Abstract:
A high-speed latch is disclosed that can function at high-speed input clocking frequencies. The active loads used within the latch design exhibit an input impedance that is inductive to the rest of the circuit to improve the driving capability of the overall latch in the presence of loading capacitances. The latch circuit, when used in a system or stand alone divider, will consume very low power while reducing the silicon die area. Possible applications include but are not limited to frequency dividing and counting applications. Of particular interest is the use of this high-speed latch in a prescaler divider as a part of a charge pump phase-locked loop design for single chip CMOS multi-band and multi-standard radio frequency transceiver integrated circuits.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims priority to U.S. Provisional Application Ser. No. 60/634,634, filed on Dec. 8, 2004. 
    
    
     TECHNICAL FIELD 
     The present disclosure relates to a low power CMOS latch that functions in a dual modulus prescaler as a high frequency divider that can be used in phase-locked loop (PLL) frequency synthesizers. The PLL application examples include but are not limited to radio frequency receivers and transmitters for all wireless communication standards including cellular 2G/2.5G/3G/4G and future generation wireless communications, optical fiber communications, network communications and storage systems. 
     BACKGROUND 
     The growing demand for wireless communications has motivated attempts to design radios that permit the integration of more components onto a single chip. The recent advances in CMOS semiconductor processing allow the integration of the radio receiver and transmitter into a single chip radio frequency (RF) transceiver to reduce cost, size and power consumption. 
     Phase-Locked Loop and Frequency Dividers 
     The Phase-locked loop (PLL) frequency synthesizer, one of the most important and challenging building blocks of the RF transceiver, is most suitable for the monolithic integration of wireless communication integrated circuits. The preferred application of the disclosed circuits is in the low cost integration of wireless communication integrated circuits using CMOS process technologies. However, the disclosed circuits can be implemented by one skilled in the state of the art using other process technologies such as bipolar, bipolar/CMOS (e.g. SiGe, Silicon Germanium), Gallium Arsenide (GaAs) and Silicon-on-Insulator (SOI). PLLs&#39; are used in but are not limited to wireless receivers and transmitters in part for frequency synthesis where a synthesized local oscillator (LO) frequency is needed to mix down the Receive Signal Carrier such that the modulated signal is down-converted and the resulting base-band signal can be processed. In wireless operation, the receive signal can operate in different bands or at discrete frequencies as part of the data transmission standard, an agile PLL frequency synthesizer is needed in order to track the receiver frequency by adjusting the LO frequency. 
     PLL frequency synthesizers perform frequency synthesis by changing a voltage-controlled oscillator (VCO) output clock signal&#39;s frequency in a precisely controlled manner using various methods. The output clock signal frequency can be controlled using a PLL as a control system. A charge pump PLL is comprised of a reference oscillator (usually crystal based), a phase-frequency detector (PFD), charge pump (operating in either voltage or current mode), a loop filter, a voltage-controlled oscillator (VCO), and a programmable feedback frequency divider. The programmable frequency divider can be composed of many design variations. Typically, high performance feedback divider designs use a front-end prescaler and a back-end programmable divider. The front-end prescaler is designed to operate at high speeds and the back-end programmable divider operates at lower speeds while extending the counting range over a wide range of values. Both dividers can interface together in different configurations so that the proper division value is achieved.  FIG. 1  shows a block diagram  100  of a frequency synthesizer design. In this design the front-end prescaler  110  divides down the high VCO frequency, Fvco, to an intermediate frequency, FH. This lower frequency is then used to clock the next divider chain (M divider  120 ) that can be programmed to different values to increase the total division value. 
     The PLL is typically able to synthesize frequencies with frequency steps equal to an integer multiple of the input reference frequencies. Typically, the PLL output clock signal is multiplied up in frequency from an input reference clock using a clock divider in the PLL feedback clock path. Clock multiplication is achieved when the controllable VCO clock signal is divided down and compared to the frequency reference input signal so that both signals have the exact frequency and proper phase alignment. Since the divided-down VCO signal is scaled down in frequency to match an input reference signal, the input reference frequency is said to be “multiplied up” to equal the VCO frequency. To adjust or tune the VCO output to another frequency, the feedback divider division modulus is changed. In many integer-M/N PLL applications, the feedback divider is capable of dividing by a fixed integer due to the fact that channel spacing is defined based upon the input reference frequency. Thus for an integer-M/N PLL synthesizer, clock multiplication and synthesis is achieved by changing the output clock frequency by an integer amount relative to the reference frequency input. Since the output clock signal of the VCO is equal to the integer (M/N) times the reference frequency, an integer adjustment to M (e.g. M+1) changes the output frequency by the same integer difference from the reference frequency (i.e. Δf=(M+1−M)*fref/N=fref/N). Thus, the channel spacing frequency is fixed and equal to the reference frequency divided by N. Fractional-N PLL synthesizers divide the VCO signal by a fractional amount using an integer feedback divider. Fractional division is achieved by dynamically modulating the division value so that the effective count length is of fractional length when averaged over an integer number of cycles of the input reference frequency. Fractional-N PLLs permit finer resolution of the output frequency changes which is very important when smaller channel spacing increments are required in a communication receiver with constrained input reference frequency. Sigma-Delta Modulation (SDM) PLLs are another example of combining modulation techniques to feedback counter divisions in a PLL control system to provide frequency synthesis and noise shaping improvements to the VCO output clock signal. There are many different PLL synthesizer design implementations that can be achieved using Integer-M/N, Fractional-N, Sigma-delta modulation, and hybrid combinations of all three. Thus, frequency synthesis can be achieved digitally by adjusting the counter division ratio in the PLL feedback loop. Due to the emphasis placed upon channel spacing, frequency acquisition, and phase noise in a PLL frequency synthesizer, the proper feedback divider implementation is crucial in achieving many PLL design parameters. 
