit dlev.sub.3H, the lower limit dlev.sub.3L and the threshold voltages V.sub.TH01, V.sub.TH12 and V.sub.TH23 generated in step S150 (S170).

(110) Thereafter, it is determined whether the value of the difference dlev.sub.3HD, the difference dlev.sub.3LD, the difference dlev.sub.1D or the difference dlev.sub.2D is zero (S180).

(111) Specifically, when the value of the difference dlev.sub.3HD, the difference dlev.sub.3LD, the difference dlev.sub.1D or the difference dlev.sub.2D is zero (“Y” in step S180), the method of training PAM4 receiver according to the first embodiment is ended. When the value of the difference dlev.sub.3HD, dlev.sub.3LD, dlev.sub.1D or dlev.sub.2D is not zero (“N” in step S180), the steps S100 through S170 are repeated until the difference dlev.sub.3HD, dlev.sub.3LD, dlev.sub.1D or dlev.sub.2D becomes zero.

(112) Here, it is not necessary that the values of the differences dlev.sub.3HD, dlev.sub.3LD, dlev.sub.1D and dlev.sub.2D be all zero. For example, the steps S100 through S170 may be repeated until the values of the differences dlev.sub.3HD and dlev.sub.3LD becomes all zero, until the value of the difference dlev.sub.3HD becomes zero, or until the values of the differences dlev.sub.3HD, dlev.sub.3LD, dlev.sub.1D, and dlev.sub.2D become all zero. In other words, it is possible to select conditions of the repetition as necessary.

(113) The repetition of the steps S100 through S170 means performing the steps S100 through S170 each time the same training pattern (e.g. the training pattern shown in FIG. 10A) is received.

(114) The reason for repeating the steps S100 through S170 is to achieve the goal which is to make the voltage level of the first signal CTLE_out equal to the upper limit dlev.sub.3H, and the second voltage level of the signal CTLE_out equal to the lower limit dlev.sub.3L.

(115) In order to achieve this, the high frequency amplification gain and the low frequency amplification gain must be adjusted such that the values of the differences dlev.sub.3HD, dlev.sub.3LD, dlev.sub.1D and dlev.sub.2D become zero or converge to zero. Specifically, since the voltage levels of the signal CTLE_out approaches the upper limit dlev.sub.3H and lower limit dlev.sub.3L each time the steps S100 through S170 is performed by adjusting the high frequency amplification gain and the low frequency amplification gain, the values of the differences dlev.sub.3HD, dlev.sub.3LD, dlev.sub.1D and dlev.sub.2D become zero or converge to zero as the steps S100 through S170 are repeated.

(116) For example, after the tuning of the high frequency amplification gain and the low frequency amplification gain using a j.sup.th training pattern (where j is a natural number) is complete, a (j+1).sup.th training pattern, which is the same as the j.sup.th training pattern, is received and used to tune the high frequency amplification gain and the low frequency amplification gain by repeating the same process as described above.

(117) Specifically, the sampler 1200a samples the difference dlev.sub.3HD between: the first voltage level of the signal CTLE_out corresponding to the data “11” of the (j+1).sup.th first training data pattern when the transition from the data “00” to the first data “11” occurs; and the upper limit dlev.sub.3H. Since the signal CTLE_out is the output of CTLE 1100 already trained using the j.sup.th first training data pattern, the difference dlev.sub.3HD between: the first voltage level of the signal CTLE_out obtained from the (j+1).sup.th first training data pattern; and the upper limit dlev.sub.3H is smaller than the difference dlev.sub.3HD between: the first voltage level of the signal CTLE_out obtained from the j.sup.th first training data pattern; and the upper limit dlev.sub.3H. Accordingly, the high frequency amplification gain of the CTLE 1100 may be fine-tuned by a more precise signal EQ_AC[N.sub.AC−1:0] generated by the controller 1500.

(118) Similarly, the difference dlev.sub.3LD obtained from the (j+1).sup.th first training data pattern is smaller than the difference dlev.sub.3LD obtained from the j.sup.th first training data pattern. Accordingly, the low frequency amplification gain of the CTLE 1100 may be fine-tuned by a more precise signal EQ_DC[N.sub.DC−1:0] generated by the controller 1500.

