Abstract:
A characterized cell library for EDA tools includes receiver model data that provides two or more capacitance values for a given receiver modeling situation (signal type and operating conditions). The receiver model can then use different capacitance values to generate different portions of the model receiver signal, thereby enabling more accurate matching of actual receiver signal timing characteristics. For example, a two-capacitance receiver model can be generated by using the first capacitance value to match the delay characteristics of an actual receiver, and by using the second capacitance (in light of the use of the first capacitance) to match the slew characteristics of that actual receiver. Because typical EDA timing analyses focus mainly on delay and slew (and not the detailed profile of circuit signals), a two-capacitance receiver model can provide a high degree of accuracy without significantly increasing cell library size and computational complexity.

Description:
RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 11/866,981, entitled “NONLINEAR RECEIVER MODEL FOR GATE-LEVEL DELAY CALCULATION” filed Oct. 3, 2007 which is a divisional of U.S. patent application Ser. No. 10/977,243, entitled “NONLINEAR RECEIVER MODEL FOR GATE-LEVEL DELAY CALCULATION” filed Oct. 29, 2004, now issued as U.S. Pat. No. 7,299,445. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The invention is in the field of electronic design automation (EDA), and more particularly, is related to receiver models for that enable accurate timing analyses. 
     2. Related Art 
     An electronic design automation (EDA) system is a computer software system used for designing integrated circuit (IC) devices. The EDA system typically receives one or more high level behavioral descriptions of an IC device (e.g., in HDL languages like VHDL, Verilog, etc.) and translates (“synthesizes”) this high-level design language description into netlists of various levels of abstraction. A netlist describes the IC design and is composed of nodes (functional elements) and edges, e.g., connections between nodes. At a higher level of abstraction, a generic netlist is typically produced based on technology independent primitives. 
     The generic netlist can be translated into a lower level technology-specific netlist based on a technology-specific (characterized) cell library that has gate-specific models for each cell (i.e., a functional element, such as an AND gate, an inverter, or a multiplexer). The models define performance parameters for the cells; e.g., parameters related to the operational behavior of the cells, such as power consumption, delay, and noise. The netlist and cell library are typically stored in computer readable media within the EDA system and are processed and verified using many well-known techniques. 
       FIG. 1  shows a simplified representation of an exemplary digital ASIC design flow. At a high level, the process starts with the product idea (step E 100 ) and is realized in an EDA software design process (step E 110 ). When the design is finalized, it can be taped-out (event E 140 ). After tape out, the fabrication process (step E 150 ) and packaging and assembly processes (step E 160 ) occur resulting, ultimately, in finished chips (result E 170 ). 
     The EDA software design process (step E 110 ) is actually composed of a number of steps E 112 -E 130 , shown in linear fashion for simplicity. In an actual ASIC design process, the particular design might have to go back through steps until certain tests are passed. Similarly, in any actual design process, these steps may occur in different orders and combinations. This description is therefore provided by way of context and general explanation rather than as a specific, or recommended, design flow for a particular ASIC. 
     A brief description of the components steps of the EDA software design process (step E 110 ) will now be provided. During system design (step E 112 ), the designers describe the functionality that they want to implement and can perform what-if planning to refine functionality, check costs, etc. Hardware-software architecture partitioning can occur at this stage. Exemplary EDA software products from Synopsys, Inc. that can be used at this step include Model Architect, Saber, System Studio, and DesignWare® products. 
     During logic design and functional verification (step E 114 ), the VHDL or Verilog code for modules in the system is written and the design is checked for functional accuracy. More specifically, does the design as checked to ensure that produces the correct outputs. Exemplary EDA software products from Synopsys, Inc. that can be used at this step include VCS, VERA, DesignWare®, Magellan, Formality, ESP and LEDA products. 
     During synthesis and design for test (step E 116 ), the VHDL/Verilog is translated to a netlist. The netlist can be optimized for the target technology. Additionally, the design and implementation of tests to permit checking of the finished chip occurs. Exemplary EDA software products from Synopsys, Inc. that can be used at this step include Design Compiler®, Physical Compiler, Test Compiler, Power Compiler, FPGA Compiler, Tetramax, and DesignWare® products. 
     During design planning (step E 118 ), an overall floorplan for the chip is constructed and analyzed for timing and top-level routing. Exemplary EDA software products from Synopsys, Inc. that can be used at this step include Jupiter and Floorplan Compiler products. 
     During netlist verification (step E 120 ), the netlist is checked for compliance with timing constraints and for correspondence with the VHDL/Verilog source code. Exemplary EDA software products from Synopsys, Inc. that can be used at this step include VCS, VERA, Formality and PrimeTime products. 
     During physical implementation (step E 122 ), placement (positioning of circuit elements) and routing (connection of the same) is performed. Exemplary EDA software products from Synopsys, Inc. that can be used at this step include the Astro product. 
     During analysis and extraction (step E 124 ), the circuit function is verified at a transistor level, this in turn permits what-if refinement. Exemplary EDA software products from Synopsys, Inc. that can be used at this step include Star RC/XT, Raphael, and Aurora products. 
     During physical verification (step E 126 ), various checking functions are performed to ensure correctness for: manufacturing, electrical issues, lithographic issues, and circuitry. Exemplary EDA software products from Synopsys, Inc. that can be used at this step include the Hercules product. 
