# Patent

## Title
Multi-phase phase interpolator

## Abstract

A multi-phase phase interpolator receives two input clocks to generate several equally spaced output clocks using several phase interpolators. A phase interpolator may include a first circuit branch and a second circuit branch with output nodes that are connected together to provide an output clock. The output clock may be generated at least based on resistor values of the phase interpolator.

## Background
CROSS-REFERENCE TO RELATED APPLICATION
This application claims the benefit of U.S. Provisional Application No. 61/043,128, filed on Apr. 8, 2008, which is incorporated herein by reference in its entirety.


BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates generally to electrical circuits, and more particularly but not exclusively to phase interpolators.
2. Description of the Background Art
Phase interpolators are widely used to generate a plurality of multi-phase clocks from two clock sources. An ideal multi-phase phase interpolator 100 is shown FIG. 1. The phase interpolator 100 receives two input clocks c1 and c2 and generates (m+1) output clocks, which in FIG. 1 comprise output clocks p0 to pm.
FIG. 2 shows the waveforms for input clocks c1 and c2 and output clocks p0 to pm of the ideal phase interpolator 100. As shown in FIG. 2, the time spacing between the input clocks c1 and c2 is equal to A. In other words, input clock c2 has the same waveform as the input clock c1 except delayed by an amount Δ. The output clock p0 and pm are simply from delaying inverted clocks c1 and c2, respectively, by a specific amount δ. That is, the output clock p0 is the input clock c1 inverted and delayed by an amount δ, and the output clock pm is the input clock c2 inverted and delayed by an amount δ. The other output clocks, i.e., output clocks p1 to Pm-1, are generated by interpolating clocks c1 and c2, and are equally spaced between p0 and pm. With (m+1) output clocks, the time spacing between any two neighboring output clocks is equal to Δ/m, which represents 1 least significant bit (LSB).
SUMMARY
In an embodiment, an (m+1)-phase phase interpolator receives a first input clock and a second input clock to generate (m+1) equally spaced output clocks. The first input clock leads the second input clock by an amount Δ. The generated (m+1) output clocks comprise a plurality of signals of the same waveform but uniformly displaced in time with a spacing of Δ/m. The (m+1)-phase phase interpolator comprises (m+1) voltage-mode phase interpolators. A first voltage-mode phase interpolator receives only the first input clock to generate a first output clock comprising the first input clock inverted and delayed by an amount δ. The (m+1)-th voltage-mode phase interpolator receives only the second input clock to generate the (m+1)-th output clock comprising the second input clock inverted and delayed by an amount δ. The other voltage-mode phase interpolators receive both the first and second input clocks to generate other output clocks interpolated from the first and second input clocks.
In an embodiment, a single-ended voltage-mode phase interpolator receives a first input clock and a second input clock to generate equally spaced output clocks. The first input clock leads the second clock by an amount Δ. The single-ended voltage-mode phase interpolator comprises two circuit branches: the first input clock controls the first circuit branch and the second input clock controls the second circuit branch. The output nodes of the first and second circuit branches are connected together. Each circuit branch comprises two sub-branches: one sub-branch is from the positive power supply to the output node, and the other sub-branch is from the negative power supply to the output node. Each sub-branch comprises a resistor and a switch. When the switch in a sub-branch is turned ON, current flows between the two terminals of this sub-branch. Otherwise, no current flows between the two terminals of this sub-branch. It is noted that only one of the two switches in each branch will be turned ON at any time. In other words, in the first circuit branch, if the switch between the positive power supply and the output node is turned ON, the switch between the negative power supply and the output node is turned OFF. Conversely, if the switch between the positive power supply and the output node is turned OFF, the switch between the negative power supply and the output node is turned ON.
In another embodiment, a differential voltage-mode phase interpolator receives a first differential pair of input clocks and a second differential pair of input clocks to generate differential pairs of output clocks. The first differential pair of input clocks leads the second differential pair of input clocks by an amount Δ. Each differential pair of input clocks comprises two complementary single-ended clocks. The differential voltage-mode phase interpolator comprises two disjoint parts. Each disjoint part processes single-ended input clock signals out of the differential input clock signals and comprises two circuit branches, with a single-ended input clock out of the first differential pair of input clocks controlling the first circuit branch and a single-ended input clock out of the second differential pair of input clocks controlling the second circuit branch. The output nodes of the first and second circuit branches are connected together. Each circuit branch comprises two sub-branches: one sub-branch is from the positive power supply to the output node, and the other sub-branch is from the negative power supply to the output node. Each sub-branch comprises a resistor and a switch. When the switch in a sub-branch is turned ON, current flows between the two terminals of this sub-branch. Otherwise, no current flows between the two terminals of this sub-branch. It is noted that only one of two switches in each branch will be turned ON at any time. In other words, in the first circuit branch, if the switch between the positive power supply and the output node is turned ON, the switch between the negative power supply and the output node is turned OFF. Conversely, if the switch between the positive power supply and the output node is turned OFF, the switch between the negative power supply and the output node is turned ON.
These and other features of the present invention will be readily apparent to persons of ordinary skill in the art upon reading the entirety of this disclosure, which includes the accompanying drawings and claims.