(119) In addition, since the differences dlev.sub.1D and dlev.sub.2D obtained from the (j+1).sup.th second training data pattern are smaller than the differences dlev.sub.1D and dlev.sub.2D obtained from the j.sup.th second training data pattern, more precise data levels dlev.sub.1 and dlev.sub.2 may be obtained.

(120) As described above, when the PAM4 receiver is trained by repeatedly receiving the same training pattern until the differences dlev.sub.3HD, dlev.sub.3LD, dlev.sub.1D and dlev.sub.2D become zero or converge to zero, the PAM4 signal received during the actual use of the PAM4 receiver may be precisely determined despite the attenuation of the transmission line.

(121) FIG. 11B is a flow diagrams illustrating a method of training the PAM4 receivers according to the first embodiment of the present invention. It is preferable to use the sampler shown in FIG. 9C when training the PAM4 receiver according to the present invention using the training pattern exemplified in FIG. 10B. However, the present invention is not limited thereto.

(122) First, for convenience of describing the present invention, equations

(123) $V_{TH01}=\frac{dle{v}_0+dle{v}_1}{2},V_{TH12}=\frac{dle{v}_1+dle{v}_2}{2},\mathrm{and}$$V_{TH23}=\frac{dle{v}_2+{\mathrm{dlev}}_3}{2}$
are assumed. That is, the threshold voltages V.sub.TH01, V.sub.TH12 and V.sub.TH23 are calculated by the controller 1500 according to the equations and provided to the sampler 1200. In addition, predetermined initial values of the data levels dlev.sub.0L and dlev.sub.0L are stored in the controller 1500 in advance, and equation

(124) ${\mathrm{dlev}}_0=\frac{dle{v}_{0H}+dle{v}_{0L}}{2}$
is assumed.

(125) Referring to FIG. 11B, the CTLE 1100 of the PAM4 receiver according to the present invention receives a signal containing the training pattern shown in FIG. 10B (S200). Specifically, the CTLE 1100 shown in FIG. 7 receives the training pattern including the first training data pattern and the second training data pattern.

(126) Thereafter, the CTLE 1100 equalizes the signal received in the step S200 based on the initial equalization parameter, and outputs the signal CTLE_out shown in FIG. 10B (S210). Here, the equalization parameter includes a high frequency amplification gain and a low frequency amplification gain of a linear equalizer.

(127) Specifically, CTLE 1100 equalizes the received signal containing the training pattern according to the initial equalization parameter, and outputs the signal CTLE_out containing equalized first training data pattern and equalized second training data pattern

(128) Thereafter, the sampler 1200c samples the signal CTLE_out at the rising edge of the clock signals DCK and DCKB to generate a signal SAMPLE_out (S220).

(129) Specifically, The sampler 1200c shown in FIG. 9C samples the difference dlev.sub.0LD which is a difference between: the voltage level of the signal CTLE_out immediately after the transition from the data “11” to the first data “00” of the first training data pattern (i.e. a first voltage level of the signal CTLE_out (denoted by .diamond-solid. in FIG. 10B) corresponding to the first data “00” of the equalized first training data pattern when a transition from the data “11” to the first data “00” occurs); and a predetermined lower limit dlev.sub.0L. The sampled difference dlev.sub.0LD is then outputted as the signal SAMPLE_out by the sampler 1200c.

(130) Here, the difference dlev.sub.0LD is sampled by the flip-flops 1240-1 and 1240-2 shown in FIG. 9C at the rising edges of the clock signals DCK and DCKB, respectively, and outputted as signals AEd.sub.0L and AOd.sub.0L, respectively. Each of the signals AEd.sub.0L and AOd.sub.0L may have value of “1” or “0” (representing whether the difference dlev.sub.0LD is a positive number or a negative number) depending on the first voltage level (magnitude) of the signal CTLE_out.