     The fact that the VCO clock needs to be divided down to a lower frequency presents problems and trade-offs in the synthesizer design. Typically, to limit the power consumption in the overall PLL divider, a first stage divider, referred to as “prescaler” is used to initially divide the high frequency VCO clock signal down to an intermediate frequency level. Then use of a following second stage programmable circuit is clocked and divides at a secondary lower clocking speed. The reason for using two or more dividers is to relax the bandwidth and power requirements of the second feedback divider for large division modulus. Thus, only a small portion of the total divider circuitry needs to operate at high switching speeds. Note that for a given switching speed, the power consumption required is proportional to a given relationship. For CMOS circuitry that operates using the full-swing variation of its own power supply, the power required is proportional to the power supply voltage-squared (square law relationship). The majority of the power required for division is typically consumed in the front-end prescaler divider of the PLL frequency synthesizer. The prescaler can have either fixed or variable moduli for division. The choice of division values and programmability is part of the overall PLL synthesizer design and depends on the required frequency synthesis resolution in a particular application. 
     Prescalers are designed in various process technologies for different applications. A typical prescaler functioning as a high frequency divider in a large divider chain may be composed simply of a front-end fully differential divide-by-two functional block, a current-mode logic (CML) divider block and a CML-to-CMOS converter. In this typical application, all clocking signal amplitudes will be a combination of either fully differential analog or full-swing CMOS digital levels. The divider input signal from the VCO can be AC-coupled and then divided by two. Most of the power is consumed in the divide-by-two and CML divider blocks. 
     Due to the high frequencies involved, a technique called Shunt-Peaked amplification will be proposed in this disclosure for enhancing amplifier bandwidths. Optimized on-chip spiral inductors or transistors whose active port appears inductive can be used as the shunt-peaking elements. The attractive feature of this technique is that the bandwidth improvement requires no additional power and can in fact lower power dissipation depending on the process technology. When Shunt-Peaked amplification is designed into a CML type latch, the bandwidth extension and power dissipation benefits apply as they would in a more straight forward amplifier design. Due to the nature of the active inductive component tending to tune out the loading capacitance, a faster latch or combination flip-flop is achieved. This speed improvement is based upon decreased times needed for the setup and hold requirements. Based upon a more efficient latch structure, the geometries of the internal switching transistors in the latch can be scaled down based upon the reduction of required switching current for a given bandwidth. In addition, internal capacitive is reduced in the circuit due to active transistor well geometry reduction such that the individual dividers are operating faster by driving less parasitic loading capacitance. 
     Prescaler Designs 
     Prescalers used for clock division are used in PLL frequency synthesizers in many computer, consumer and communication applications. Prescalers can be designed to operate in CMOS, Bipolar-CMOS (Bi-CMOS), Gallium Arsenide (GaAs), Bipolar and other process technologies. Prescalers used as frequency dividers operate in voltage mode and are implemented in different ways with fully differential or single-ended signal designs. Within these two classifications, there are multiple design options with their own inherent benefits and flaws. The simplest prescaler design is the single-ended signal design where the division ratio is fixed and not programmable. A flip-flop circuit composed of two latch circuits, one master and one slave, can be used to reduce an input signal frequency by half and thereby accomplish a divide-by-two division function. Divide-by-two is defined to mean that one output clock period is produced for every two input clock periods. More complicated architectures permit variable division or counting by using digital control signals to change an input clock signal&#39;s different dividing paths. For example, one divide-path may require two input clock pulses to generate one output clock signal (e.g., divide-by-two). Digitally changing this clock division path may permit the divide-by-two circuit to ignore or “pulse swallow” an additional clock pulse such that three input clock pulses are needed to generate one output clock signal (e.g., divide-by-three). 
     High Frequency Dividers Used in Prescalers 
     Frequency division is typically done with master-slave flip-flops configured as a cascade connection of two latches in series. The maximum frequency allowable is limited by the time constants in the circuit consisting of gate delays (Td), capacitances and resistances in the circuit. Different frequency dividers have been proposed to improve the prescaler performance relating to PLL applications in frequency synthesizers. 
       FIG. 2  shows a widely used divide-by-two circuit  200  that consists of two latches in a master-slave configuration. This configuration is limited in function to just scaling down the input frequency and depending on the particular process technology, can only be used for relatively low input clock frequencies. Note, when using such a simple feedback divider in a PLL application, the frequency division resolution will be limited therefore the synthesizer channel spacing will be coarse. 
       FIG. 3  shows a similar divide-by-two circuit  300  where the input and output clocks are fully differential. The circuit block consists of a clock input stage  310  with level-shift, a master-slave D flip-flop (two latches  320 ,  330 ) and two output buffers  340 ,  350 . This divider design is useful for generating differential outputs that differ by 90 degrees (quadrature). VCO_I leads VCO_Q by 90 degrees. This differential design configuration can have a higher bandwidth than the divider shown in  FIG. 2  because the internal node voltage swings are lower in amplitude permitting internal voltage states to switch in a shorter time. 
     More complicated prescaler designs have been published and used in situations whereby the division rate or division modulus has to be controlled in real-time applications such as high performance PLL designs.  FIG. 4  shows a dual-modulus prescaler circuit design  400 . This architecture is a conventional divide-by-64/65 dual-modulus prescaler. The circuit block consists of two separate dividers, the top section divides by 4 or 5 and the bottom section divides by sixteen. By changing the polarity of the modulus control input  410 , the top feedback ring of 3 D-type flip-flops (dff)  415 ,  420 ,  425  will change the internal divide-by modulus of the Fin clock from 4 to 5 by pulse-swallowing one more period of the input clock. With both dividers working together, this circuit constitutes a conventional divide-by 64/65 dual-modulus prescaler. 
