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Modelling and Simulation Concepts


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Modelling and Simulation Concepts

  1. 1. Outline - Structural Modeling - Analog Behavioral Modeling Modelling and Simulation Concepts - Hierarchical simulation - Ideal Switches KTH/IMIT/LECS/ARusu Structural and Functional Modeling Describing the circuits using circuit elements, like resistors, Modeling and Simulation inductors, capacitors, diodes, transistors, for which there is a direct correspondence with the physical components from the printed circuit board or from an integrated circuit, is based on a structuralStructural Modeling – semiconductor devices (nonlinear representation (structural modeling based on describing theelements) physical structure of the circuit element by means of a set ofFunctional Modeling – any linear/nonlinear elements model parameters described with .MODEL).(devices or integrated circuits) For simulating the complex circuit elements (like OpAmp) is used the method of functional (behavioral) description which consists Hierarchical Simulation – high level circuits (high of grouping more components in a block, by the criteria of thecomplexity) function that it generates (for example: gain function, integration function, derivative function, NAND function, NOR function etc). The SPICE description of the block will then be an equivalent circuit that generates the same function as the implementation at component level (SPICE primitives). This functional model may be built with less physical elements and specific SPICE elements for functional description, like the controlled sources (especially those from Analog Behavioral Modeling) and ideal switches.The simulation time for the functional models is considerably The hierarchical simulation using subcircuits (.SUBCKT)shorter than the time needed for simulating the circuitdescribed at the physic level of used components in physicalassembling. For modeling at high level (describing complex circuits) it isIn SPICE exists the possibility of defining and using recommended hierarchical method, assured by the capacitysubnetworks or blocks that functionally describe various of PSPICE of describing and repeated calling of subcircuits.circuits (OpAmp, filter, comparator, bistable, etc.), by the In hierarchical description, different blocks can be describedsubcircuits (described by .SUBCKT, the body of the at different levels of precision. The simplest representation ofsubcircuit .ENDS). a given block function is the ideal model (i.e. ideal OpAmp asThe most general and powerful modeling concept is the a gain function, described by a controlled source). For themacromodeling. simulation with sufficient precision and an adequateMacromodels put together functional elements (as controlled convergence, were elaborated more complex models, basedsources) for describing some elements with precise nonlinear on using of some pure functional models which gives themodels of other elements (as diodes, transistors). In this way relation input/output of the circuit, reproducing thewe obtain a simple circuit - the macromodel, with which we characteristics of the circuit. In this models we put togetherobtain the original circuit behavior and a short time of the primitives PSPICE and ABM functions (defined with thesimulation. Boyle who described the first macromodel of controlled sources).OpAmp applied this concept for the first time. 1
