Abstract:
A computer program product and method of simulation involve the present computer simulation model of a lossy transmission line. The model uses hybrid model at each end of the transmission line, each hybrid model coupled to a port of the transmission line. Each hybrid model is coupled to a forward path model and a reverse path model, such that simulated signals pass through the forward path mode enroute from a first hybrid to the second hybrid, and through the reverse path model enroute from the second hybrid to the first hybrid. At each end of the transmission line there is also a reflection model coupling between the reverse path model and the forward path model.

Description:
FIELD OF THE DISCLOSURE  
         [0001]    The present disclosure relates to the field of simulation of analog circuits on digital computers. In particular, a new model is disclosed of particular utility for simulating lossy transmission lines using conventional circuit simulators.  
         BACKGROUND  
         [0002]    Since the introduction of Berkeley Spice in the early 1970&#39;s, circuit simulation has become an invaluable tool in the design of analog and digital circuits. It is common for modern designers to use circuit simulators not only to test designs before constructing them, but to optimize many circuit parameters. Spice is capable of DC, AC, and transient simulations of a wide variety of circuits. Many circuit simulators available today trace many of their features, including syntax and capabilities, to Spice, and several use algorithms derived from those of Spice. Common analog circuit simulators include Hspice, Pspice, and other Berkeley-Spice derivatives including Hpspice, Powerspice Ispice, Eldo, Ispec, Mtime, and Spectre.  
           [0003]    Over recent decades, simulation models for active devices like transistors have become quite accurate and efficient even for the high-speed, small geometry, devices found in modem integrated circuits. Simulation models for ideal passive devices like resistors and capacitors are also efficient and accurate.  
           [0004]    Real world circuits contain circuitry beyond active devices and ideal passive devices. Real circuits have internal and external interconnect that can be considered lossy transmission lines. Real transmission lines are typically lossy due to conductor resistances, including skin effect resistance, and dielectric losses. Transmission lines also have delay, and frequency-dependent reflections may arise because of impedance mismatches at ends of the transmission line. Accurate modeling and simulation of delay and reflections can be of great importance to circuit and system designers.  
           [0005]    In the early days of integrated circuits, designers were able to ignore the lossy transmission line characteristics of internal interconnect. As circuit speed increased in recent years, it has become necessary to consider transmission line effects that historically were ignored.  
           [0006]    It is therefore necessary to have a fast, efficient, accurate, lossy transmission line simulation model for circuit simulation of circuitry containing lossy transmission lines. It is also desirable that the simulation model function for DC, AC and transient simulations.  
           [0007]    Some circuit simulators incorporate proprietary transmission line models. For example, the Hspice W element uses a set of proprietary algorithms for modeling transmission lines. The Hspice W element description of the transmission line characteristics is prepared in terms of frequency, the analysis by Spice during AC analysis is done in the frequency domain. This model does not readily transfer to the time domain, forcing use of a completely different algorithm for transient simulations. The Hspice W element therefore executes AC and transient simulations with separate algorithms. It is known in the industry that the W-Element had significant errors in the time domain algorithm for several years after its introduction. The Hspice W element transmission line is not found on most other simulators, circuit simulations that use them are not portable to those simulators.  
           [0008]    It is desirable to model lossy transmission lines in a simple, fast, efficient, portable, and accurate way. To ensure portability, it is desirable that a transmission-line model be built from those circuit elements commonly found in Spice, Spice-derived, and Spice-like analog circuit simulators. It is also desirable that the model be implemented in Spice components that can executed without alteration in AC and transient analysis.  
           [0009]    Spice, Spice-like, and Spice-derived circuit simulators generally use the first character of each line of source to determine a component type. They provide primitives for the following component types:  
                                   First Character   Component Type                   R   Resistor       C   Capacitor       L   Inductor       E   Voltage Dependent Voltage Source       T   Ideal (lossless) Transmission Line       X   Subcircuit invocation       V   Voltage source       G   Voltage Dependent Current Source       H   Current Dependent Voltage Source                  
 