DESCRIPTION OF THE DRAWINGS
FIG. 1 shows a schematic diagram of an ideal multi-phase phase interpolator.
FIG. 2 shows waveforms of input clocks and output clocks of an ideal phase interpolator.
FIG. 3 shows a block diagram of a multi-phase phase interpolator in accordance with an embodiment of the present invention.
FIG. 4 shows a schematic diagram of a single-ended voltage-mode phase interpolator in accordance with an embodiment of the present invention.
FIG. 5 shows example waveforms of output clocks of a multi-phase phase interpolator in accordance with an embodiment of the present invention.
FIG. 6 shows the integral nonlinearity (INL) and differential nonlinearity (DNL) of each output clock in the example of FIG. 5.
FIG. 7 shows a schematic diagram of a differential voltage-mode phase interpolator in accordance with an embodiment of the present invention.
FIG. 8 shows a schematic diagram of a single-ended voltage-mode phase interpolator in accordance with an embodiment of the present invention.
FIG. 9 shows a schematic diagram of a differential voltage-mode phase interpolator in accordance with an embodiment of the present invention.
FIG. 10 shows example waveforms of output clocks of a multi-phase phase interpolator in accordance with an embodiment of the present invention.
FIG. 11 shows corresponding INL and DNL of the waveforms of FIG. 10.
FIG. 12 shows INL for three different scenarios.
FIG. 13 shows DNL for the scenarios of FIG. 12.
FIG. 14 shows a schematic diagram of a single-ended voltage-mode phase interpolator in accordance with an embodiment of the present invention.
FIG. 15 shows a schematic diagram of a differential voltage-mode phase interpolator in accordance with an embodiment of the present invention.
FIG. 16 shows a schematic diagram of a circuit branch in accordance with an embodiment of the present invention.
FIG. 17 shows a schematic diagram of a circuit branch implemented using several identical circuit branches in accordance with an embodiment of the present invention.