     During resolution enhancement (step E 128 ), geometric manipulations of the layout are performed to improve manufacturability of the design. Exemplary EDA software products from Synopsys, Inc. that can be used at this step include the iN-Phase, Proteus, and AFGen products. 
     Finally, during mask data preparation (step E 130 ), the “tape-out” data for production of masks for lithographic use to produce finished chips is performed. Exemplary EDA software products from Synopsys, Inc. that can be used at this step include the CATS(R) family of products. 
     As indicated in  FIG. 1 , timing analyses can be performed at various points along the EDA process, such as during synthesis, design planning, netlist verification, and analysis (as indicated by the bolded chevrons). The accuracy of these timing analyses is critical to the quality of final IC produced using EDA systems. A timing analysis is performed at the transistor level, and makes use of the performance data included in the characterized cell library. To perform a timing analysis, the IC design (or a portion of the IC) is modeled as a network of drivers and receivers. Cells designated as drivers provide stimuli to the network, and the resulting waveforms are received by the cells designated as receivers. 
     For example,  FIG. 2A  shows a schematic diagram of a sample driver-receiver network  200  that includes a driver  210  and a receiver  230 . An input pin  211  of driver  210  receives a driver input signal S_IND and generates a driver output signal S_OUTD at a driver output pin  212 . This signal is transmitted across an interconnect element  220  and is received as a receiver input signal S_INR at a receiver input pin  231  of receiver  230  (depicted as an inverter for exemplary purposes). Receiver  230  processes receiver input signal S_INR and generates a receiver output signal S_OUTR at a receiver output pin  232 . Note that receiver  230  can also function as a driver for downstream cells, as indicated by load  240  connected to receiver output pin  232 . 
     Because signals do not propagate instantly through a real-world circuit (e.g., due to propagation delays and parasitics), signals S_IND, S_OUTD, S_INR, and S_OUTR will have differing slew and delay characteristics. In the context of a timing analysis, “slew” represents the time required for a signal to transition between an upper threshold voltage and a lower threshold voltage (or vice versa), while “delay” represents the time required for the signal to transition from either the upper or lower rail (supply voltage) to a gate threshold voltage. Meanwhile, the gate threshold voltage typically represents the voltage at which the transistor switches state (from off to on, or vice versa). 
     The concepts of slew and delay are depicted in  FIG. 2B , which shows a graph of a sample signal S_SAMP that represents a general signal provided to, or generated by, a cell within an IC design. Signal S_SAMP transitions between a lower rail voltage RL and an upper rail voltage RU, which represent the operating (supply) voltages for the cell. To define the slew and delay characteristics of signal S_SAMP, an upper threshold voltage THU, a lower threshold voltage THL, and a gate threshold voltage THG are selected. Upper threshold voltage THU, lower threshold voltage THL, and gate threshold voltage THG are typically selected to be predetermined percentages of the difference between rail voltages RU and RL. For example, lower threshold THL and upper threshold THU could be selected to be 20% and 80%, respectively, of the difference between upper rail voltage RU and lower rail voltage RL. Likewise, gate threshold voltage THG could be selected to be midway (i.e., 50% of the difference) between upper rail voltage RU and lower rail voltage RL. 
     Once lower threshold voltage THL, gate threshold voltage THG, and upper threshold voltage THV have been defined, delay and slew values can be determined for signal S_SAMP. For example, signal S_SAMP reaches gate threshold voltage THG at a time T 2 . Therefore, the delay value for signal S_SAMP is equal to the difference between times T 2  and T 0  (i.e., T 2 −T 0 ). Similarly, since signal S_SAMP reaches lower threshold voltage THL and upper threshold voltage THU at times T 1  and T 3 , respectively, the slew value for signal S_SAMP is the difference between times T 3  and T 1  (i.e., T 3 −T 1 ). Delay and slew values can be determined in a similar manner for a signal transitioning from upper rail voltage RU to lower rail voltage RL. 
     In an EDA system, a characterized cell library is generated by fitting mathematical models to actual delay data (i.e., measured data or simulated (SPICE) data). Typically, a CMOS cell operating as a receiver is modeled as a single capacitor. For example,  FIG. 3A  shows receiver cell  230  of  FIG. 2A  replaced with a conventional receiver model  230 -ST that includes a resistor R_ST and a capacitor C_ST serially coupled between receiver input pin  231  and ground. The value of capacitor C_ST is selected such that a model receiver input signal S_INR-ST generated by the RC circuit in response to driver output signal S_OUTD fits the actual (measured or simulated) receiver input signal S_INR. Typically, a different capacitance value is determined for rising signals, falling signals, “best case” (fastest) transitions, and “worst case” (slowest) transitions. Furthermore, since cell performance generally changes with operating conditions such as temperature and voltage, a new set of capacitance values are often generated across a range of operating conditions. 
     Thus, a receiver model entry in a conventional characterized cell library generally includes a set of capacitance values, with each single capacitance value being referenced by a signal type (rise, fall, best case, worst case) and set of operating conditions. For example,  FIG. 3B  shows a characterized library cell entry  300  for a receiver model of cell  230  (shown in  FIG. 3A ). Cell entry  300  includes a set of capacitance values C_ST referenced by signal type and operating conditions. For example, for a rising signal generated under operating conditions OP 1 , cell  230  is modeled (as a receiver) using a capacitance value C_ST(R 1 ). Likewise, for a falling signal under the same operating conditions, cell  230  is modeled using a capacitance value C_ST(F 1 ), while a rising signal under a set of operating conditions OP 2  leads to the selection of a capacitance value C_ST(R 2 ) to model cell  230 . 