           [0010]    While Spice provides an integral transmission line model, this typically models an ideal, lossless, transmission line as opposed to a lossy transmission line.  
           [0011]    A commonly used circuit model for lossy transmission lines is an R-L-C ladder. The R-L-C ladder model uses cells containing a resistor, an inductor, and a capacitor. For balanced transmission lines, each cell contains two resistors, two inductors, and a capacitor. The cell is repeated multiple times, repetition increases accuracy of the model. While an R-L-C ladder model can provide portability and, if sufficient cells are used, reasonable accuracy, it has drawbacks at higher frequencies. Lossy transmission lines have a complex frequency dependence which can be difficult to model with fixed, discrete elements. For good accuracy, each frequency dependent resistor in FIG. 1 may need to be modeled using as many as 30 elements. High frequencies demand many R-L-C sections for accuracy, so the component count of the model can become quite large. The geometry of the model can also generate an ill-conditioned matrix which can cause severe round-off errors in the Spice engine. Round-off errors are undesirable because, the Spice simulation loses accuracy and may fail to converge. Failure to converge causes simulation to cease, and data is lost beyond this point in the analysis. What is needed is a new approach to the modeling of lossy transmission lines that does not require a large number of elements, can be used for transient and frequency analysis, and can accommodate variable lengths and frequencies without requiring large numbers of elements.  
         SUMMARY  
         [0012]    A transmission line circuit simulation model is disclosed that utilizes hybrids at each end, with separate forward and reverse paths. In one embodiment, each of the forward and reverse paths includes sections for modeling loss, including frequency-dependent loss, and delay. In one embodiment, a balanced transmission line is modeled. In another embodiment, an unbalanced transmission line is modeled. 
       
    
    
     BRIEF DESCRIPTION OF THE FIGURES  
       [0013]    [0013]FIG. 1 is a schematic diagram of a conventional R-L-C model of a transmission line.  
         [0014]    [0014]FIG. 2 is a block diagram of a model of balanced transmission line having separate paths in forward and reverse directions.  
         [0015]    [0015]FIG. 3 is a schematic diagram of a model of frequency-dependent dielectric loss.  
         [0016]    [0016]FIG. 4 is a flowchart of a method for simulation with the model herein described.  
         [0017]    [0017]FIG. 5 is a block diagram of a computer system for simulating with the model herein described. 
     