The use of the same reference label in different drawings indicates the same or like components.
DETAILED DESCRIPTION
In the present disclosure, numerous specific details are provided, such as examples of circuits, components, and methods, to provide a thorough understanding of embodiments of the invention. Persons of ordinary skill in the art will recognize, however, that the invention can be practiced without one or more of the specific details. In other instances, well-known details are not shown or described to avoid obscuring aspects of the invention.
The present invention pertains to circuits and methods for generating equally spaced clocks. Embodiments of the present invention allow for phase interpolators with reduced integral nonlinearity (INL) and differential nonlinearity (DNL), and may employ static interpolation circuits to reduce standby power consumption.
Referring now to FIG. 3, there is shown a block diagram of a multi-phase phase interpolator 130 in accordance with an embodiment of the present invention. In the example of FIG. 3, the phase interpolator 130 receives two input clocks c1 and C2 to generate (m+1) equally spaced output clocks p0 to pm using (m+1) voltage-mode phase interpolators 131 (i.e., 131-0, 131-1, . . . 131-(m−1), 131-m). As a particular example, with m=3, the phase interpolator 130 will generate four (i.e., 3+1) output clocks p0 to p3 using four voltage-mode phase interpolators 131.
In the example of FIG. 3, each voltage-mode phase interpolator 131 is parameterized by a variable n. The first (i.e., n=0 or phase interpolator 131-0) and last (i.e., n=m or phase interpolator 131-m) interpolators function as delay elements. More specifically, the phase interpolator 131-0 generates the output clock PO by inverting and delaying the input clock c1 by an amount δ. Similarly, the phase interpolator 131-m generates the output clock pm by inverting and delaying the input clock C2 by an amount δ. The input clock c1 leads the input clock c2 by an amount Δ. As can be appreciated by those of ordinary skill in the art, the amounts Δ and δ may be in terms of phase (e.g., degrees) or time (e.g., seconds). As will be more apparent below, a voltage-mode phase interpolator 131 may be implemented as a single-ended or differential circuit.
In the example of FIG. 3, each phase interpolator 131 except the first and last ones (i.e., phase interpolators 131-0 and 131-m) receives both input clocks c1 and c2 to generate an interpolated output clock pn. More specifically, the phase interpolators 131-1 to 131-(m−1) generate output clocks p1 to pm-1, respectively, by interpolating the input clocks c1 and c2 such that the output clocks p0 to pm are equally spaced and have linearly distributed phases as in the timing diagram of FIG. 2. That is, the multi-phase phase interpolator 130 is configured to generate ideal waveforms as in FIG. 2 as much as practically possible.
FIG. 4 shows a schematic diagram of a single-ended voltage-mode phase interpolator 400 in accordance with an embodiment of the present invention. The phase interpolator 400 receives the two input clocks c1 and c2 to generate an output clock pn at a node 401. The single-ended voltage-mode phase interpolator 400 is a particular embodiment of a phase interpolator 131 shown in FIG. 3. That is, the phase interpolator 400 may be used as a phase interpolator 131 in the multi-phase phase interpolator 130.
In the example of FIG. 4, the phase interpolator 400 comprises a first circuit branch and a second circuit branch. The outputs of the first and second circuit branches are connected together at the node 401. The first circuit branch comprises a first sub-branch comprising a resistor R1 and a p-type metal oxide semiconductor (PMOS) transistor MP1 and a second sub-branch comprising an n-type metal oxide semiconductor (NMOS) transistor MN1 and a resistor R2. The second circuit branch comprises a first sub-branch comprising a resistor R3 and a PMOS transistor MP2 and a second sub-branch comprising an NMOS transistor MN2 and a resistor R4. Embodiments of the present invention are especially advantageous in phase interpolators comprising MOS transistors because of tendency of MOS transistors to introduce phase inaccuracy. The resistors R1, R2, R3, and R4 may be configured to generate a particular output clock pn.
In the example of FIG. 4, the input clock c1 is connected to the gates of the PMOS transistor MP1 and NMOS transistor MN1 to control the first circuit branch. Similarly, the input clock c2 is connected to the gates of the PMOS transistor MP2 and NMOS transistor MN2 to control the second circuit branch.
In the example of FIG. 4, PMOS transistors MP1 and MP2 are ON and OFF when their respective control input is a logical LOW (zero) and a logical HIGH (one), respectively. On the other hand, NMOS transistors MN1 and MN2 are ON and OFF when their respective control input is a logical HIGH (one) and a logical LOW (zero), respectively. Transistors MP1, MP2, MN1 and MN2 serve as ideal switches. The positive and negative supply voltages are arbitrarily set to V and zero volts, respectively, in this case. The initial output voltage of any voltage-mode phase interpolator is set to zero and the associated loading at the output load is equal to a capacitance C. Assume that input clocks c1 and c2 are switching from HIGH to LOW at time instants of 0 and Δ, respectively. In that case, the switch MP1 is turned ON and the switch MN1 is turned OFF at time instant of 0. Subsequently, the switch MP2 is turned ON and the switch MN2 is turned OFF at time instant of Δ.
The resistors R1 to R4 are selected based on the number of phases and the position of the interpolator 400 in the multi-phase interpolator 130 (see FIG. 3). The resistors R1 to R4 advantageously allow for improved linearity. In the example of FIG. 4, the resistors R1 and R2 in the first circuit branch each has a value




  
    
      
        R
        ⁢
        
          m
          
            (
            
              m
              -
              n
            
            )
          
        
      
    
    
      
        (
        
          EQ
          .
          
            
          
          ⁢
          1
        
        )
      
    
  




and the resistors R3 and R4 in the second circuit branch each has a value





  
    
      
        R
        ⁢
        
          m
          n
        
      
    
    
      
        (
        
          EQ
          .
          
            
          
          ⁢
          2
        
        )
      
    
  




where R is a constant resistance value. As explained, the phase interpolator 130 has (m+1) phases. For example, for a 5-phase interpolator 130, m=4 for all phase interpolators 400, n=0 for the first phase interpolator 400, n=1 for the second phase interpolator 400, n=2 for the third phase interpolator 400, and so on.

For the first voltage-mode phase interpolator (i.e., n=0), the output voltage V0(t) of the phase interpolator 400 may be represented as

V(1−e−t/τ0) where τ0=RC for t≧0  (EQ. 3)

Assume that the threshold voltage of succeeding circuits following the phase interpolator is equal to V/2. V0(t) crosses over the threshold voltage at time instant of t0=τ0·ln(2). For the phase interpolator 400 parameterized from n=1 to n=(m−1), the output voltage Vn(t) is equal to




  
    
      
        
          V
          ⁢
          
            
              m
              -
              n
            
            m
          
          ⁢
          
            (
            
              1
              -
              
                e
                
                  
                    -
                    t
                  
                  /
                  
                    τ
                    0
                  
                
              
            
            )
          
          ⁢
          
            
          
          ⁢
          for
          ⁢
          
            
          
          ⁢
          t
        
        <
        
          Δ
          ⁢
          
            
          
          ⁢
          and
        
      
    
    
      
        (
        
          EQ
          .
          