     Unfortunately, as device sizes continue to shrink, the behavior of a signal at a receiver can no longer be modeled by a single (static) capacitance value, as dynamic effects (e.g., the Miller Effect) begin to affect the signal shape. For example,  FIG. 3C  shows an actual signal S_INR-A 1  (indicated by the bold curve) measured at the input pin of a receiver cell instantiated using 0.12 μm technology. Also depicted are model signals S_INR-ST 1 , S_INR-ST 2 , and S_INR-ST 3  (indicated by the dashed curves), each having been generated using the above-described single-capacitance receiver model (with each of the signals being generated using a different capacitance value). 
     Because the curvature of signal S_INR-A 1  varies significantly over the course of the signal transition, none of model signals S_INR-ST 1 , S_INR-ST 2 , and S_INR-ST 3  can accurately model both the delay and slew characteristics of actual signal S_INR-A 1 . For example, model signal S_INR-ST 1  provides a relatively good match to the actual delay of actual signal S_INR-A 1 . However, because model signal S_INR-ST 1  reaches the upper threshold voltage THU much sooner than does actual signal S_INR-A 1 , the slew value generated by model signal S_INR-ST 1  is much lower than the actual slew value of signal S_INR-A 1 . Unfortunately, while the model capacitance can be adjusted to reduce the slew error, such as in model signals S_INR-ST 2  and S_INR-ST 3 , any such adjustment increases the model delay error. 
     Thus, conventional cell receiver models can be inadequate for the timing analysis of modern IC designs. Accordingly, it is desirable to provide a cell receiver model that can accurately represent the delay and slew characteristics of a CMOS cell. 
     SUMMARY OF THE INVENTION 
     To improve receiver modeling accuracy without unduly increasing cell library size or analytical complexity, a multi-capacitance receiver model can be used. For example, in one embodiment, the static capacitor used in conventional receiver models can be replaced by a two-stage non-linear capacitor. The two-stage non-linear capacitor provides a first capacitance value while the receiver model is generating a first portion of a model receiver signal, and then switches to a second capacitance value when the model receiver signal reaches a predetermined switching voltage. In other embodiments, the non-linear capacitor can switch between three or more capacitance values. 
     In one embodiment, a two-stage non-linear capacitor in a receiver model can include a switching voltage set to the gate threshold voltage of the cell being modeled. Then, the first capacitance value can be selected such that the delay of the model receiver signal matches the delay of the actual receiver signal, and the second capacitance value can be selected such that the slew of the model receiver signal matches the slew of the actual receiver signal. Further accuracy can be achieved by making the first and/or the second capacitances a function of the load capacitance coupled to the output of the receiver and/or the input slew of the signal provided at the input of the receiver. For example, the first and/or the second capacitances could actually be tables of capacitance values indexed (referenced by) different receiver load capacitances and/or input slew values. 
     In another embodiment, a cell library entry for a receiver can be generated by translating actual receiver timing data into a receiver model that incorporates a non-linear capacitor receiver model. For example, the non-linear capacitor can be defined as a two-stage capacitor. A first value of the two-stage capacitor can be selected such that the receiver model exhibits the same delay as the actual receiver cell, while a second value of the two-stage capacitor can be selected such that the receiver model exhibits the same slew as the actual receiver cell. 
     The matching of the model receiver signal portions to the actual receiver signal portions can be performed using receiver input signals or receiver output signals. Furthermore, instead of matching timing characteristics such as delay and slew, the matching operation can compare the profiles of the model receiver signal portions and the corresponding actual receiver signal portions. In another embodiment, greater accuracy (i.e., a closer fit to the actual signal profile) can be achieved by increasing the number of different capacitance values assigned to the non-linear capacitor during generation of the model receiver signal. 
     In another embodiment, a timing analysis can be performed using a receiver model incorporating a non-linear capacitor. The non-linear capacitor is initially assigned a first capacitance value, and a driver output signal is applied to the receiver model to cause the receiver model to generate a receiver signal. When the receiver signal reaches a first signal voltage, the non-linear capacitor switches to a second capacitance value. Generation of the receiver signal continues in this manner (i.e., switching capacitance values at predetermined signal voltages) until the receiver signal reaches a maximum voltage (generally a supply voltage). The receiver signal can then be applied to downstream cells, or signal characteristics (such as delay and slew) can be extracted from the receiver signal as part of the timing analysis. 
     The invention will be more fully understood in view of the following description and drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a process flow diagram for a general EDA design flow. 
         FIG. 2A  is a schematic diagram of a sample driver-receiver network. 
         FIG. 2B  is a graph of a sample signal within a load-receiver network. 
         FIG. 3A  is a schematic diagram of a conventional receiver model. 
         FIG. 3B  is a sample cell entry for a conventional receiver model in a cell library. 
         FIG. 3C  is a graph of conventional model receiver signals compared to an actual receiver signal. 
         FIG. 4A  is a schematic diagram of a driver-receiver network that incorporates a multi-capacitance receiver model. 
         FIG. 4B  is a graph of a multi-capacitance model receiver signal compared to an actual receiver signal. 
         FIG. 5A  is a flow diagram of a multi-capacitance receiver model generation process. 
         FIGS. 5B-5E  are sample cell libraries that include multi-capacitance receiver models. 
         FIG. 6  is a diagram of a computing system that includes logic for generating a multi-capacitance receiver model. 
         FIG. 7  is a flow diagram of a process for performing a timing analysis using a multi-capacitance receiver model. 
     