(131) In addition, the sampler 1200c shown in FIG. 9C samples the difference dlev.sub.0HD which is a difference between: a second voltage level of the signal CTLE_out (denoted by □ in FIG. 10B) corresponding to one of the data after the first data “00” of the first training data pattern (i.e. any one of the second data “00” through the min data “00” of the equalized first training data pattern, where m is a natural number equal to or greater than 2, and an example wherein m=4 is shown in FIG. 10B); and a predetermined upper limit dlev.sub.0H. The sampled difference dlev.sub.0HD is then outputted as the signal SAMPLE_out by the sampler 1200c.

(132) Here, the difference dlev.sub.0HD is sampled by the flip-flops 1230-1 and 1230-2 shown in FIG. 9C at the rising edges of the clock signals DCK and DCKB, respectively, and outputted as signals AEd.sub.0H and AOd.sub.0H, respectively. Each of the signals AEd.sub.0H and AOd.sub.0H may have value of “1” or “0” (representing whether the difference dlev.sub.0HD is a positive number or a negative number) depending on the voltage level (magnitude) of the signal CTLE_out.

(133) Thereafter, the signal SAMPLE_out outputted by the sampler 1200c is parallelized and the parallelized signal SAMPLE_out is outputted as the signal DATA_out (S230). Specifically, the DEMUX 1300 generates the signal DATA_out by parallelizing the signal SAMPLE_out. Here, since the signal DATA_out is obtained by parallelizing signal SAMPLE_out, the signal DATA_out contains the signals included in the signal SAMPLE_out of the sampler 1200 such as the differences dlev.sub.0LD and dlev.sub.0HD.

(134) Thereafter, the signals EQ_AC[N.sub.AC−1:0] and EQ_DC[N.sub.DC−1:0] for adjusting the high and the low frequency amplification gains of the CTLE 1100, respectively, are generated from the signal DATA_out (S240).

(135) Specifically, the signals EQ_AC[N.sub.AC−1:0] and EQ_DC[N.sub.DC−1:0] are generated based on the first training data pattern which is used for adjusting the high and the low frequency amplification gains of the CTLE 1100.

(136) Hereinafter, a method of generating the signal EQ_AC[N.sub.AC−1:0] will be described in detail, and a method of generating the signal EQ_DC[N.sub.DC−1:0] will be described in detail thereafter.

(137) The signal EQ_AC[N.sub.AC−1:0] is generated based on the difference dlev.sub.0LD contained in the signal DATA_out.

(138) Specifically, as described above, the difference dlev.sub.0LD is the difference between: the first voltage level of the signal CTLE_out (denoted by .diamond-solid. in FIG. 10B); and the lower limit dlev.sub.0L. The reason for generating the signal EQ_AC[N.sub.AC−1:0] and using the same to adjust the high frequency amplification gain of CTLE 1100 is to make the first voltage level of the signal CTLE_out equal to the lower limit dlev.sub.0L.

(139) In the case of the example shown in FIG. 10B, the difference dlev.sub.0LD has a positive value since the first voltage level of the signal CTLE_out is higher than the lower limit dlev.sub.0L.

(140) As a result, the first voltage level of the signal CTLE_out should be decreased in the example shown in FIG. 10B since the goal is to make the first voltage level of the signal CTLE_out equal to the lower limit dlev.sub.0L.

(141) However, when the transition from the data “11” to the first data “00” of the first training data pattern occurs, the first voltage level of the signal CTLE_out corresponding to the first data “00” varies depending on the high frequency amplification gain of CTLE 1100. Therefore, in order to decrease the first voltage level of the signal CTLE_out, the controller 1500 generates the signal EQ_AC[N.sub.AC−1:0] that increases the high frequency amplification gain of the CTLE 1100 and provides the same to the CTLE 1100. For example, the controller 1500 generates the signal EQ_AC[N.sub.AC−1:0] with increased number of value “1” contained therein and provides the same to the CTLE 1100 such that the number of capacitors C.sub.unit turned on by the signal EQ_AC[N.sub.AC−1:0] increases.