       FIG. 5  depicts another type of full-swing D-type flip-flop  500  that can be used in a frequency divider application. This flip-flop  500  is called a true single phase clock (TSPC) dynamic flip-flop. The dynamic core of the flip-flop  500  contains multiple transistors directly clocked at their inputs. Additionally, there are 3 transistors (M 1   505 , M 3   515  and M 5   525 ) with input data on their gates, 2 transistor gates (M 7 , M 9 ) connected to a pre-charged node, A, and 1 pre-charged node, B, with 3 transistors (M 2 , M 3  and M 5 ). Pre-charging of internal nodes based upon the state of the input clock leads to faster clocking and transferring of the input data. Due to the full swing voltage node switching, there would still be a maximum bandwidth limitation using this circuit as core cells in a design similar to  FIG. 4 . 
       FIG. 6 ,  FIG. 7 , and  FIG. 8  show fully differential sample-hold CML latches  600 ,  700 ,  800  where the load elements are either passive resistive, active or passive inductive. 
       FIG. 6  details a fully differential sample-hold CML latch  600  where the input data is sampled or latched (held) dependent on the state of the input clock. Two such circuits of this type can be used in series with local feedback to achieve a master-slave flip-flop divider circuit while  FIG. 3  is an example of two differential CML latches used as a frequency divider. The load elements  610 ,  615  in  FIG. 6  are shown to be resistive. For a monolithic circuit, conventional circuit techniques can be used to design the bias current reference-I  620  depicted in  FIG. 6 , such that it will vary inversely proportional to the resistor variation. For example, using a Poly resistor requires bias current inversely proportional to the Poly resistor variation. This will limit the voltage swing across the resistor to a constant value over process variations. As a result, additional series circuits can reliably operate based upon the latch output voltages. Other load elements as part of a latch can be used such as an active PMOS transistor biased in the triode region, passive inductor and an active inductor. 
       FIG. 7  shows a design similar to  FIG. 6  where the load elements are active PMOS transistor loads  720 ,  725  with the transistor gates biased from a separate replica bias circuit  710 . The replica bias circuit  710  is used outside of the actual latch/flip-flop design to bias the gates of the active loads inside the latch circuit. The proper bias voltage developed in the replica bias circuit and applied to the gates of the active PMOS loads keeps the PMOS transistors in the triode region of operation to make reliable voltage swings. Parasitic capacitance is higher in this design than using pure resistive loading. 
       FIG. 8  shows a latch  800  or similar bi-stable circuit requiring a passive inductive load  810  used in critical noise applications. This approach will implement a shunt-peaked loading approach as discussed earlier. However depending on the process technology and frequencies involved, it may not be practical to get a tight, compact multiple cell layout with relatively big spiral inductor load elements due to the monolithic die area being too large. 
       FIG. 9  shows a circuit  900  of two DSTC, (Dynamic-Single-Transistor Clocked)n-latches that are used to construct a master-slave D-flip-flop. The cross-coupled PMOS transistor pairs M 3   910 , M 4   915  in each latch pair form a positive feedback loop that will hold the value of the latch at their common drain nodes after leaving the sample mode and entering the hold mode of operation. The loop gain of the cross-coupled PMOS load, as a part of the latch in the hold mode, must be greater than unity for latching action to be reliable. The overall latch design does reduce circuit complexity due to the fact that only one clock transistor, namely M 5   925  in each latch, is required to implement a flip-flop. However, because the output voltage of this latch is being developed across the gate-to-source of the PMOS transistors M 3   910 , M 4   915 , a larger output voltage swing will be necessary. The only way to control and lower this voltage level swing is to make the crossed-coupled PMOS transistor widths larger and thus add loading capacitance to the circuit. In addition, the full-swing output voltage signals used for clocking feedback may not be necessary to fully switch the input NMOS differential pairs, M 1   930  and M 2   935  of the latch circuit. The circuit of  FIG. 6  is preferred for higher bandwidth designs. 
     In  FIG. 10 , another circuit option for frequency division is shown. This divider circuit  1000  is similar in structure to a static frequency dual latch design in a divide-by-two configuration. This design contains two identical stages as does a typical dual latch D-type master-slave flip flop. The difference here is that the internal second stage cross-coupled latch transistors are not needed. The internal second stage (negative trans-conductance) adds capacitance and is not necessary at high frequencies. This design of this circuit operates like a four-stage ring oscillator. This circuit  1000  relies on internal nodal capacitance for memory storage (latching) and is used for very high frequencies. In fact, the frequency range for this circuit can be limited due to this reason. 
     The described techniques can provide an improved prescaler design for high performance Frequency Synthesizers. The application is intended for the very stringent design specifications of high integration RF receivers and/or transmitters requiring low cost, small size and low power. Though the application of the described techniques is intended for CMOS circuits, they can be applied to other technologies using BICMOS and Bipolar processes. In a common PLL architecture of a prescaler and a lower frequency divider driven by a VCO, the majority of the power consumption in the feedback divider is used in the prescaler in dividing the highest VCO frequency. This translates directly to the AC performance of the overall PLL control loop system. 
     The following lists some advantages that may be obtained with respect to previous prescaler dividers.
         1. Higher input frequency clock signals can be divided using lower power compared to the prior art prescaler divider designs and other types of divider designs.   2. The amplifier gain in the dividers is a ratio of transistor transconductances and track over temperature and manufacturing process variations.   3. Shunt peaked active inductive loads tune out a given circuits loading capacitance to achieve a higher bandwidth latch and overall divider capable of being clocked at higher frequencies.   4. Active monolithic area is far less than with spiral inductors to achieve a shunt-peaked effect.   5. The operating frequency range is not limited compared to other high speed designs which use internal nodal capacitance for latching.       