    
    
     DETAILED DESCRIPTION 
     Because of the various dynamic effects that become more significant as device geometries are reduced in size, conventional single-capacitance receiver models used in EDA systems can no longer provide accurate timing simulations.  FIG. 4A  shows a multi-capacitance receiver model that overcomes this deficiency. 
       FIG. 4A  models driver-receiver network  200  shown in  FIG. 2A  by replacing receiver  230  with a cell receiver model  430 -NL that includes a resistor R_NL and a non-linear capacitor C_NL serially coupled between receiver input pin  231  and ground. Like cell receiver model  230 -ST shown in  FIG. 3A , cell receiver model  430 -NL generates a model receiver input signal S_INR-NL in response to driver output signal S_OUTD provided by driver cell  210 . 
     However, unlike static capacitor C_ST in cell receiver model  230 -ST, non-linear capacitor C_NL in cell receiver model  430 -NL does not provide a single, static capacitance over an entire signal transition. Rather, non-linear capacitor C_NL switches between different capacitance values at predetermined signal voltages as receiver model  430 -NL is generating model receiver input signal S_INR-NL (or model receiver output signal S_OUTR-NL). The capacitance values for non-linear capacitor C_NL are selected such that the signals generated by cell receiver model  430 -NL match the timing characteristics of the actual signals (S_INR and/or S_OUTR) generated within the driver-receiver network  200  (shown in  FIG. 2A ). 
     For example, in one embodiment, non-linear capacitor C_NL provides two different capacitance values, switching from the first capacitance value to the second capacitance value when the model receiver input signal reaches the gate threshold voltage of the cell being modeled. The first capacitance value can be selected to cause the delay of model receiver input signal S_INR-NL to match the delay of actual receiver input signal S_INR, while the second capacitance value can be selected to cause the slew of signal S_INR-NL to match the slew of signal S_INR. Note that for this and other types of non-linear capacitance-based models, different sets of first capacitance and second capacitance values (and gate threshold voltages) could be generated for different signal types (e.g., rising, falling, best case, and worst case signals) and for different operating conditions (e.g., different temperatures and operating voltages). 
     Note further that while the non-linear capacitance-based model is described with respect to a single driver and single cell receiver model for clarity, in various other embodiments, any number of additional drivers  210 ( 1 ) and any number of additional cell receiver models  430 -NL( 1 ) can be coupled to interconnect  220 . Each additional cell receiver models  430 -NL( 1 ) could then include a non-linear capacitor as described with respect to cell receiver model  430 -NL. 
       FIG. 4B  shows an example of this “two-stage capacitance” approach used to fit a receiver model to actual data. The graph of  FIG. 4B  includes same actual receiver input signal S_INR shown in  FIG. 3C  (i.e., 0.12 μm technology cell acting as a receiver). As described above with respect to  FIG. 3C , signal S_INR exhibits the type of curvature variations that can become more prominent as device sizes are reduced in size. 
     However, rather than modeling signal S_INR using a conventional single capacitance model, in  FIG. 4B  actual signal S_INR is modeled by a two-capacitance receiver model that generates a model receiver input signal S_INR-NL. The portion of signal S_INR-NL from 0V to gate threshold voltage THG is generated using a first capacitance C_NL 1 , while the portion of signal S_INR-NL from gate threshold voltage THG to upper rail 1.08V is generated using a second capacitance C_NL 2 . Capacitances C_NL 1  and C_NL 2  are selected such that the delay and slew characteristics of model receiver input signal S_INR-NL match those of actual receiver input signal S_INR (to within a desired tolerance). 
     Note that switching from capacitance C_NL 1  to C_NL 2  when the model receiver signal reaches the gate threshold voltage essentially covers switching from capacitance C_NL 1  to C_NL 2  exactly at, just before, or just after the model receiver signal reaches gate threshold voltage, since the timing model accuracy will generally not be affected significantly by any of these situations. Note also that while the graph of  FIG. 4B  depicts the capacitance switch as being performed at the gate threshold voltage of the cell being modeled (i.e., either the actual gate threshold voltage of the cell (from measurements or simulations) or a predetermined gate threshold voltage such as 50% of the rail-to-rail voltage), according to other embodiments, the switch can be performed at any selected receiver signal voltage. 
     Note further that even though the specific profile of model receiver input signal S_INR-NL does not exactly match the profile of actual receiver input signal S_INR, the timing characteristics of interest (i.e., the delay and slew) of model receiver input signal S_INR-NL are substantially the same as those of actual receiver input signal S_INR. Therefore, the dual-capacitance model (capacitance values C_NL 1  and C_NL 2 ) can be used to provide an accurate cell receiver model. 
     For exemplary purposes, capacitance values C_NL 1  and C_NL 2  are described as being derived by fitting the model receiver input signal S_INR-NL to the actual receiver input signal S_INR. In another embodiment, first capacitance C_NL 1  could be selected to cause the delay of model receiver output signal S_OUTR-NL to match the delay of actual receiver output signal S_OUTR, while second capacitance C_NL 2  could be selected to cause the slew of model receiver output signal S_OUTR-NL to match the slew of actual receiver output signal S_OUTR (shown in  FIG. 4A ). 
     Because the goal of a model is typically to provide an accurate output, selecting first and second capacitances C_NL 1  and C_NL 2  based on a fit to the receiver output signal can often provide the most accurate modeling results. However, since such an approach will generally depend on the load connected to receiver output pin  232  (e.g., capacitance C_OUT in load model  440 -ST), a different set of capacitance values for non-linear capacitor C_NL could be required for each different loading configuration (each different value of a load capacitance C_OUT at receiver output pin  232  (shown in  FIG. 4A )). Because a given receiver may be coupled to a wide variety of different loads in an IC design, this output-based receiver modeling can sometimes result in increased library file size. 
     In another embodiment, the first capacitance C_NL 1  and/or the second capacitance C_NL 2  can themselves be sets of capacitances that are based on the load capacitance C_OUT at receiver output pin  232  and/or the input slew at receiver input pin  231 . This allows cell receiver model  430 -NL to account for any coupling that occurs between receiver input pin  231  and receiver output pin  232  once the cell “turns on”. Thus, for example, the first capacitance C_NL 1  and/or the second capacitance C_NL 2  could be represented by tables of capacitance values indexed by input slew and/or output capacitance. Exemplary capacitance tables for first capacitance C_NL 1  and second capacitance C_NL 2  are provided below as tables 1 and 2, respectively. 
     