(142) On the other hand, when the first voltage level of the signal CTLE_out is lower than the lower limit dlev.sub.0L, the difference dlev.sub.0LD has a negative value.

(143) Similarly, the first voltage level of the signal CTLE_out should be increased since the goal is to make the first voltage level of the signal CTLE_out equal to the lower limit dlev.sub.0L,

(144) However, when the transition from the data “11” to the first data “00” of the first training data pattern occurs, the first voltage level of the signal CTLE_out corresponding to the first data “00” varies depending on the high frequency amplification gain of CTLE 1100. Therefore, in order to increase the first voltage level of the signal CTLE_out, the controller 1500 generates the signal EQ_AC[N.sub.AC−1:0] that decreases the high frequency amplification gain of the CTLE 1100 and provides the same to the CTLE 1100. For example, the controller 1500 the signal EQ_AC[N.sub.AC−1:0] with increased number of value “0” contained therein and provides the same to the CTLE 1100 such that the number of capacitors C.sub.unit turned on by the signal EQ_AC[N.sub.AC−1:0] decreases.

(145) The signal EQ_DC[N.sub.DC−1:0] is generated based on the difference dlev.sub.0HD contained in the signal DATA_out.

(146) Specifically, as described above, the difference dlev.sub.0HD is the difference between: the second voltage level of the signal CTLE_out (denoted by □ in FIG. 10B); and the upper limit dlev.sub.0H. The reason for generating the signal EQ_DC[N.sub.DC−1:0] and using the same to adjust the low frequency amplification gain of CTLE 1100 is to make the second voltage level of the signal CTLE_out equal to the upper limit dlev.sub.0H.

(147) In the case of the example shown in FIG. 10B, the difference dlev.sub.0HD has a positive value since the second voltage level of the signal CTLE_out is higher than the upper limit dlev.sub.0H.

(148) As a result, the second voltage level of the signal CTLE_out should be decreased in the example shown in FIG. 10B since the goal is to make the second voltage level of the signal CTLE_out equal to the upper limit dlev.sub.0H.

(149) However, the second voltage level of the signal CTLE_out corresponding to any one of the second data “00” through the min data “00” of the equalized first training data pattern varies depending on the low frequency amplification gain of CTLE 1100. Therefore, in order to decrease the second voltage level of the signal CTLE_out, the controller 1500 generates the signal EQ_DC[N.sub.DC−1:0] that increases the low frequency amplification gain of the CTLE 1100 and provides the same to the CTLE 1100. For example, the controller 1500 generates the signal EQ_DC[N.sub.DC−1:0] with increased number of value “1” contained therein and provides the same to the CTLE 1100 such that the number of resistors R.sub.unit turned on by the signal EQ_DC[N.sub.DC−1:0] increases.

(150) On the other hand, when the second voltage level of the signal CTLE_out is lower than the upper limit dlev.sub.0H, the difference dlev.sub.0HD has a negative value.

(151) Similarly, the second voltage level of the signal CTLE_out should be increased since the goal is to make the second voltage level of the signal CTLE_out equal to the upper limit dlev.sub.0H,

(152) However, the second voltage level of the signal CTLE_out corresponding to any one of the second data “00” through the min data “00” of the equalized first training data pattern varies depending on the low frequency amplification gain of CTLE 1100. Therefore, in order to increase the second voltage level of the signal CTLE_out, the controller 1500 generates the signal EQ_DC[N.sub.DC−1:0] that decreases the low frequency amplification gain of the CTLE 1100 and provides the same to the CTLE 1100. For example, the controller 1500 generates the signal EQ_DC[N.sub.DC−1:0] with increased number of value “0” contained therein and provides the same to the CTLE 1100 such that the number of resistors R.sub.unit turned on by the signal EQ_DC[N.sub.DC−1:0] decreases.

(153) Thereafter, the threshold voltages V.sub.TH01, V.sub.TH12 and V.sub.TH23 of the sampler 1200c (or the sampler 1200d) are generated from the data level dlev.sub.1 or dlev.sub.2 (S250).