     Described below is a prescaler that functions as a high speed frequency divider in a frequency synthesizer. The following lists some design features of the prescaler described below.
         1. A fully differential latch using shunt peaked active loads with inductive behavior to partially tune out the loading capacitance to achieve a higher circuit bandwidth for a given power consumption.   2. The gain of the latch circuit is a ratio of transistor transconductances that enable the gain to be relatively constant over process and operating conditions.   3. Higher operating frequency for a given power consumption.   4. Reduced die size of the overall prescaler design due to the lower bias currents required.       

    
    
     
       DESCRIPTION OF DRAWINGS 
         FIG. 1  is a schematic of a PLL synthesizer with a feedback divider chain with a prescaler and secondary M divider to control the VCO output frequency and channel spacing. 
         FIG. 2  is a schematic of an example two latch master-slave flip-flop circuit that divides an input clock frequency by two. 
         FIG. 3  is a schematic of an example fully differential circuit using two latches that divide an input clock frequency by two. 
         FIG. 4  is a schematic of an example dual modulus prescaler divider that divides an input clock frequency by 64 or 65. 
         FIG. 5  is a schematic of an example single phase clock (TSPC) dynamic D-type flip-flop. 
         FIG. 6  is an schematic of an example fully differential sample-hold CML latch using resistive loads where the input data is sampled or latched dependent on the state of the input clock. 
         FIG. 7  is a schematic showing an example replica bias arrangement to use a PMOS transistor load as an active load in a sample-hold latch design. 
         FIG. 8  is a schematic of an example fully differential sample-hold latch using a passive inductor load where the input data is sampled or latched dependent on the state of the input clock. 
         FIG. 9  is a schematic of an example two-stage master-slave flip-flop using two Dynamic-Single-Transistor Clocked (DSTC)n-latches that reduce the number of clocking transistors and does not require bias current transistors. 
         FIG. 10  is a schematic of an example two-stage master-slave flip-flop that does not use latching transistors, but relies on internal nodal capacitance for memory storage. 
         FIG. 11  is an example circuit diagram of a dual modulus prescaler design that can divide an input clock frequency by eight or nine. 
         FIG. 12  is an example clock timing diagram of a dual modulus prescaler circuit as in  FIG. 10  dividing an input clock frequency by nine. 
         FIG. 13  is an example circuit diagram of a dual modulus prescaler design that can divide an input clock frequency by two or three. 
         FIG. 14  is an example clock timing diagram of a dual modulus prescaler circuit as in  FIG. 12  dividing an input clock frequency by two. 
         FIG. 15  is an example clock timing diagram of a dual modulus prescaler circuit as in  FIG. 12  dividing an input clock frequency by three. 
         FIG. 16  is an example schematic of a proposed CML latch using shunt-peaked active transistor loads and replica biasing. 
         FIG. 17  is an example clock timing diagram of a CML latch using shunt-peaked active transistor loads and replica biasing of  FIG. 16 , where the latch is defined to sample/latch the input data when the input clock, Clkp-Clkn is negative/positive. 
         FIG. 18  is an example of a small-signal model and analysis of an active inductive load element useful in CML latches for high frequency dividers. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
       FIG. 16  illustrates an example schematic of a circuit  1600  that has depicts a CML latch  5  that is biased using a replica biasing circuit  2 . The CML latch is a two-state circuit that is either used in the data sampling or data latching mode. The differential voltage of the clock input pair Clkp-Clkn determines latch mode of operation. Differential input clocking signals Clkp/Clkn  1605  drive the differential input transistor pair M 5 /M 6   1610 . The differential voltage across M 5 /M 6  switches the current required by current source transistor M 9   1615 . When the voltage of Clkp-Clkn is negative, the latch is in the sampling mode of operation. In the sampling mode, bias current from transistor M 9   1615  is flowing through transistor load of M 7 /M 8   1620 , differential pair M 1 /M 2   1625  and transistor M 5 . Based upon the differential input data Dp-Dn  1635 , the differential output voltage Voutp-Voutn  1640  is defined. A positive/negative voltage of Dp-Dn  1635  defines a positive/negative voltage of Voutp-Voutn  1640 , respectively. When the voltage of Clkp-Clkn is positive, the latch is in the latching mode of operation. In the latching mode of operation, current is supplied through transistor load of M 7 /M 8   1620  and the second stage of the latch consisting of transistor pair M 3 /M 4   1630  and transistor M 6  to current source transistor M 9   1615 . Transistor pair M 3 /M 4   1630  are connected in a cross-coupled configuration. In the latching mode, transistor pair M 3 /M 4   1630  provide positive feedback to latch and retain the voltage at nodes Voutp and Voutn. The voltages at nodes Voutp and Voutn are bi-stable in that their high and low values are controlled to only two levels. The data on differential lines Dp/Dn  1635  are first sampled and then latched. To form a flip-flop, two of these latches are used in series while using opposite input clocking polarities such that one latch stage is in sample/latch mode while the other latch stage is in latch/sample mode. 