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 First Capacitance Values 
               
             
          
           
               
                   
                 C_OUT1 
                 C_OUT2 
                 C_OUT3 
                 C_OUT4 
                 C_OUT5 
               
               
                   
                   
               
             
          
           
               
                 IN_SLEW1 
                 C_NL1-a1 
                 C_NL1-b1 
                 C_NL1-c1 
                 C_NL1-d1 
                 C_NL1-e1 
               
               
                 IN_SLEW2 
                 C_NL1-a2 
                 C_NL1-b2 
                 C_NL1-c2 
                 C_NL1-d2 
                 C_NL1-e2 
               
               
                   
               
             
          
         
       
     
                                                                         TABLE 2                   Second Capacitance Values                C_OUT1   C_OUT2   C_OUT3   C_OUT4   C_OUT5                        IN_SLEW1   C_NL2-a1   C_NL2-b1   C_NL2-c1   C_NL2-d1   C_NL2-e1       IN_SLEW2   C_NL2-a2   C_NL2-b2   C_NL2-c2   C_NL2-d2   C_NL2-e2                    
The first capacitance values C_NL 1  and second capacitance values C_NL 2  in tables 1 and 2, respectively, are indexed by input slew values IN_SLEW 1  and IN_SLEW 2 , and output capacitances C_OUT 1  through C_OUT 5 . Note that just as with the above-described two-value non-linear capacitance models, different sets (tables) of capacitance values and switching voltages could be determined for different signal type-operating condition combinations.
 