  2. 2. Remarks:* A circuit block which appears more than once in a circuit or Example: OpAmp 741 Subcircuitmore and consists of SPICE primitives is defined as a subcircuit * connections: | non-inverting inputand is accessed as an individual component. * | | inverting input * Between the .MODEL and .SUBCKT definitions have the * | | | positive power supplyfollowing similarity: while .MODEL defines a set of modelparameters that are to be used in common by all the devices that * | | | | negative power supplyaccess it, .SUBCKT represents the topology of a circuit that, by * | | | | | outputits terminals or external nodes, can be connected anywhere and .subckt uA741 1 2 3 4 5anytime in the external circuit. c1 11 12 8.661E-12* The number of hierarchical levels which can be defined byusing the .SUBCKT definition, is unlimited (a subcircuit may c2 6 7 30.00E-12contain another subcircuit, except for a circular one). dc 5 53 dy* After the hierarchy of a circuit has been defined, the designer de 54 5 dymust choose different detail and precision levels for eachhierarchical block, the same as in the case of choosing the dlp 90 91 dxtransistors’ models (more simple or more complex, function of dln 92 90 dxthe specified model parameters for representing the various dp 4 3 dxsecondary effects). egnd 99 0 poly(2),(3,0),(4,0) 0 .5 .5 fb 7 99 poly(5) vb vc ve vlp vln ro1 8 5 50 +0 10.61E6 -1E3 1E3 10E6 -10E6 ro2 7 99 100 ga 6 0 11 12 188.5E-6 rp 3 4 18.16E3 gcm 0 6 10 99 5.961E-9 vb 9 0 dc 0 iee 10 4 dc 15.16E-6 vc 3 53 dc 1 hlim 90 0 vlim 1K ve 54 4 dc 1 q1 11 2 13 qx vlim 7 8 dc 0 q2 12 1 14 qx vlp 91 0 dc 40 r2 6 9 100.0E3 vln 0 92 dc 40 rc1 3 11 5.305E3 .model dx D(Is=800.0E-18 Rs=1) rc2 3 12 5.305E3 .model dy D(Is=800.00E-18 Rs=1m Cjo=10p) re1 13 10 1.836E3 .model qx NPN(Is=800.0E-18 Bf=93.75) re2 14 10 1.836E3 .ends ree 10 99 13.19E6 Functional Modeling: Controlled Sources Analog Behavioral Modeling Using Controlled Sources In PSPICE there exists the next models for controlled source:The real subcircuits describe the function generated by a · Voltage controlled voltage source (E):circuit block using several SPICE primitives, of which the Linear: Vout=E(Vin)basic ones are the linear controlled sources, the nonlinear Non-linear: Vout=E(Vin1, Vin2,…, Vink)(polynomial) ones and the controlled sources using the · Current controlled current source (F):analog behavioral modeling. Unlike the structural models,the functional (behavioral) models generate the same function Linear: Iout=F(Iin)as the block it represents, using only few controlled sources Non-linear: Iout=F(Iin1, Iin2, …, Iink)within a circuit whose topology is different from the original · Voltage controlled current source (G):one. Using the properties of the controlled sources, along the Linear: Iout=G(Vin)years in SPICE there have been developed different Non-linear: Iout=G(Vin1, Vin2, …, Vink)functional models which afterwards stood at the basis ofelaborating the macromodels for all the components and the · Current controlled voltage source (H):physical circuits ( analogue, digital and mixed analogue- Linear: Vout=H(Iin)digital IC). Non-linear: Vout=H(Iin1, Iin2,…, Iink) 2
  3. 3. Observations: The input of a voltage-controlled source has infinite impedance, which produce a null current. To avoid the errors of type floating nodes, we can put in series with the controlled source very high resistance (usually E1 F1 G1 H1 very high value 1MEGohm) + + + + For the current controlled sources (F and H) the input - - - - is a voltage source of which current controls the EPOLY FPOLY GPOLY HPOLY controlled source. Linear <Xout>=<Xin><gain> Examples: Nonlinear (polynomial) Linear: <Xout>=f(<Xin1>,…,<Xink>) E1 (6, 0) (11,12) 188.5E-6 ; V(6,0)=v(11,12)*(188.5e-6) Defined by a polynomial function of dimension k, POLY(k) given by the polynomial coefficients P0,P1,P2,…,Pk; k can GIee (20,7),(24,0) 1.0 ; I(Giee)=v(24,0)*1 be: 1,2,… Nonlinear: The polynomial function of dimension 3(when the control is Egnd 99 0 poly(2) (3,0),(4,0) 0 .5 .5 given by three sources), POLY(3) is: *v(99,0)=0+0.5*v(3,0)+0.5*v(4,0)Xout=f(X1,X2,X3)= P0+ Fb 7 99 poly(5) vb vc ve vlp vln +P1X1+P2X2+P3X3+ +0 10.61E6 -1E3 1E3 10E6 -10E6 Hvref 22 7 POLY(1) Vmon 