            
          
          ⁢
          4
        
        )
      
    
  
  
    
      
        
          
            V
            ⁡
            
              [
              
                1
                -
                
                  
                    n
                    m
                  
                  ⁢
                  
                    e
                    
                      
                        -
                        
                          (
                          
                            t
                            -
                            Δ
                          
                          )
                        
                      
                      /
                      
                        τ
                        0
                      
                    
                  
                
                -
                
                  
                    
                      m
                      -
                      n
                    
                    m
                  
                  ⁢
                  
                    e
                    
                      
                        -
                        t
                      
                      /
                      
                        τ
                        0
                      
                    
                  
                
              
              ]
            
          
          ⁢
          
            
          
          ⁢
          for
          ⁢
          
            
          
          ⁢
          t
        
        ≥
        
          Δ
          .
        
      
    
    
      
        (
        
          EQ
          .
          
            
          
          ⁢
          5
        
        )
      
    
  




The time instant tn at which Vn(t) crosses over the threshold voltage of V/2 can be calculated accordingly. Although a closed-form solution does not exist, a first-order approximation gives the following result:




  
    
      
        
          t
          n
        
        =
        
          
            τ
            o
          
          ·
          
            [
            
              
                ln
                ⁡
                
                  (
                  2
                  )
                
              
              +
              
                
                  n
                  m
                
                ⁢
                
                  Δ
                  
                    τ
                    o
                  
                
              
              +
              
                
                  
                    
                      (
                      
                        m
                        -
                        n
                      
                      )
                    
                    ⁢
                    n
                  
                  
                    2
                    ⁢
                    
                      
                    
                    ⁢
                    
                      m
                      2
                    
                  
                
                ⁢
                
                  
                    (
                    
                      Δ
                      
                        τ
                        o
                      
                    
                    )
                  
                  2
                
              
            
            ]
          
        
      
    
    
      
        (
        
          EQ
          .
          
            
          
          ⁢
          6
        
        )
      
    
  




The output voltage Vm(t) of the last phase interpolator is the time-shift of the waveform V0(t) by Δ. Therefore, tm is equal τ0·ln(2)+Δ. The integral nonlinearity (INL) and differential nonlinearity (DNL) of the n-th output clock pn are represented with respect to one LSB and defined as follows:




  
    
      
        
          I
          ⁢
          
            
          
          ⁢
          N
          ⁢
          
            
          
          ⁢
          
            L
            n
          
        
        =
        
          
            (
            
              
                t
                n
              
              -
              
                t
                o
              
              -
              
                
                  Δ
                  /
                  m
                
                ·
                n
              
            
            )
          
          
            Δ
            /
            m
          
        
      
    
    
      
        (
        
          EQ
          .
          
            
          
          ⁢
          7
        
        )
      
    
  
  
    
      
        
          D
          ⁢
          
            
          
          ⁢
          N
          ⁢
          
            
          
          ⁢
          
            L
            n
          
        
        =
        
          
            (
            
              
                t
                n
              
              -
              
                t
                
                  n
                  -
                  1
                
              
              -
              
                Δ
                /
                m
              
            
            )
          
          
            Δ
            /
            m
          
        
      
    
    
      
        (
        
          EQ
          .
          
            
          
          ⁢
          8
        
        )
      
    
  




For a first-order approximation, the INL and DNL for the phase interpolator 400 may be calculated as follows:




  
    
      
        
          I
          ⁢
          
            
          
          ⁢
          N
          ⁢
          
            
          
          ⁢
          
            L
            n
          
        
        =
        
          
            
              
                (
                
                  m
                  -
                  n
                
                )
              
              ⁢
              n
            
            
              2
              ⁢
              
                
              
              ⁢
              m
            
          
          ⁢
          
            Δ
            
              τ
              o
            
          
        
      
    
    
      
        (
        
          EQ
          .
          
            
          
          ⁢
          9
        
        )
      
    
  
  
    
      
        
          D
          ⁢
          
            
          
          ⁢
          N
          ⁢
          
            
          
          ⁢
          
            L
            n
          
        
        =
        
          
            
              (
              
                m
                -
                
                  2
                  ⁢
                  
                    
                  
                  ⁢
                  n
                
                +
                1
              
              )
            
            
              2
              ⁢
              
                
              
              ⁢
              m
            
          
          ⁢
          
            Δ
            
              τ
              o
            
          
        
      
    
    
      
        (
        
          EQ
          .
          