       FIG. 5A  shows a flow diagram for an exemplary process for generating a two-stage capacitance receiver model (as described above with respect to  FIGS. 4A and 4B ). The receiver model can be defined in an optional “DEFINE RECEIVER MODEL” step N 500 . Specifically, the characteristics of the non-linear capacitor (e.g., capacitor C_NL in  FIG. 4B ) in the receiver model can be defined (e.g., switching voltage(s), static or load-dependent capacitance values). 
     In a “DEFINE OPERATING PARAMETERS” step N 510 , values for the relevant operating parameters are defined. For example, an output (load) capacitance for receiver can be specified. Also, a current input signal for the receiver is determined. For example, the receiver cell (e.g., receiver  230  in  FIG. 2A ) is provided with a voltage signal (e.g., driver output signal S_OUTD) having a predetermined slew, and the current flow into the receiver cell is determined (via testing or simulation). This current input signal can then be used for model generation purposes. Alternatively, the current input signal for the receiver can be derived by applying the driver output current signal to the receiver cell (where only a portion of the driver output current may flow into the receiver cell as the current input signal). 
     In a “SELECT FIRST CAPACITANCE VALUE(S)” step N 520 , a test first capacitance value (e.g., capacitance C_NL 1  in  FIG. 4B ) is selected for the receiver model. Then, in a “MODEL SIGNAL COMPARISON” step N 530 , the receiver model performance is evaluated using the output capacitance value and the current input signal determined in step N 510 . 
     As noted above with respect to  FIGS. 4A and 4B , the comparison performed in step N 530  can be between the receiver model input voltage signal and the actual receiver input voltage signal, or between the receiver model output voltage signal and the actual receiver output voltage signal. In either case, a target fit between the receiver model (input/output) signal and the actual receiver (input/output) signal is assessed in a “FIT?” step N 535 . In one embodiment, the target fit could be a match between the model delay value and the actual delay value (generally a match to within 5% of the actual delay value will provide sufficient accuracy for most timing analyses). In another embodiment, the target fit could be a match between the profile of the portion of the model receiver signal generated using the first capacitance value and the profile of the corresponding portion of the actual receiver signal. Various other fit definitions can be used in other embodiments. In any case, if the target fit is achieved, the first capacitance value is finalized in a “FINALIZE FIRST CAPACITANCE VALUE(S)” step N 540 . Otherwise, the process iterates back to step N 510  where a new first capacitance value is selected. 
     Once the first capacitance value is determined, a test second capacitance value (e.g., capacitance C_NL 2  in  FIG. 4B ) is selected in a “SELECT SECOND CAPACITANCE VALUE(S)” step N 550 . Once again, in a “MODEL SIGNAL COMPARISON” step N 560 , the receiver model performance with the test second capacitance value is evaluated using the output capacitance value and the current input signal determined in step N 510 . 
     As described with respect to steps N 530  and N 535 , a target fit between the receiver model signal and the actual receiver signal is evaluated in a “FIT?” step N 565 . In this case, the target fit could be a match between the profile of the receiver model signal generated using the second capacitance value and the profile of the corresponding portion of the actual receiver signal. Alternatively, the target fit could be a match between the model slew and the actual slew (as with the delay modeling described above, a match to within 5% of the actual slew value will generally provide sufficient accuracy for most timing analyses). 
     Note that the slew performance of a two-capacitance receiver model depends on both the value of the first capacitance and the value of the second capacitance. This slew-dependence on both capacitances is due to the fact that delay is measured between a rail voltage and a switching voltage (as described with respect to  FIG. 2B ), whereas slew is measured between a lower threshold voltage and an upper threshold voltage. Therefore, the first capacitance controls the portion of the slew between the lower threshold voltage and the switching voltage (or between the upper threshold voltage and the switching voltage for a falling signal). 