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS  
       [0018]    [0018]FIG. 1 illustrates a conventional R-L-C model of a transmission line  100 . This model is assembled from a repeating unit  102  containing inductors  104 , resistors  106 , and capacitors  108 . While only three repeating units  102  are illustrated, practical models may require many times this number. In this model, resistors  106  provide loss. Additional resistors, capacitors, and inductors (not shown) may be necessary to properly model frequency-dependent components of loss such as skin-effect loss; for example each resistor  106  may need to be modeled with a large number of resistor and inductor models connected in series-parallel.  
         [0019]    Most Spice, Spice-like, and Spice-derived simulators available today allow use of node names in place of node numbers, node numbers are retained in the example code for utmost portability. Further, node  0  is ground, as it is in standard Berkeley Spice and derivatives such as Synopsys HSpice. The reader is referred to any standard text on Spice for a description of Spice syntax.  
         [0020]    A transmission line model  200  having separate forward and reverse conduction paths is illustrated in FIG. 2. Each port of the transmission line model, such as input Port C, couples to a bidirectional port of a model of a hybrid, such as hybrid  201 . Hybrid  201  serves to couple separate forward and reverse signal paths to bidirectional Port C. The forward signal path couples to an output port of modeled hybrid  201 , the reverse signal path couples to an input port of hybrid  201 . Hybrid  201  couples simulated energy from the reverse path to Port C, and from Port C to the forward path. Both the forward and reverse paths are modeled in subcircuit loss block  202  as illustrated.  
         [0021]    A top level subcircuit for the lossy transmission line of FIG. 2 is as follows.  
                                                                                 .subckt tran_wh in inrtn out outrtn P_Lo=0 P_Co=0 P_Ro=0       P_Go=0       P_Rs=0 P_Gd=0 P_len=0       * Terminals:            * in   Port 1 signal           * inrtn   Port 1 return       * out   Port 2 signal       * outrtn   Port 2 return            * Returns are isolated from node 0 and each other       * Parameters:       * Lo = Inductance Henrys/unit length       * Co = Capacitance Farads/unit length       * Ro = DC resistance Ohms/unit length       * Go = DC parallel conductance Siemens/unit length       * Rs = Skin effect resistance Ohms/sqrt(Hertz)/unit length       * Gd = Dielectric conductance Siemens/Hertz/unit length       * len = Length of trans line (same length unit as above!!)       .param Td=‘sqrt(P_Lo*P_Co)*P_len’       * Time delay of trans line       .param Zo=‘sqrt(P_Lo/P_Co)’       * Characteristic impedance of trans line       .param kdc=‘P_Ro/2/Zo*P_len+1e−12’       * ONE HALF DC resistance of trans line normalized to Zo       .param cdc=‘1/2/kdc*(P_Rs/(P_Ro+1e−12))**2’       .param tand=‘P_Gd/6.283/P_Co’       * Loss tangent of dielectric       .param Fs=‘1/(P_Rs*P_len/Zo/2+1e−12)**2’       * Characteristic frequency of skin effect loss       .param Fd=‘1/(3.142*tand*P_len*sqrt(P_Lo*P_Co)+1e−20)’       * Characteristic frequency of dielectric loss            Xhy1 in inrtn 10 21 hybrid P_Zhy=‘Zo’   $ Hybrid splitter            Xloss1 10 11 20 21 loss P_kdc=‘kdc’ P_cdc=‘cdc’ P_Td=‘Td’       P_Fs=‘Fs’       P_Fd=‘Fd’       * Loss circuit two way includes scattering parameters       * S21 S12            Xhy2 out outrtn 20 11 hybrid P_Zhy=‘Zo’   $ Hybrid splitter       .ends tran_wh                  
 
         [0022]    Example Spice code for each hybrid  201 ,  212  is as follows, where P_Zhy is a characteristic impedance of the transmission line:  
                                                   .subckt hybrid 1 2 5 6 P_Zhy=0           *(terms 1 &amp; 2) to forward (5,0) and reverse (6,0) signal paths            * 1 = line + (single mode only)            * 2 = line − (isolated from ground)            * 5 = fwd/rev out            * 6 = rev/fwd in           V1 1 3 0           V2 3 4 0           Rterm1 4 2 ‘P_Zhy’           G1 2 3 6 0 ‘2/P_Zhy’           H1 5 0 poly(2) V1 V2 0 ‘P_Zhy/2’ ‘P_Zhy/2’           .ends hybrid                      
 
         [0023]    The forward path models energy transfer, including time delay and loss, from port C to port D, while the reverse path models energy transfer, including time delay and loss, from port D to port C. The reverse path is coupled to the forward path with reflector model  203 . Reflector  203  allows a portion of signals on the reverse path to be reflected onto the forward path, while Reflector  214  allows a portion of signals on the forward path to be reflected onto the reverse path. Reflectors  203 , 214 , include a model of the impedance increase resulting from the series resistance of the transmission line. This reflection is helps to correctly model the DC resistance of the line. Example Spice code for the reflector model  203  is as follows, where the characteristic impedance of the transmission line within the loss subcircuit is set as one ohm; reflector  214  is similar.  
         [0024]    In the example code, subcircuit “loss” models both forward and reverse paths  
                                                             .subckt loss 11 16 21 26 P_kdc=0 P_cdc=0 P_Td=0 P_Fs=0 P_Fd=0       * 11 = line_1 forward in       * 16 = line_1 forward out       * 21 = line_2 reverse in       * 26 = line_2 reverse out       R1 11 17 1            R2 17 0 ‘P_kdc’   $P_kdc parameter determines the amount of            reflection.       C2 17 0 ‘P_Td/P_kdc’            E1 26 25 17 0 1.0   $coupling of reverse path into forward path                  
 