            
          
          ⁢
          10
        
        )
      
    
  




FIG. 5 shows example waveforms of output clocks of a multi-phase phase interpolator in accordance with an embodiment of the present invention. The vertical axis represents voltage, while the horizontal axis represents time. The waveforms of FIG. 5 are from a multi-phase phase interpolator 130 with 9 single-ended voltage-mode phase interpolators 400. The waveforms, from left to right, are output clocks of phase interpolators for n=0, n=1, . . . , n=7, and n=8. In the example of FIG. 5, Δ is 20 ps and τ0 is 40 ps.
FIG. 6 shows the INL and DNL of each output clock in the example of FIG. 5. In FIG. 6, the top plot is for the INL, and the bottom plot is for the DNL. The vertical axis represents LSB, and the horizontal axis represents phase. As can be seen from FIG. 6, the INL has its largest error at the center phase whereas the DNL has its largest errors at the boundary phases.
FIG. 7 shows a schematic diagram of a differential voltage-mode phase interpolator 500 in accordance with an embodiment of the present invention. The phase interpolator 500 receives two differential input clocks c1 and c2 to generate a differential output clock pn across nodes 501 and 502. The different input clock c1 comprises a pair of single-ended complementary input clocks c1(+) and c1(−). Similarly, the different input clock c2 comprises a pair of single-ended complementary input clocks c2(+) and c2(−). The differential voltage-mode phase interpolator 500 is a particular embodiment of a phase interpolator 131 shown in FIG. 3. That is, the phase interpolator 500 may be used as a phase interpolator 131 in the multi-phase phase interpolator 130.
The phase interpolator 500 is a differential version of the phase interpolator 400 of FIG. 4. Accordingly, the equations derived for the phase interpolator 400 also apply to the phase interpolator 500.
In the example of FIG. 7, the phase interpolator 500 comprises two disjoint parts. The first disjoint part comprises resistors R1, R2, R3, and R4, PMOS transistors MP1 and MP2, and NMOS transistors MN1 and MN2. The second disjoint part comprises resistors R5, R6, R7, and R8, PMOS transistors MP3 and MP4, and NMOS transistors MN3 and MN4. Note that each disjoint part is essentially a single-ended voltage-mode phase interpolator 400. The analysis with regards to the circuit branches and sub-branches of each circuit branch in each disjoint part is thus the same as in the phase interpolator 400. It also follows that the values of resistors R1, R2, R5, and R6 are selected in accordance with EQ. 1, and the values of resistors R3, R4, R7, and R8 are selected in accordance with EQ. 2. The output nodes of the disjoint parts are connected together to provide a differential output clock pn, which comprises a single-ended output clock pn(+) at a node 501 and a single-ended output clock pn(−) at a node 502.
In order to reduce INL and DNL, different RC constants τn can be assigned to each voltage-mode phase interpolator. This aspect of the present invention is now explained beginning with FIG. 8.
FIG. 8 shows a schematic diagram of a single-ended voltage-mode phase interpolator 400A in accordance with an embodiment of the present invention. The phase interpolator 400A may be employed as a phase interpolator 131 in the multi-phase interpolator 130. The phase interpolator 400A is a particular embodiment of the phase interpolator 400 of FIG. 4. The phase interpolator 400A is the same as the phase interpolator 400 except that the phase interpolator 400A has different resistance values.
FIG. 9 shows a schematic diagram of a differential voltage-mode phase interpolator 500A in accordance with an embodiment of the present invention. The phase interpolator 500A may be employed as a phase interpolator 131 in the multi-phase interpolator 130. The phase interpolator 500A is a particular embodiment of the phase interpolator 500 of FIG. 7. The phase interpolator 500A is the same as the phase interpolator 500 except that the phase interpolator 500A has different resistance values.
In the embodiments of FIGS. 8 and 9, the resistance of a voltage-mode phase interpolator is multiplied with an error correction term en to adjust its value. In doing so, the RC constants τn of each voltage-mode phase interpolator can be changed individually. Similarly, if the resistance values remain unchanged, the capacitance loading of each phase interpolator can be multiplied with the same error correction term en to adjust the time constant.
For a time constant τn, the time instant tn at which Vn(t) crosses over the threshold voltage of V/2 can be calculated. Although a closed-form solution does not exist, a first-order approximation gives the following:




  
    
      
        
          
            t
            n
          
          =
          
            
              τ
              n
            
            ·
            
              [
              
                
                  ln
                  ⁡
                  
                    (
                    2
                    )
                  
                
                +
                
                  
                    n
                    m
                  
                  ·
                  
                    Δ
                    
                      τ
                      n
                    
                  
                
                +
                
                  
                    
                      
                        (
                        
                          m
                          -
                          n
                        
                        )
                      
                      ⁢
                      n
                    
                    
                      2
                      ⁢
                      
                        
                      
                      ⁢
                      
                        m
                        2
                      
                    
                  
                  ⁢
                  
                    
                      (
                      
                        Δ
                        
                          τ
                          n
                        
                      
                      )
                    
                    2
                  
                
              
              ]
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            where
            ⁢
            
              
            
            ⁢
            
              τ
              n
            
          
          =
          
            
              e
              n
            
            ⁢
            RC
          
        
      
    
    
      
        (
        
          EQ
          .
          