(154) Specifically, the data level dlev.sub.1 or dlev.sub.2 is generated from the difference dlev.sub.1D or dlev.sub.2D, respectively, and the threshold voltages V.sub.TH01, V.sub.TH12 and V.sub.TH23 of the sampler 1200c (or the sampler 1200d) are generated from the lower limit dlev.sub.0L, the upper limit dlev.sub.0H and the data levels dlev.sub.0, dlev.sub.1, dlev.sub.2 and dlev.sub.3.

(155) The step S250 includes a step S250a and a step S250b shown in FIG. 12B. Hereinafter, the step S250 will be described in detail with reference to FIG. 12B.

(156) Referring to FIG. 12B, the data level dlev.sub.1 and dlev.sub.2 are determined according to the signs of the differences dlev.sub.1D and dlev.sub.2D, respectively (S250a).

(157) Specifically, the data levels dlev.sub.1 and dlev.sub.2 are determined using the second training data pattern.

(158) As shown in FIG. 9C, the sampler 1200c samples the difference dlev.sub.2D which is a difference between: a third voltage level (denoted by .box-tangle-solidup. in FIG. 10B) of the signal CTLE_out corresponding to the data “10” of the second training data pattern at the rising edge of the clock signals DCK and DCKB; and the data level dlev.sub.2. Here, the data level dlev.sub.2 has an initial value, and the controller 1500 then adjusts the data level dlev.sub.2 according to the sign of the difference dlev.sub.2D. That is, depending on which one of the third voltage level of the signal CTLE_out and the data level dlev.sub.2 is higher, the data level dlev.sub.2 is increased or decreased by a predetermined value.

(159) While the sampler 1200c samples the difference dlev.sub.2D in FIG. 9C, the difference dlev.sub.1D, which is a difference between: a fourth voltage level (denoted by .circle-solid. in FIG. 10B) of the signal CTLE_out corresponding to the data “01” of the second training data pattern at the rising edge of the clock signals DCK and DCKB; and the data level dlev.sub.1, may be sampled. In particular, when the data levels dlev.sub.1 and dlev.sub.2 have the same magnitude and opposite signs (i.e., dlev.sub.2=−dlev.sub.1), it is sufficient when only one of the data levels dlev.sub.1 and dlev.sub.2 is determined since the other can be automatically determined. However, when the data levels dlev.sub.1 and dlev.sub.2 have different magnitudes or have the same sign, both of the differences dlev.sub.1D and dlev.sub.2D may be sampled to adjust both of the data levels dlev.sub.1 and dlev.sub.2.

(160) Thereafter, the threshold voltages V.sub.TH01, V.sub.TH12 and V.sub.TH23 of the sampler 1200c (or the sampler 1200d) are calculated from the lower limit dlev.sub.0L, the upper limit dlev.sub.0H and the data levels dlev.sub.0, dlev.sub.1, dlev.sub.2 and dlev.sub.3 according to the equation 2 below (S250b).

(161) 0$\begin{array}{cc}dle{v}_0=\frac{dle{v}_{0H}+dle{v}_{0L}}{2},V_{TH01}=\frac{dle{v}_0+dle{v}_1}{2},V_{TH12}=\frac{dle{v}_1+dle{v}_2}{2},V_{TH23}=\frac{dle{v}_2+dle{v}_3}{2}& \left[\mathrm{Equation}2\right]\end{array}$

(162) Thereafter, as shown in FIG. 11B, the equalization parameter is adaptively adjusted according to the signals EQ_AC[N.sub.AC−1:0] and EQ_DC[N.sub.DC−1:0] generated in the step S240 (S260).

(163) The step S260 will be described in detail with reference to FIG. 13B.

(164) Referring to FIG. 13B, the plurality of capacitors C.sub.unit included in the CTLE 1100 are selectively turned on using the signal EQ_AC[N.sub.AC−1:0] generated in the step S240 to adjust the high frequency amplification gain of the CTLE 1100 (S260a).