         [0025]    The forward path continues with a DC resistance loss model  204  of the transmission line. Example Spice code for the DC resistance model is as follows, where the characteristic impedance of the attenuation circuit is 1 ohm:  
                                                       R3 11 12 ‘P_kdc’   $S21 DC loss term           C3 11 12 ‘P_cdc’                      
 
         [0026]    Skin resistance replaces the DC resistance at a frequency where the two are of equal magnitude, so the capacitor C 3  effectively removes DC resistance R3 from the model at the proper frequency.  
         [0027]    Next is an ideal transmission line modeling transmission line delay  206 .  
                                                                 T1 12 0 13 0 Z0=1 TD=‘P_Td’                R4 13 0 1   $S21 delay term                      
 
         [0028]    Next are models for skin loss  208  and dielectric loss  210 .  
                                       Xs1 13 14 attn_skin P_Fs=‘P_Fs’   $S21 skin loss term       Xd1 14 15 attn_diel P_Fd=‘P_Fd’   $S21 dielectric loss term       E2 16 15 27 0 1.0   $S22 buffer output of lossy line                  
 
         [0029]    The reverse path  216  is similar to the forward path:  
                                       R5 21 27 1           R6 27 0 ‘P_kdc’   $S22 reflection term couples to E2       C6 27 0 ‘P_Td/P_kdc’       R7 21 22 ‘P_kdc’   $S12 DC loss term       C7 21 22 ‘P_cdc’       T2 22 0 23 0 Z0=1 TD=‘P_Td’       R8 23 0 1   $S12 delay term       Xs2 23 24 attn_skin P_Fs=‘P_Fs’   $S12 skin loss term       Xd2 24 25 attn_diel P_Fd=‘P_Fd’   $S12 dielectric loss term       .ends loss                  
 
         [0030]    Frequency-dependent skin effect resistance loss  208  is modeled with the following model, illustrated in more detail in FIG. 3:  
                                                   *Fs is frequency at which transmission is exp(−1)=.3679           This circuit approximates v(out)/v(in)=exp(−sqrt(f/fs))           .subckt attn_skin 10 9 P_Fs=0           .param frad=‘6.283*P_Fs’           .param a1=.008           .param a2=.0075           .param a3=.033           .param a4=.105           .param a5=.310           .param a6=1.00           .param a7=1.90           .param a8=130.           .param c1=.145                      
 
         [0031]    Skin-effect model  208  device E 1   302  is a voltage-dependent voltage source, dependent on an input  304  to the skin effect mode, that partially isolates this portion of the transmission line model from other circuitry of the model. It is anticipated that the voltage-dependent voltage source model may be substituted with a voltage-sensing resistor and a current-dependent voltage source model. Partial isolation simplifies the modeling and makes it easier to calculate model parameters. The model has several sets of resistor-inductor pairs, such as R 1   306  and L 1   308 , R 2   310  and L 2   312 , and R 6   314  and L 6   316  that combine to provide a series impedance that increases with frequency. The skin-effect model  208  also has at least one capacitor, such as C 0   318 , that provides a shunt impedance that decreases with frequency. The skin-effect model  208  output  320  therefore has a frequency-dependent characteristic. It is anticipated that the number of resistor-inductor pairs may vary from the six pairs illustrated, greater accuracy can be achieved at a cost in simulation time if eight pairs are used, while four pairs may suffice for some simulations; a pair count between four and eight will suffice for most simulation purposes.  
                                                   E1 1 0 10 0 1.000           R1 1 2 ‘a1’           L1 1 2 ‘a1*100000/frad’           R2 2 3 ‘a2’           L2 2 3 ‘a2*10000/frad’           R3 3 4 ‘a3’           L3 3 4 ‘a3*1000/frad’           R4 4 5 ‘a4’           L4 4 5 ‘a4*100/frad’           R5 5 6 ‘a5’           L5 5 6 ‘a5*10/frad’           R6 6 7 ‘a6’           L6 6 7 ‘a6/frad’           R7 7 8 ‘a7’           L7 7 8 ‘a7/10/frad’           R8 8 9 ‘a8’           L8 8 9 ‘a8/100/frad’           R0 9 0 1.000           C0 9 0 ‘c1/frad’           .ends attn_skin                      
 