7.15 0.01 +P4X21+P5X1X2+P6X1X3+P7X22+P8X2X3+P9X23+ *v(22,7)=7.15+0.01*I(Vmon) +P10X31+P11X21X2+… Analog Behavioral Modeling Implementation Analog Behavioral Modeling (ABM) Transfer functions fall into two broad categories: : The Analog Behavioral Modeling feature allows for flexible Modeling Non-linear (and linear), Instantaneous descriptions of electronic components in terms of a transfer Relationships – these models enforce a direct function. In other words, a mathematical relationship is used response to the output at each moment in time: to model a circuit segment instead of designing the circuit - mathematical expressions (VALUE) segment component by component. ABM functions are applicable only at voltage controlled - lookup table (TABLE) sources: E,G. Frequency-Domain Device Modeling – these The input-output relation: models are characterized by output that depends on <Xout>=f(<Xin>) the current input as well as the input history: is described by a transfer function using the analog behavior - Laplace transform (LAPLACE) modeling. - frequency response table (FREQ) 3
  4. 4. Lookup TablesMathematical Expressions ETABLE and GTABLE – the transfer function is described by aEVALUE and GVALUE - the transfer function is written as a table with values (<input>, <output>) Example: mathematical expression in standard format. E_demod_Comparator 59 0Examples: +TABLE { V(11, 0) } ( (-1uv,0.2v) (1uv,3.5v) )E_opamp_ideal out 0 VALUE {(2e+5)*v(inp,inn)} G_diode a k TABLE {V(a,k)}E_Test_VCO_EVCO 53 0 +(-4.71,100m) (-4.7, 10m) (-3,10n) (0,0) (0.2, 1p) +(0.4, 1n) (0.6,0.1m) (0.7, 0.5m) (0.8,1m)+VALUE { SIN(6.28*1E6*TIME*V(19, 0)) } Laplace Transforms Note that the VALUE controlling function is the recommended ELAPLACE and GLAPLACE – the transfer function is described alternative to the POLY form. by a function Laplace Transform (in s)ESUM and GSUM, EMULT and GMULT – realize the sum Example: function respectively multiplication between the two inputs. ELP 7 0 LAPLACE {v(6)}Examples: +{1/(1+0.001*s)} G_lossy 1 2 LAPLACE {V(in)}E_Test_Summer 47 0 VALUE {V(84,0)+V(104,0)} +{exp(-sqrt(C*s*(R+L*s)))}E_Test_Multiplicator 5 0 VALUE {V(3,0)*V(7,0)} EHP 2 3 LAPLACE {V(4)} +{(1+0.01*s)/(1+0.001*s)} Example: R1 1k E1 R2 Frequency Response Tables IN+ OUT+ 1k V2 EFREQ and GFREQ – the transfer function is described by R3IN- OUT- a table with the frequency response (<freq>, <amplitude 1meg ELAPLACE [db]>, <phase [degrees]>) 0 V(%IN+, %IN-) Example: {(1-0.01*s)/(0.001*s*s)} EBP 5 7 FREQ {V(3)} 100GV +(0, -80, -180) +(1k,-3,0) +(10k, 0, 0) 50GV +(100k,-3,0) +(1meg,-80,+180) 0V 1.0uHz 100uHz 1.0Hz 10KHz V(R2:1) Frequency Ideal Switches Ideal Switches The available switch device types are:Ideal switches are implemented to allow circuit connections Voltage-Controlled Switch (S)to be changed during simulation. The switches may be Current-Controlled Switch (W)voltage or current controlled. To create a time controlled S3 SW+ SW- CTRL+ CTRL- SBREAKswitch, simply connect the switch control nodes to a voltage .MODEL SBREAK VSWITCH (RON=1ROFF=1E+6 VON=1 VOFF=0)source with the appropriate voltage vs. time values. W1 SW+ SW- VCTRLI WBREAKThe switch is not “ideal” because it has a finite “on” .MODEL WBREAK ISWITCH (RON=1 ROFF=1E+6 ION=1E-3 IOFF=0)resistance and “off” resistance , and changes smoothly S3between the two as its control voltage changes. This behavior + +is important to allow PSpice to find a continuous set of - - outsolutions to the circuit being simulated. In practice, the “on” Sbreak inresistance may be made very small compared to their other W1circuit impedances, and the “off” resistance may be made +very large compared to the other circuit impedances. ctrl - Wbreak 4
  5. 5. Example: S1 - - R1 + + out 15V Sbreak1 {rp} V1 S2 C1 - - + 0 1u 0 + 0 Sbreak2 Vctrl 0 0 2V 0 1V 0 0V 0s 5s m 1m 0s VR:) VS:) (12 (21 Tm ie 5