     In the proposed prescaler design, each CML flip-flop latch uses a shunt-peaked loading technique with an NMOS transistor pair M 7 /M 81620  which acts as inductive active load elements. The biasing of the gates of transistor pair M 7 /M 8   1620  is important to the ac performance of the CML latch and to how these transistors respond at high switching speeds. The gates of transistors M 7 /M 8   1620  are biased to a voltage (vbias gate  1640 ) by the replica bias circuitry  2 . The replica biasing technique is well understood in the present art but various other circuit design techniques can also be used to bias the gates of M 7 /M 8   1620 . The replica bias design depicted here consists of transistors M 10   1654 , M 11   1655 , M 12   1656  and M 13   1657 , operational amplifier (OPAMP) OP 1   1653  and reference voltages Vbias 1   1651  and Vbias 2   1652 . The replica bias circuitry  2  functions as a low-frequency circuit for the high-speed CML latch  5 . The transistor stack in the replica bias block  2  replicates the voltage drop across the active switching transistors M 7  or MS in the CML latch. The purpose of the replica bias circuit is to control the voltage at the source of either transistor M 7  or MS with a constant current flow. This situation occurs in the data sampling mode with the differential input signal Clkp-Clkn negative and Dp-Dn  1635  either positive or negative. In the data sampling mode, current will be sourced from power supply Vcc 1   1660  through either transistor series circuit of M 7 , M 1 , M 5  and M 9  or the transistor series circuit of MS, M 2 , M 5  and M 9 . Since transistor M 9   1615  acts as a current source the value of the total current flow in both data sampling states will be constant. 
     To ensure proper biasing from the replica bias circuit, the power supply level for Vcc 2   1658  must be greater than Vcc 1   1660  such that the gate voltages of transistors M 7 /M 8   1620  can exceed the CML latch power supply, Vcc 1   1660 . The higher gate voltage  7  is needed such that when no current is flowing in either transistor M 7  or transistor MS, the source voltage will float up to within a threshold of its own gate voltage. It is desirable to have this off-state voltage reach the power supply of Vcc 1   1660  such that power supply headroom within the CML latch is not wasted. 
     Reference voltage Vbias 1   1651  uses conventional circuit techniques well documented to one skilled in the present art. Vbias 1   1651  represents the low voltage level that either Voutp or Voutn will approach in active switching. This reference voltage is applied to the negative terminal of OPAMP OP 1   1653 . Through negative feedback, Vbias 1   1651  is also present at the source of transistor M 10   1654 . Reference voltage Vbias 2   1652  represents the common mode plus one half of the differential voltage of clock signals Clkp-Clkn. Thus, when full current is flowing from power supply Vcc 1   1660  to ground terminal Vss  1670  through the series circuit replica bias transistors M 10   1654 , M 11   1655 , M 12   1656  and M 13   1657 , the voltage at the source of M 10   1654  will be equal to Vbias 1   1651 . The current in transistor chain M 10   1654  through M 13   1657  tracks the current in the CML latch input stage when the latch is in the data sampling mode. Transistors M 13   1657  and M 9   1615  are gate-connected and therefore it is preferred to scale down the current in current source transistor M 13   1657  to save power in the replica bias circuit. In addition, transistors M 11   1655  and M 12   1656  can be scaled down relative to transistors M 1  and M 5 , respectively. The voltage in the replica bias circuitry at the gate of transistor M 10   1654  is a fixed voltage above its source voltage Vbias 1   1651 . In the replica bias circuit  2  this node is labelled as Vbias_gate  1648 . The reference voltage Vbias_gate  1648  is connected to each individual CML latch in the overall prescaler through an individual input bias filter network  6 . Capacitor C_filter  1675  establishes an ac ground potential at the input bias node  7  connected to the two resistors labeled R 4 . 
       FIGS. 18   a - c  show an Analysis of CML latch Active Inductive Load 
     As shown in  FIG. 18(   a ) and ( b ) 
     
       
         
           
             
               
                 
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                           + 
                           