            
          
          ⁢
          11
        
        )
      
    
  




In order to reduce INL and DNL, the INL of each phase interpolator is set to zero and the required τn can then be calculated. A closed form solution cannot be derived. However, a first-order approximation of the required τn gives the following result:




  
    
      
        
          τ
          n
        
        =
        
          
            τ
            0
          
          ⁡
          
            [
            
              1
              -
              
                
                  
                    
                      (
                      
                        m
                        -
                        n
                      
                      )
                    
                    ⁢
                    n
                  
                  
                    2
                    ⁢
                    
                      
                    
                    ⁢
                    
                      ln
                      ⁡
                      
                        (
                        2
                        )
                      
                    
                    ⁢
                    
                      m
                      2
                    
                  
                
                ⁢
                
                  
                    (
                    
                      Δ
                      
                        τ
                        0
                      
                    
                    )
                  
                  2
                
              
            
            ]
          
        
      
    
    
      
        (
        
          EQ
          .
          
            
          
          ⁢
          12
        
        )
      
    
  




From EQ. 12, the error correction term en in the resistors shown in FIGS. 8 and 9 is then set to




  
    
      
        1
        -
        
          
            
              
                (
                
                  m
                  -
                  n
                
                )
              
              ⁢
              n
            
            
              2
              ⁢
              
                
              
              ⁢
              
                ln
                ⁡
                
                  (
                  2
                  )
                
              
              ⁢
              
                m
                2
              
            
          
          ⁢
          
            
              (
              
                Δ
                
                  τ
                  0
                
              
              )
            
            2
          
        
      
    
    
      
        (
        
          EQ
          .
          
            
          
          ⁢
          13
        
        )
      
    
  




The effective resistance at each phase interpolator is changed accordingly. More specifically, in phase interpolators 400A and 500A, resistors R1, R2, R5, and R6 each has a value




  
    
      
        
          e
          n
        
        ⁢
        R
        ⁢
        
          m
          
            (
            
              m
              -
              n
            
            )
          
        
      
    
    
      
        (
        
          EQ
          .
          
            
          
          ⁢
          14
        
        )
      
    
  




and the resistors R3, R4, R7, and R8 each has a value





  
    
      
        
          e
          n
        
        ⁢
        R
        ⁢
        
          m
          n
        
      
    
    
      
        (
        
          EQ
          .
          
            
          
          ⁢
          15
        
        )
      
    
  




where en is the error correction term given by EQ. 13. Note that EQ. 14 is EQ. 1 multiplied by the error correction term en, and EQ. 15 is EQ. 2 multiplied by the error correction term en.

FIG. 10 shows example waveforms of output clocks of a multi-phase phase interpolator in accordance with an embodiment of the present invention. The vertical axis represents voltage, while the horizontal axis represents time. The waveforms of FIG. 10 are from a multi-phase phase interpolator 130 with 9 single-ended voltage-mode phase interpolators 400A. A first-order error correction en (see EQ. 13) is applied to the resistance values of the phase interpolators 400A.
In FIG. 10, the waveforms, from left to right, are output clocks of phase interpolators 400A for n=0, n=1, . . . , n=7, and n=8. The corresponding INL (plot 491) and DNL (plot 492) plots are shown in FIG. 11. The vertical axis represents LSB, and the horizontal axis represents phase.
Using computer simulations, an exact value of τn that gives zero INL can be calculated. FIG. 12 shows the INL for three different scenarios of “no error correction” (plot 551), “first-order error correction” (plot 552), and “exact error correction” (plot 553). FIG. 13 shows the DNL for three different scenarios of “no error correction” (plot 561), “first-order error correction” (plot 562), and “exact error correction” (plot 533). The values of error correction term en for these three scenarios are shown in Table 1.