(165) Thereafter, the plurality of resistors R.sub.unit included in the CTLE 1100 are selectively turn on using the signal EQ_DC[N.sub.DC−1:0] generated in step S240 to adjust the low frequency amplification gain of the CTLE 1100 (S260b).

(166) Thereafter, it is determined whether the high frequency amplification gain of the CTLE 1100 is at its maximum (S260c). The reason for determining whether the high frequency amplification gain is at its maximum is to determine whether the lower limit dlev.sub.0L is excessively low. For example, when the first voltage level of the signal CTLE_out is higher than the lower limit dlev.sub.0L even with the high frequency amplification gain at its maximum by turning on entirety of N.sub.AC capacitors C.sub.unit, the lower limit dlev.sub.0L must be elevated as the high frequency amplification gain cannot be increased any further. Therefore, it is necessary to determine whether the high frequency amplification gain is at its maximum.

(167) When the high frequency amplification gain is not at its maximum (“N” in step S260c), the step S260 ends since the high frequency amplification gain can be further increased if necessary.

(168) On the other hand, when the high frequency amplification gain is at its maximum (“Y” in step S260c), it is determined that which one of the first voltage level of the signal CTLE_out and the lower limit dlev.sub.0L is higher (S260d).

(169) When the first voltage level of the signal CTLE_out is higher than the lower limit dlev.sub.0L even with the high frequency amplification gain at its maximum (“Y” in step S260d), the lower limit dlev.sub.0L and the upper limit dlev.sub.0H are elevated as the high frequency amplification gain cannot be increased any further (S260e).

(170) When the first voltage level of the signal CTLE_out is lower than or equal to the lower limit dlev.sub.0L (“N” in step S260d), the step S260 ends.

(171) The steps S260c through S260e for elevating the lower limit dlev.sub.0L and the upper limit dlev.sub.0H may be performed when the steps S200 through S270 shown in FIG. 11B are repeatedly performed.

(172) For example, when the first voltage level of the signal CTLE_out obtained from the (k+1).sup.th first training data pattern (where k is a natural number equal to or greater than 2) is not as low as the lower limit dlev.sub.0L although the high frequency amplification gain was adjusted to its maximum due to the insufficient first voltage level of the signal CTLE_out obtained from the k.sup.th first training data pattern, the controller 1500 may elevate both of the lower limit dlev.sub.0L and the upper limit dlev.sub.0H instead of adjusting the high frequency amplification gain. That is, after elevating the lower limit dlev.sub.0L and the upper limit dlev.sub.0H until the first voltage level of the signal CTLE_out is between the lower limit dlev.sub.0L and upper limit dlev.sub.0H, the high frequency amplification gain may then be tuned.

(173) Thereafter, as shown in FIG. 11B, the sampling parameter of the sampler is adaptively adjusted according to the data levels dlev.sub.1 and dlev.sub.2, the lower limit dlev.sub.0L, the upper limit dlev.sub.0H and the threshold voltages V.sub.TH01, V.sub.TH12 and V.sub.TH23 generated in step S250 (S270).

(174) Thereafter, it is determined whether the value of the difference dlev.sub.0LD, the difference dlev.sub.0HD, the difference dlev.sub.1D or the difference dlev.sub.2D is zero (S280).

(175) Specifically, when the value of the difference dlev.sub.0LD, the difference dlev.sub.0HD, the difference dlev.sub.1D or the difference dlev.sub.2D is zero (“Y” in step S280), the method of training PAM4 receiver according to the first embodiment is ended. When the value of the difference dlev.sub.0LD, dlev.sub.0HD, dlev.sub.1D or dlev.sub.2D is not zero (“N” in step S280), the steps S200 through S270 are repeated until the difference dlev.sub.0LD, dlev.sub.0HD, dlev.sub.1D or dlev.sub.2D becomes zero.