                             
                               ( 
                               
                                 
                                   g 
                                   mb 
                                 
                                 + 
                                 
                                   g 
                                   ds 
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   
                                     sR 
                                     1 
                                   
                                   ⁢ 
                                   
                                     C 
                                     gs 
                                   
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                         
                           
                             
                               sR 
                               1 
                             
                             ⁢ 
                             
                               C 
                               gs 
                             
                           
                           + 
                           1 
                         
                       
                       ] 
                     
                   
                 
               
               = 
               
                 
                   
                     i 
                     x 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     V 
                     gs 
                   
                 
                 = 
                 
                   
                     [ 
                     
                       
                         
                           R 
                           1 
                         
                         
                           
                             R 
                             1 
                           
                           + 
                           
                             1 
                             
                               sC 
                               gs 
                             
                           
                         
                       
                       - 
                       1 
                     
                     ] 
                   
                   ⁢ 
                   
                     V 
                     x 
                   
                 
               
             
           
         
       
       
         
           
             
               Z 
               o 
             
             = 
             
               
                 
                   V 
                   x 
                 
                 
                   i 
                   x 
                 
               
               = 
               
                 [ 
                 
                   
                     ( 
                     
                       
                         
                           sR 
                           1 
                         
                         ⁢ 
                         
                           C 
                           gs 
                         
                       
                       + 
                       1 
                     
                     ) 
                   
                   
                     
                       
                         sC 
                         gs 
                       
                       ⁡ 
                       
                         ( 
                         
                           1 
                           + 
                           
                             
                               ( 
                               
                                 
                                   g 
                                   mb 
                                 
                                 + 
                                 
                                   g 
                                   ds 
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               R 
                               1 
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                       ( 
                       
                         
                           g 
                           m 
                         
                         + 
                         
                           g 
                           mb 
                         
                         + 
                         
                           g 
                           ds 
                         
                       
                       ) 
                     
                   
                 
                 ] 
               
             
           
         
       
       
         
           
             
               V 
               gs 
             
             = 
             
               
                 
                   - 
                   1 
                 
                 
                   ( 
                   
                     
                       
                         sR 
                         1 
                       
                       ⁢ 
                       
                         C 
                         gs 
                       
                     
                     + 
                     1 
                   
                   ) 
                 
               
               ⁢ 
               
                 V 
                 x 
               
             
           
         
       
       
         
           
             
               Z 
               o 
             
             = 
             
               
                 1 
                 
                   ( 
                   
                     
                       g 
                       m 
                     
                     + 
                     
                       g 
                       mb 
                     
                     + 
                     
                       g 
                       ds 
                     
                   
                   ) 
                 
               
               [ 
               
                 
                   ( 
                   
                     
                       
                         sR 
                         1 
                       
                       ⁢ 
                       
                         C 
                         gs 
                       
                     
                     + 
                     1 
                   
                   ) 
                 
                 
                   
                     
                       
                         sC 
                         gs 
                       
                       ( 
                       
                         1 
                         + 
                         
                           
                             ( 
                             
                               
                                 g 
                                 mb 
                               
                               + 
                               
                                 g 
                                 ds 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                             ( 
                             
                               R 
                               1 
                             
                             ) 
                           
                         
                       
                     
                     
                       ( 
                       
                         
                           g 
                           m 
                         
                         + 
                         
                           g 
                           mb 
                         
                         + 
                         
                           g 
                           ds 
                         
                       
                       ) 
                     
                   
                   + 
                   1 
                 
               
               ] 
             
           
         
       
     
     At low frequencies: 
     
       
         
           
             
               
                 Z 
                 o 
               
               ⁢ 
               
                 ❘ 
                 
                   ω 
                   = 
                   0 
                 
               
             
             = 
             
               1 
               
                 ( 
                 
                   
                     g 
                     m 
                   
                   + 
                   
                     g 
                     mb 
                   
                   + 
                   
                     g 
                     ds 
                   
                 
                 ) 
               
             
           
         
       
     
     At high frequencies: 
     
       
         
           
             
               
                 Z 
                 o 
               
               ⁢ 
               
                 ❘ 
                 
                   ω 
                   = 
                   ∞ 
                 
               
             
             = 
             
               
                 
                   1 
                   
                     ( 
                     
                       
                         g 
                         m 
                       
                       + 
                       
                         g 
                         mb 
                       
                       + 
                       
                         g 
                         ds 
                       
                     
                     ) 
                   
                 
                 [ 
                 
                   
                     
                       R 
                       1 
                     
                     ⁢ 
                     
                       C 
                       gs 
                     
                   
                   
                     
                       
                         C 
                         gs 
                       
                       ⁡ 
                       
                         ( 
                         
                           1 
                           + 
                           
                             
                               ( 
                               
                                 
                                   g 
                                   mb 
                                 
                                 + 
                                 
                                   g 
                                   ds 
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               R 
                               1 
                             
                           
                         
                         ) 
                       
                     
                     
                       ( 
                       
                         
                           g 
                           m 
                         
                         + 
                         
                           g 
                           mb 
                         
                         + 
                         
                           g 
                           ds 
                         
                       
                       ) 
                     
                   
                 
                 ] 
               
               = 
               
                 
                   
                     R 
                     1 
                   
                   
                     1 
                     + 
                     
                       
                         ( 
                         
                           
                             g 
                             mb 
                           
                           + 
                           
                             g 
                             ds 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         R 
                         1 
                       