TABLE 1







No Correction
First-Order Correction
Exact Correction



















e0
1
1
1


e1
1
0.9803
0.9771


e2
1
0.9662
0.9620


e3
1
0.9577
0.9542


e4
1
0.9549
0.9532


e5
1
0.9577
0.9582


e6
1
0.9662
0.9681


e7
1
0.9803
0.9823


e8
1
1
1









FIG. 14 shows a schematic diagram of a single-ended voltage-mode phase interpolator 400B in accordance with an embodiment of the present invention. The phase interpolator 400B may be employed as a phase interpolator 131 in the multi-phase interpolator 130. The phase interpolator 400B is a particular embodiment of the phase interpolator 400 of FIG. 4. The phase interpolator 400B is the same as the phase interpolator 400 except that the phase interpolator 400B has different resistance values.
FIG. 15 shows a schematic diagram of a differential voltage-mode phase interpolator 500B in accordance with an embodiment of the present invention. The phase interpolator 500B may be employed as a phase interpolator 131 in the multi-phase interpolator 130. The phase interpolator 500B is a particular embodiment of the phase interpolator 500 of FIG. 7. The phase interpolator 500B is the same as the phase interpolator 500 except that the phase interpolator 500B has different resistance values.
In the embodiments of FIGS. 14 and 15, different RC time constants are assigned to the first and second circuit branches whereas their total RC time constant is kept the same. In these embodiments, the resistors in the first and second circuit branches are multiplied by an error correction term een and ean, respectively, to adjust its value. More specifically, in FIGS. 14 and 15, the resistors R1, R2, R5, and R6 are multiplied by an error correction term een, while the resistors R3, R4, R7, and R8 are multiplied by an error correction term ean so that the RC constants of the circuit branches in each phase interpolator can be changed individually. If the total RC time constant is set to τ0, where τ0=RC, this constraint can be written as:




  
    
      
        1
        =
        
          
            
              n
              ⁡
              
                (
                
                  m
                  -
                  n
                
                )
              
            
            ⁢
            
              e
              en
            
            ⁢
            
              e
              an
            
          
          
            
              n
              ·
              
                e
                en
              
            
            +
            
              
                (
                
                  m
                  -
                  n
                
                )
              
              ⁢
              
                e
                an
              
            
          
        
      
    
    
      
        (
        
          EQ
          .
          
            
          
          ⁢
          16
        
        )
      
    
  




For the phase interpolator 400B or 500B parameterized from n=1 to n=m−1, its output voltage Vn(t) is equal to




  
    
      
        
          V
          ⁢
          
            
              
                (
                
                  m
                  -
                  n
                
                )
              
              ⁢
              
                e
                an
              
            
            
              
                n
                ·
                
                  e
                  en
                
              
              +
              
                
                  (
                  
                    m
                    -
                    n
                  
                  )
                
                ⁢
                
                  e
                  an
                
              
            
          
          ⁢
          
            (
            
              1
              -
              
                e
                
                  
                    -
                    t
                  
                  /
                  
                    τ
                    0
                  
                
              
            
            )
          
          ⁢
          
            
          
          ⁢
          for
          ⁢
          
            
          
          ⁢
          t
        
        <
        
          Δ
          ⁢
          
            
          
          ⁢
          and
        
      
    
    
      
        (
        
          EQ
          .
          
            
          
          ⁢
          17
        
        )
      
    
  
  
    
      
        
          
            V
            ⁡
            
              [
              
                
                  
                    
                      1
                      -
                      
                        
                          
                            n
                            ·
                            
                              e
                              en
                            
                          
                          
                            
                              n
                              ·
                              
                                e
                                en
                              
                            
                            +
                            
                              
                                (
                                
                                  m
                                  -
                                  n
                                
                                )
                              
                              ⁢
                              
                                e
                                an
                              
                            
                          
                        
                        ⁢
                        
                          e
                          
                            
                              -
                              
                                (
                                
                                  t
                                  -
                                  Δ
                                
                                )
                              
                            
                            /
                            
                              τ
                              0
                            
                          
                        
                      
                      -
                    
                  
                
                
                  
                    
                      
                        
                          
                            (
                            
                              m
                              -
                              n
                            
                            )
                          
                          ⁢
                          
                            e
                            an
                          
                        
                        
                          
                            n
                            ·
                            
                              e
                              en
                            
                          
                          +
                          
                            
                              (
                              
                                m
                                -
                                n
                              
                              )
                            
                            ⁢
                            
                              e
                              an
                            
                          
                        
                      
                      ⁢
                      
                        e
                        
                          
                            -
                            t
                          
                          /
                          
                            τ
                            0
                          
                        
                      
                    
                  
                
              
              ]
            
          
          ⁢
          
            
          
          ⁢
          for
          ⁢
          
            
          
          ⁢
          t
        
        ≥
        Δ
      
    
    
      
        (
        
          EQ
          .
          
            
          
          ⁢
          18
        
        )
      
    
  




For each voltage-mode phase interpolator, the time instant tn at which Vn(t) crosses over the threshold voltage of V/2 can be calculated. In order to reduce INL and DNL, the INL of each phase interpolator is set to zero and the required een and ean are calculated. The values of een and ean to achieve exact cancellations are shown in Table 2.