         [0032]    Parameters a1 through a8, and c1 are chosen to approximate a mathematical function Vout/Vin=exp(−sqrt(f/Fs)) where f is the frequency variable, and Fs is a scaling parameter that centers the response at a desired frequency. The mathematical function depicts the frequency-dependent loss caused by the skin effect in typical conductors used in electronic circuitry. Once a1-a8 and c1 are chosen, scaling parameter Fs specifies the skin effect loss function for a particular transmission line length and metal conduction characteristics.  
         [0033]    Dielectric loss  210  of the transmission line is modeled with the following attenuator model:  
                                                   *Fd is frequency at which transmission is exp(−1)=.3679           *This circuit approximates v(out)/v(in)=exp(−f/fd)           .subckt attn_diel 10 7 P_Fd=0           .param frad=‘6.283*P_Fd’           .param a1=.018           .param a2=.093           .param a3=.340           .param a4=.760           .param a5=.160           .param c6=.440           .param a6=13.0           .param c7=1.42           E1 1 0 10 0 1.000           R1 1 2 ‘a1’           L1 1 2 ‘a1*100/frad’           R2 2 3 ‘a2’           L2 2 3 ‘a2*10/frad’           R3 3 4 ‘a3’           L3 3 4 ‘a3*3.162/frad’           R4 4 5 ‘a4’           L4 4 5 ‘a4/frad’           R5 5 6 ‘a5’           L5 5 6 ‘a5/3.162/frad’           C6 6 0 ‘c6/frad’           R6 6 7 ‘a6’           L6 6 7 ‘a6/10/frad’           R0 7 0 1.000           C7 7 0 ‘c7/frad’           .ends attn_diel                      
 
         [0034]    Dielectric loss parameters a1 through a6, c6 and c7 are chosen to approximate a mathematical function Vout/Vin=exp(−f/Fd) where f is the frequency variable, and Fd is a scaling parameter that centers the response at a desired frequency. The mathematical function depicts the frequency-dependent loss for typical dielectrics used in electronic circuitry. Once a1-a6, c6 and c7 are chosen, scaling parameter Fd is sufficient to specify the dielectric loss function for any line length or dielectric loss characteristic.  
         [0035]    It is anticipated that the order of model elements in the forward and reverse conduction paths may vary from that illustrated. For example, it is expected that Dielectric Loss module  210  may be swapped in the forward path with Skin Effect Resistance Loss module  208  with no noticeable change in model performance.  
         [0036]    The forward path couples to an In port of the transmission line&#39;s modeled output hybrid  212 , the reverse path couples to the modeled hybrid&#39;s Out port.  
         [0037]    In a particular embodiment, the present transmission line model is provided as a subcircuit. The subcircuit is instantiated in a user&#39;s circuitry model wherever a transmission line is required in the simulated circuit. The model is typically invoked with the following parameters:  
                                                       P_Lo   A characteristic inductance of the line,           P_Co   A characteristic capacitance of the line,           P_len   A length of the line,           P_Ro   A DC resistance of the line           P_Go   A DC leakage conductance line-line.           P_Rs   A skin-effect loss resistance of the line,           P_Gd   A dielectric loss parameter,                      
 