                     
                   
                 
                 ≈ 
                 
                   R 
                   1 
                 
               
             
           
         
       
     
     For large bias currents: 
     
       
         
           
             
               1 
               
                 ( 
                 
                   
                     g 
                     m 
                   
                   + 
                   
                     g 
                     mb 
                   
                   + 
                   
                     g 
                     ds 
                   
                 
                 ) 
               
             
             &lt; 
             
               R 
               1 
             
           
         
       
     
     Construct model for Z o (ω) as shown in  FIG. 18(   c ): 
     
       
         
           
             
               
                 
                   
                     
                       Z 
                       a 
                     
                     ⁢ 
                     
                       ❘ 
                       
                         ω 
                         = 
                         0 
                       
                     
                   
                   = 
                   
                     
                       
                         r 
                         1 
                       
                       // 
                       
                         r 
                         2 
                       
                     
                     = 
                   
                 
               
               
                 
                   
                     
                       r 
                       1 
                     
                     ⁢ 
                     
                       r 
                       2 
                     
                   
                   
                     
                       r 
                       1 
                     
                     + 
                     
                       r 
                       2 
                     
                   
                 
               
               
                 
                   
                     
                       Z 
                       a 
                     
                     ⁢ 
                     
                       ❘ 
                       
                         ω 
                         = 
                         ∞ 
                       
                     
                   
                   = 
                   
                     r 
                     2 
                   
                 
               
             
           
         
       
     
     Assume: 
     
       
         
           
             
               
                 
                   
                     Z 
                     a 
                   
                   ⁢ 
                   
                     ❘ 
                     
                       ω 
                       = 
                       ∞ 
                     
                   
                   &lt;&lt; 
                 
               
               
                 
                   
                     Z 
                     a 
                   
                   ⁢ 
                   
                     ❘ 
                     
                       ω 
                       = 
                       0 
                     
                   
                 
               
               
                 -&gt; 
               
               
                 
                   
                     r 
                     2 
                   
                   &gt;&gt; 
                   
                     r 
                     1 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     Z 
                     a 
                   
                   = 
                   
                     
                       
                         
                           ( 
                           
                             
                               r 
                               1 
                             
                             + 
                             sL 
                           
                           ) 
                         
                         ⁢ 
                         
                           r 
                           2 
                         
                       
                       
                         
                           r 
                           1 
                         
                         + 
                         
                           r 
                           2 
                         
                         + 
                         sL 
                       
                     
                     = 
                     
                       
                         
                           r 
                           1 
                         
                         ⁢ 
                         
                           r 
                           2 
                         
                       
                       
                         
                           r 
                           1 
                         
                         + 
                         
                           r 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   
                     
                       sL 
                       
                         r 
                         1 
                       
                     
                     + 
                     1 
                   
                   
                     
                       sL 
                       
                         
                           r 
                           1 
                         
                         + 
                         
                           r 
                           2 
                         
                       
                     
                     + 
                     1 
                   
                 
               
             
           
         
       
     
     Equate Z a  to Z o   
     
       
         
           
             
               L 
               
                 r 
                 1 
               
             
             = 
             
               
                 R 
                 1 
               
               ⁢ 
               
                 C 
                 gs 
               
             
           
         
       
       
         
           
             
               L 
               
                 
                   r 
                   1 
                 
                 + 
                 
                   r 
                   2 
                 
               
             
             = 
             
               
                 
                   C 
                   gs 
                 
                 ⁡ 
                 
                   ( 
                   
                     1 
                     + 
                     
                       
                         ( 
                         
                           
                             g 
                             mb 
                           
                           + 
                           
                             g 
                             ds 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         R 
                         1 
                       
                     
                   
                   ) 
                 
               
               
                 
                   g 
                   m 
                 
                 + 
                 
                   g 
                   mb 
                 
                 + 
                 
                   g 
                   ds 
                 
               
             
           
         
       
       
         
           
             
               
                 L 
                 
                   
                     r 
                     1 
                   
                   + 
                   
                     r 
                     2 
                   
                 
               
               ≈ 
               
                 L 
                 
                   r 
                   2 
                 
               
             
             = 
             
               
                 
                   C 
                   gs 
                 
                 ⁡ 
                 
                   ( 
                   
                     1 
                     + 
                     
                       
                         ( 
                         
                           
                             g 
                             mb 
                           
                           + 
                           
                             g 
                             ds 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         R 
                         1 
                       
                     
                   
                   ) 
                 
               
               
                 
                   g 
                   m 
                 
                 + 
                 
                   g 
                   mb 
                 
                 + 
                 
                   g 
                   ds 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     Z 
                     o 
                   
                   = 
                   
                     
                       
                         
                           ( 
                           
                             
                               r 
                               1 
                             
                             + 
                             sL 
                           
                           ) 
                         
                         ⁢ 
                         
                           r 
                           2 
                         
                       
                       
                         
                           r 
                           1 
                         
                         + 
                         
                           r 
                           2 
                         
                         + 
                         sL 
                       
                     
                     = 
                     
                       
                         
                           r 
                           1 
                         
                         ⁢ 
                         
                           r 
                           2 
                         
                       
                       