     Thus, the model slew in the comparison of step N 570  can be generated by adding the time required for the model signal to transition from the lower threshold voltage to the switching voltage using the first capacitance value, and the time required for the model signal to transition from the switching voltage to the upper threshold voltage using the test second capacitance value. The resulting model slew (for either the receiver input signal or the receiver output signal) can then be compared with the actual receiver slew (for the input signal or output signal, respectively). 
     If the target fit is detected in step N 575 , then the second capacitance value is finalized in a “FINALIZE SECOND CAPACITANCE VALUE(S)” step N 570 . Otherwise, the process iterates back to step N 550 , where a new test second capacitance value is selected. As part of this finalization, both the first and second capacitance values can be associated with the cell in a cell library (described in greater detail below with respect to  FIG. 53 ). 
     Note that once a particular first capacitance/second capacitance set of values is finalized in step N 570 , the process can loop back to step N 510  (indicated by the dotted line). Then, new input slew and/or output capacitance values can be specified for the generation of additional first capacitance/second capacitance sets. Note further that while the flow diagram in  FIG. 5A  provides a two-stage model generation process for exemplary purposes, the process can be readily extended for any number of stages (i.e., any number of different capacitance values for non-linear capacitor C_NL in  FIG. 4B ). 
       FIG. 5B  shows an embodiment of a characterized cell library  500  that incorporates a non-linear capacitance receiver model, such as described with respect to  FIG. 4A . A cell entry  510  in library  500  includes a cell identifier  511  and multiple sets of model definition values. Each set of model definition values includes first capacitance C_NL 1 , a second capacitance C_NL 2 , and a switching voltage V_SW. As described above with respect to  FIGS. 4A and 4B , first capacitance C_NL 1  can be used as the receiver model until the receiver input signal reaches switching voltage V_SW, at which point second capacitance C_NL 2  (which can comprise a single (static) capacitance value or table of capacitances) is used for the receiver model. 
     Each set of model values is referenced by a particular combination of operating conditions (OP 1 -OP 3 ) and signal types (RISE, FALL, BEST CASE, and WORST CASE). For example, for a rising receiver input signal under operating conditions OP 1 , cell  230  is modeled as a receiver by a first capacitance C_NL 1 (R 1 ), a second capacitance C_NL 2 (R 1 ), and a switching voltage V_SW(R 1 ). Similarly, for a falling receiver input signal under operating conditions OP 2 , cell  230  is modeled as a receiver by a first capacitance C_NL 1 (F 2 ), a second capacitance C_NL 2 (F 2 ), and a switching voltage V_SW(F 2 ). Each set of model values could be generated by the process described with respect to  FIG. 5A . 
     Note that while four different signal types and three different operating conditions are shown for exemplary purposes, a cell entry for a multi-capacitance receiver model can include any number of signal types and any number of operating conditions. Note further that the same switching voltage can be applied to all receiver models in a library to simplify library generation and usage. The use of a standard switching voltage (e.g., midway between the upper and lower power rail for all receiver models) can also reduce library size, since each set of model definition values would then only include two capacitance values, as shown in  FIG. 5C . A cell entry  510 -C on a library  500 -C is substantially similar to cell entry  510  shown in  FIG. 5B , except that each set of model definition values only includes a first capacitance value C_NL 1  and a second capacitance value C_NL 2 . The switching voltage is associated with cell identifier  511  (or even library  500 -C) as a whole, and therefore need not be included within individual sets of model definition values. 
     Note also that as described above with respect to  FIG. 4B , second capacitance C_NL 2  can itself comprise multiple capacitance values that are based on the load capacitance applied to the receiver. For example,  FIG. 5D  shows a cell library  500 -D that includes a cell entry  510 -D. Cell entry  510 -D is substantially similar to cell entry  510 -C shown in  FIG. 5C , except that each first capacitance entry C_NL 1  and each second capacitance value C_NL 2  is now a function of the receiver load capacitance and/or input slew. For example, the set of model definition values referenced by a rising signal and operating conditions OP 1  includes a second capacitance C_NL 2  (R 1 )[1:N], indicating that second capacitance C_NL 2 (R 1 )[1:N] can take any of N different values, with each of the capacitance values being indexed by a particular combination of load capacitance and/or input slew applied to cell  230 . In one embodiment, first capacitance values C_NL 1  and second capacitance values C_NL 2  can be represented as tables of capacitance values, such as tables 1 and 2, respectively. 