TABLE 2





n
een
ean

















0
1
1


1
0.9716
1.2573


2
0.9437
1.2180


3
0.9163
1.1796


4
0.8894
1.1420


5
0.8630
1.1053


6
0.8371
1.0693


7
0.8118
1.0343


8
1
1









FIG. 16 shows a schematic diagram of a circuit branch 600 in accordance with an embodiment of the present invention. In the example of FIG. 16, the circuit branch 600 comprises a first sub-branch comprising a PMOS transistor MP and a resistor R20, and a second sub-branch comprising an NMOS transistor MN and a resistor R21. The circuit branch 600 may be employed as a circuit branch of the voltage-mode phase interpolators described above.
In the example of FIG. 16, the resistors R20 and R21 each has a value




  
    
      
        
          e
          k
        
        ⁢
        R
        ⁢
        
          m
          k
        
      
    
    
      
        (
        
          EQ
          .
          
            
          
          ⁢
          19
        
        )
      
    
  




In situations where the resistance value given by EQ. 19 is not readily available or implementable in an integrated circuit, an equivalent circuit branch can be implemented by shutting k identical circuit branches. This is shown in FIG. 17, where the circuit branch 600 is implemented using k identical circuit branches.
Improved multi-phase phase interpolators have been disclosed. While specific embodiments of the present invention have been provided, it is to be understood that these embodiments are for illustration purposes and not limiting. Many additional embodiments will be apparent to persons of ordinary skill in the art reading this disclosure.

## Claims

1. A multi-phase phase interpolator having a plurality of voltage-mode phase interpolators, the multi-phase interpolator receiving a first input clock and a second input clock to generate a plurality of equally spaced output clocks, the first input clock leading the second input clock, a first voltage-mode phase interpolator in the plurality of voltage-mode phase interpolators being configured to generate a first output clock in the plurality of output clocks, the first voltage-mode phase interpolator comprising:
a first circuit branch configured to be controlled by the first input clock, the first circuit branch comprising a first sub-branch and a second sub-branch, the first sub-branch of the first circuit branch comprising a first transistor in series with a first resistor, the second sub-branch of the first circuit branch comprising a second transistor in series with a second resistor, the first transistor and the second transistor being coupled to the first input clock such that the first transistor is ON when the second transistor is OFF and vice versa, the first sub-branch of the first circuit branch being configured such that current flows through the first resistor and the first transistor when the first transistor is ON, the second sub-branch of the first circuit branch being configured such that current flows through the second resistor and the second transistor when the second transistor is ON, a terminal of the first transistor and a terminal of the second transistor being coupled together to an output node of the first voltage-mode phase interpolator; and
a second circuit branch configured to be controlled by the second input clock, the second circuit branch comprising a first sub-branch and a second sub-branch, the first sub-branch of the second circuit branch comprising a third transistor in series with a third resistor, the second sub-branch of the second circuit branch comprising a fourth transistor in series with a fourth resistor, the third transistor and the fourth transistor being coupled to the second input clock such that the third transistor is ON when the fourth transistor is OFF and vice versa, the first sub-branch of the second circuit branch being configured such that current flows through the third resistor and the third transistor when the third transistor is ON, the second sub-branch of the second circuit branch being configured such that current flows through the fourth resistor and the fourth transistor when the fourth transistor is ON, a terminal of the third transistor and a terminal of the fourth transistor being coupled together to the output node of the first voltage-mode phase interpolator.

2. The multi-phase phase interpolator of claim 1 wherein the first input clock, the second input clock, and the plurality of output clocks comprise differential signals.

3. The multi-phase phase interpolator of claim 1 wherein the first input clock, the second input clock, and the plurality of output clocks comprise single-ended signals.

4. The multi-phase phase interpolator of claim 1 wherein the first and third transistor comprise PMOS transistors and the second and fourth transistors comprise NMOS transistors.

5. The multi-phase phase interpolator of claim 1 wherein the first sub-branch of the first circuit branch flows current from a positive power supply through the first resistor and the first transistor when the first transistor is ON.

6. The multi-phase phase interpolator of claim 1 wherein the first transistor comprises a PMOS transistor, the second transistor comprises an NMOS transistor, and the first input clock is coupled to a gate of the first transistor and a gate of the second transistor to control the first circuit branch.

7. The multi-phase phase interpolator of claim 6 wherein the third transistor comprises a PMOS transistor, the fourth transistor comprises an NMOS transistor, and the second input clock is coupled to a gate of the third transistor and a gate of the fourth transistor to control the second circuit branch.

8. The multi-phase phase interpolator of claim 1 wherein a second voltage-mode phase interpolator in the plurality of voltage-mode phase interpolators is configured as a delay element to generate a second output clock in the plurality of output clocks, the second output clock being the first input clock inverted and delayed by a first amount.

9. The multi-phase phase interpolator of claim 8 wherein a third voltage-mode phase interpolator in the plurality of voltage-mode phase interpolators is configured as a delay element to generate a third output clock in the plurality of output clocks, the third output clock being the second input clock inverted and delayed by a second amount.