         [0038]    P_L o  is the inductance per meter of the transmission line structure. The inductance and other parameters are distributed through the length of the line, and the actual response of the line is determined from the solution of the telegrapher&#39;s equation.  
         [0039]    P_C o  is the capacitance per meter. In the two line model, P_C o  must be the sum of the line to ground capacitance and mutual capacitance between the lines (C m ). The two line model is assumed to be symmetric, so C o1 =C o2 .  
         [0040]    P_R o  is the series resistance per meter at DC. This is specified as the resistance of the center conductor, since for practical DC cases, ground return resistance is small. This resistance increases slightly at frequencies in the hundred KHz range, because the ground return currents are forced by the EM fields to gather in the nearest vicinity of the signal within the ground return structure  
         [0041]    P_R s  is the skin effect parameter. At higher frequencies in the tens of MHz range, the widely known skin effect causes currents in the conductors to move away toward the surface of the metal. This causes the effective series resistance of the conductors to increase proportional to the square root of frequency: R effective =R s *sqrt(freq). In this case, the return path resistance is very important, because the EM fields are determining the pattern of the ground return currents. The single line model P_R s  includes the ground return resistance in the P_R s  parameter. The units for P_R s  are ohms/sqrt(Hz)/meter.  
         [0042]    P_G o  is the DC component of the leakage conductance from line to ground. Because low leakage insulators are used in computer systems, this parameter is ignored.  
         [0043]    P_G d  is the dielectric loss parameter. Although insulators have a nearly infinite DC resistance, their polarization properties are not perfect. All dielectrics will exhibit an energy loss on polarization akin to hysteresis loss. Each polarization reversal causes a fixed loss of energy, so that there is a power loss under AC excitation that is proportional to the frequency. This is a material property, so different materials will exhibit different losses. The P_G d  parameter models the dielectric loss as a conductance from signal to ground: G effective =P_G d *freq. The units of P_G d  are Siemens/Hz/meter, or for old timers, Mhos/Hz/meter.  
         [0044]    P_Len is the length of the transmission line in meters.  
         [0045]    [0045]FIG. 4 illustrates a method  400  of simulating circuits with the herein described transmission line model. A user models  402  the circuit in a format suitable for a Spice, Spice-like, or Spice-derived circuit simulator. The circuit is a circuit for which the user needs a transmission line model. The user then determines appropriate parameters  404  for the transmission line model. These parameters may be calculated based on measurements of a transmission line, or extracted from a table having parameters for typical transmission lines whether they be stripline, twisted pair, coaxial cable, or integrated circuit internal interconnect. The user invokes  406  the model with the determined parameters in simulation source. The simulation source, with circuit model and transmission line model, is then read  408  into a memory system  502  of a simulation system  500  such as the circuit simulation system illustrated in FIG. 5, and the simulation is run  410  by simulator code  503  running on a processor  504  of the simulation system  500 .  
         [0046]    A computer program product is any machine-readable media, such as an EPROM, ROM, RAM, DRAM, disk memory, or tape, having recorded on it computer readable code that, when read by and executed on a computer, instructs that computer to perform a particular function or sequence of functions. The computer readable code of a program product may be a program, such as a Spice-like simulator, or a computer model readable and executable by a program. A computer system having memory, the memory containing the heretofore described circuit model, such that the model may be read by a processor of the computer and induce a simulator running on the processor to simulate a transmission line, is a computer program product.  
         [0047]    While the forgoing has been particularly shown and described with reference to particular embodiments thereof, it will be understood by those skilled in the art that various other changes in the form and details may be made without departing from the spirit and hereof. It is to be understood that various changes may be made in adapting the description to different embodiments without departing from the broader concepts disclosed herein and comprehended by the claims that follow.