     Note further that while only two different capacitances are shown for each set of model definition values, according to other embodiments, each set of model definition values can include any number of capacitance values. For example, multiple capacitance values could be selected to generate a model receiver signal that closely matches the actual receiver signal (rather than simply matching the delay and slew characteristics of the actual receiver signal). For example, the actual receiver signal could be divided into segments, and a different capacitance value could be selected for each segment. 
       FIG. 5E  shows an exemplary embodiment of a characterized cell library  500 -E that incorporates a non-linear capacitance receiver model based on more than two capacitance values. Each set of model definition values in a cell entry  510 -E in library  500 -E includes first capacitance C_NL 1 , a second capacitance C_NL 2 , a third capacitance C_NL 3 , a first switching voltage V_SW 1 , and a second switching voltage V_SW. First capacitance C_NL 1  can be used as the receiver model until the receiver input signal reaches first switching voltage V_SW 1 , at which point the receiver model switches to second capacitance C_NL 2 . Modeling is performed using second capacitance C_NL 2  until the receiver input signal reaches second switching voltage V_SW 2 , at which point the receiver model switches to third capacitance C_NL 3  to generate the remainder of the receiver signal. 
       FIG. 6  shows a block diagram of a computer system  600  that includes a library generator  620  for translating an uncharacterized cell library  610  (which includes actual receiver signal data) into a characterized cell library  660 . The embodiment of library generator  620  shown in  FIG. 6  includes a first capacitance generator for generating a first capacitance for a two-capacitance receiver model (e.g., steps N 510 -N 540  in  FIG. 5A ), a second capacitance generator for generating a second capacitance (or set of capacitances) for the two-capacitance receiver model (steps N 550 -N 570  in  FIG. 5A ), and a model definition compiler  650  for compiling model definition data (one or more sets generated by generators  630  and  640 ) into a characterized cell library  660 . Characterized cell library  660  can be written to some form of computer-readable medium, such as memory within computer system  600 , a removable storage medium (e.g., CDROM or DVD), or a network storage location. 
       FIG. 7  shows a flow diagram for an embodiment of an analysis process (e.g., synthesis or static timing analysis) using a characterized cell library that includes a two-capacitance receiver model. In a “READ FIRST CAPACITANCE VALUE” step N 710 , a first capacitance value (e.g., C_NL 1  described with respect to  FIG. 5B ) is read from the cell library. In an optional “READ SWITCHING VOLTAGE” step N 720 , a switching voltage (e.g., V_SW described with respect to  FIG. 5B ) is also read from the cell library. Note that if a general switching voltage has been predefined (e.g., as in cell entry  510 -C in  FIG. 5C ), step N 720  can be skipped. 
     Then, a first portion of the model receiver signal (either the input signal or the output signal) is generated in a “GENERATE FIRST RECEIVER SIGNAL PORTION” step N 730 . A second capacitance value (e.g., C_NL 2  from  FIG. 5B ) is then read from the cell library in a “READ SECOND CAPACITANCE VALUE(S)” step N 740 . Note that if the second capacitance is a function of the receiver load capacitance (e.g., as described with respect to  FIG. 5D ), the load capacitance coupled to the receiver can be read in an optional “READ RECEIVER LOAD CAPACITANCE” step N 750 . 
     The remainder of the model receiver signal is generated in a “GENERATE SECOND RECEIVER SIGNAL PORTION” step N 760 . Then, from the completed model receiver signal, the model delay and slew values can be determined, in a “DELAY/SLEW DETERMINATION” step N 770 . 
     The various embodiments of the structures and methods of this invention that are described above are illustrative only of the principles of this invention and are not intended to limit the scope of the invention to the particular embodiments described. Thus, the invention is limited only by the following claims and their equivalents.