(176) Here, it is not necessary that the values of the differences dlev.sub.0LD, dlev.sub.0HD, dlev.sub.1D and dlev.sub.2D be all zero. For example, the steps S200 through S270 may be repeated until the values of the differences dlev.sub.0LD and dlev.sub.0HD becomes all zero, until the value of the difference dlev.sub.0LD becomes zero, or until the values of the differences dlev.sub.0LD, dlev.sub.0HD, dlev.sub.1D, and dlev.sub.2D become all zero. In other words, it is possible to select conditions of the repetition as necessary.

(177) The repetition of the steps S200 through S270 means performing the steps S200 through S270 each time the same training pattern (e.g. the training pattern shown in FIG. 10B) is received.

(178) The reason for repeating the steps S200 through S270 is to achieve the goal which is to make the first voltage level of the signal CTLE_out equal to the lower limit dlev.sub.0L and the second voltage level of the signal CTLE_out equal to the upper limit dlev.sub.0H.

(179) In order to achieve this, the high frequency amplification gain and the low frequency amplification gain must be adjusted such that the values of the differences dlev.sub.0LD, dlev.sub.0HD, dlev.sub.1D and dlev.sub.2D become zero or converge to zero. Specifically, since the voltage levels of the signal CTLE_out approaches the lower limit dlev.sub.0L and upper limit dlev.sub.0H each time the steps S200 through S270 is performed by adjusting the high frequency amplification gain and the low frequency amplification gain, the values of the differences dlev.sub.0LD, dlev.sub.0HD, dlev.sub.1D and dlev.sub.2D become zero or converge to zero as the steps S200 through S270 are repeated.

(180) For example, after the tuning of the high frequency amplification gain and the low frequency amplification gain using a j.sup.th training pattern (where j is a natural number) is complete, a (j+1).sup.th training pattern, which is the same as the j.sup.th training pattern, is received and used to tune the high frequency amplification gain and the low frequency amplification gain by repeating the same process as described above.

(181) Specifically, the sampler 1200c samples the difference dlev.sub.0LD between: the first voltage level of the signal CTLE_out corresponding to the data “00” of the (j+1).sup.th first training data pattern when the transition from the data “11” to the first data “00” occurs; and the lower limit dlev.sub.0L. Since the signal CTLE_out is the output of CTLE 1100 already trained using the j.sup.th first training data pattern, the difference dlev.sub.0LD between: the first voltage level of the signal CTLE_out obtained from the (j+1).sup.th first training data pattern; and the lower limit dlev.sub.0L is smaller than the difference dlev.sub.0LD between: the first voltage level of the signal CTLE_out obtained from the j.sup.th first training data pattern; and the lower limit dlev.sub.0L. Accordingly, the high frequency amplification gain of the CTLE 1100 may be fine-tuned by a more precise signal EQ_AC[N.sub.AC−1:0] generated by the controller 1500.

(182) Similarly, the difference dlev.sub.0HD obtained from the (j+1).sup.th first training data pattern is smaller than the difference dlev.sub.0HD obtained from the j.sup.th first training data pattern. Accordingly, the low frequency amplification gain of the CTLE 1100 may be fine-tuned by a more precise signal EQ_DC[N.sub.DC−1:0] generated by the controller 1500.

(183) In addition, since the differences dlev.sub.1D and dlev.sub.2D obtained from the (j+1).sup.th second training data pattern are smaller than the differences dlev.sub.1D and dlev.sub.2D obtained from the j.sup.th second training data pattern, more precise data levels dlev.sub.1 and dlev.sub.2 may be obtained.

(184) As described above, when the PAM4 receiver is trained by repeatedly receiving the same training pattern until the differences dlev.sub.0LD, dlev.sub.0HD, dlev.sub.1D and dlev.sub.2D become zero or converge to zero, the PAM4 signal received during the actual use of the PAM4 receiver may be precisely determined despite the attenuation of the transmission line.

(185) The PAM4 receiver and the method for training the same according to the present invention has the following advantages.

(186) (1) The PAM4 receiver and the method for training the same according to the present invention are advantageous in that accurate data reception is achieved by adaptively tuning the PAM4 receiver using the training pattern.

(187) (2) The PAM4 receiver and the method for training the same according to the present invention are advantageous in that long-distance, high-speed communication may be achieved.