                         
                           r 
                           1 
                         
                         + 
                         
                           r 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   
                     
                       sL 
                       
                         r 
                         1 
                       
                     
                     + 
                     1 
                   
                   
                     
                       sL 
                       
                         
                           r 
                           1 
                         
                         + 
                         
                           r 
                           2 
                         
                       
                     
                     + 
                     1 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     r 
                     1 
                   
                   ⁢ 
                   
                     r 
                     2 
                   
                 
                 
                   
                     r 
                     1 
                   
                   + 
                   
                     r 
                     2 
                   
                 
               
               ≈ 
               
                 r 
                 1 
               
             
             = 
             
               1 
               
                 
                   g 
                   m 
                 
                 + 
                 
                   g 
                   mb 
                 
                 + 
                 
                   g 
                   ds 
                 
               
             
           
         
       
       
         
           
             
               r 
               1 
             
             ≈ 
             
               1 
               
                 g 
                 m 
               
             
           
         
       
       
         
           
             
               L 
               
                 r 
                 1 
               
             
             = 
             
               
                 R 
                 1 
               
               ⁢ 
               
                 C 
                 gs 
               
             
           
         
       
       
         
           
             L 
             = 
             
               
                 
                   
                     R 
                     1 
                   
                   ⁢ 
                   
                     C 
                     gs 
                   
                 
                 
                   
                     g 
                     m 
                   
                   + 
                   
                     g 
                     mb 
                   
                   + 
                   
                     g 
                     ds 
                   
                 
               
               ≈ 
               
                 
                   
                     R 
                     1 
                   
                   ⁢ 
                   
                     C 
                     gs 
                   
                 
                 
                   g 
                   m 
                 
               
             
           
         
       
       
         
           
             
               r 
               2 
             
             = 
             
               
                 
                   L 
                   ⁡ 
                   
                     ( 
                     
                       
                         g 
                         m 
                       
                       + 
                       
                         g 
                         mb 
                       
                       + 
                       
                         g 
                         ds 
                       
                     
                     ) 
                   
                 
                 
                   
                     C 
                     gs 
                   
                   ⁡ 
                   
                     ( 
                     
                       1 
                       + 
                       
                         
                           ( 
                           
                             
                               g 
                               mb 
                             
                             + 
                             
                               g 
                               ds 
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           R 
                           1 
                         
                       
                     
                     ) 
                   
                 
               
               = 
               
                 
                   
                     
                       R 
                       1 
                     
                     ⁢ 
                     
                       C 
                       gs 
                     
                   
                   
                     
                       C 
                       gs 
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           g 
                           m 
                         
                         + 
                         
                           g 
                           mb 
                         
                         + 
                         
                           g 
                           ds 
                         
                       
                       ) 
                     
                   
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   
                     ( 
                     
                       
                         g 
                         m 
                       
                       + 
                       
                         g 
                         mb 
                       
                       + 
                       
                         g 
                         ds 
                       
                     
                     ) 
                   
                   
                     
                       C 
                       gs 
                     
                     ⁡ 
                     
                       ( 
                       
                         1 
                         + 
                         
                           
                             ( 
                             
                               
                                 g 
                                 mb 
                               
                               + 
                               
                                 g 
                                 ds 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                             R 
                             1 
                           
                         
                       
                       ) 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               r 
               2 
             
             = 
             
               
                 
                   R 
                   1 
                 
                 
                   1 
                   + 
                   
                     
                       ( 
                       
                         
                           g 
                           mb 
                         
                         + 
                         
                           g 
                           ds 
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       R 
                       1 
                     
                   
                 
               
               = 
               
                 R 
                 1 
               
             
           
         
       
     
     The above analysis is significant since the benefits of a shunted peaked amplifier will apply here. The active load transistor can now be optimized for maximum bandwidth response characteristics. The required shunt impedance modeling values, L, r 1  and r 2 , can be determined for the appropriate theoretical response. Then, based upon the small signal modeling equations defined above, the thick gate transistor&#39;s (M 3 , M 4 ) W/L ratio geometry can be specified for the proper g m  as well as resistor R 1 . Thus, the amplifier design using an active load can be optimized for the appropriate response given the driving point load impedance just as is done in the shunt-peaked amplifier analysis using spiral inductors. 
     As demonstrated in  FIG. 18  and applied to  FIG. 16 , resistors R connected to the gates of shunt-peaking transistors M 7  and M 8  partially influence the amount of inductive impedance that the CML latch sees looking into the source of transistor M 7  and M 8 . Controlling this inductance in the CML active load to the proper value will tune out the driving load capacitance that the latch must drive. To control the inductive impedance accurately is a major goal of the CML latch since an optimized design will translate to a higher bandwidth circuit that can accommodate higher input clock frequencies and higher input data rates. Higher bandwidth will be achieved with the decreased setup and hold times of the latch. In addition, with the driving load capacitance partially cancelled by the inductive component, the switching current of the latch circuit is reduced when operating at a specific clocking and sampling frequency. 
     To summarize, as demonstrated in  FIG. 18 , and the accompanying small-signal ac analysis, the small signal output impedance looking into the source of transistor M 7  and M 8  appear inductive. Active inductor tunes out the driving load capacitance and achieves a higher bandwidth. The required monolithic die area for this type of active load is minimized and requires no additional power dissipation.