hspice book hspice ch25 1 Thu Jul 23 19 10 43 1998 Chapter 24 Performing Pole Zero Analysis Pole zero analysis is a useful method for studying the behavior of linear timeinvariant networks and may be applied to the design of analog circuits such as amplifiers and filters It may be used for determining the stability of a design and it may also be used to calculate the poles and zeroes for specification in a POLE statement as Using Pole Zero Analysis on page 24 3 describes Pole zero analysis is characterized by the use of the PZ statement as opposed to pole zero and Laplace transfer function modeling which employ the LAPLACE and POLE functions respectively These are described in Using Pole Zero Analysis on page 24 3 This chapter covers these topics Understanding Pole Zero Analysis Using Pole Zero Analysis Star Hspice Manual Release 1998 2 24 1 hspice book hspice ch25 2 Thu Jul 23 19 10 43 1998 Understanding Pole Zero Analysis Performing Pole Zero Analysis Understanding Pole Zero Analysis In pole zero analysis a network is described by its network transfer function which for any linear time invariant network can be written in the general form a0 s m a1 s m 1 am N s H s D s b0 s n b1 s n 1 bn In the factorized form the general function is a 0 s z 1 s z 2 s z i s z m H s b 0 s p 1 s p 2 s p j s p m The roots of the numerator N s that is zi are called the zeros of the network function and the roots of the denominator D s that is pj are called the poles of the network function S is a complex frequency1 The dynamic behavior of the network depends upon the location of the poles and zeros on the network function curve The poles are called the natural frequencies of the network In general you can graphically deduce the magnitude and phase curve of any network function from the location of its poles and zeros2 The section References at the end of this chapter lists a variety of source material addressing transfer functions of physical systems3 design of systems and physical modeling4 and interconnect transfer function modeling5 6 24 2 Star Hspice Manual Release 1998 2 hspice book hspice ch25 3 Thu Jul 23 19 10 43 1998 Performing Pole Zero Analysis Using Pole Zero Analysis Using Pole Zero Analysis Star Hspice uses the Muller method7 to calculate the roots of polynomials N s and D s This method approximates the polynomial with a quadratic equation that fits through three points in the vicinity of a root Successive iterations toward a particular root are obtained by finding the nearer root of a quadratic whose curve passes through the last three points In Muller s method the selection of the three initial points affects the convergence of the process and accuracy of the roots obtained If the poles or zeros are spread over a wide frequency range choose X0R X0I close to the origin to find poles or zeros at zero frequency first Then find the remaining poles or zeros in increasing order The values X1R X1I and X2R X2I may be orders of magnitude larger than X0R X0I If there are poles or zeros at high frequencies X1I and X2I should be adjusted accordingly Pole zero analysis results are based on the circuit s DC operating point so the operating point solution must be accurate Consequently the NODESET statement not IC is recommended for initialization to avoid DC convergence problems PZ Pole Zero Statement The syntax is PZ output input PZ invokes the pole zero analysis input input source which may be any independent voltage or current source name output output variables which may be any node voltage V n or any branch current I element name Examples PZ PZ PZ V 10 I RL I1 M1 VIN ISORC VSRC Star Hspice Manual Release 1998 2 24 3 hspice book hspice ch25 4 Thu Jul 23 19 10 43 1998 Using Pole Zero Analysis Performing Pole Zero Analysis Pole Zero Control Options CSCAL sets the capacitance scale Capacitances are multiplied by CSCAL Default 1e 12 FMAX sets the maximum pole and zero frequency value Default 1 0e 12 FSCAL FSCAL sets the frequency scale Frequency is multiplied by FSCAL Default 1e 9 GSCAL sets the conductance scale Conductances are multiplied by GSCAL and resistances are divided by GSCAL Default 1e 3 ITLPZ sets the pole zero analysis iteration limit Default 100 LSCAL sets the inductance scale Inductances are multiplied by LSCAL Default 1e 6 Note The scale factors must satisfy the following relations GSCAL CSCAL FSCAL 1 GSCAL LSCAL FSCAL If scale factors are changed the initial Muller points X0R X0I X1R X1I and X2R X2I may have to be modified even though internally the program multiplies the initial values by 1e 9 GSCAL PZABS sets absolute tolerances for poles and zeros This option affects the low frequency poles or zeros It is used as follows If X real X imag PZABS then X real 0 and X imag 0 This option is also used for convergence tests Default 1e 2 PZTOL 24 4 sets the relative error tolerance for poles or zeros Default 1 0e 6 Star Hspice Manual Release 1998 2 hspice book hspice ch25 5 Thu Jul 23 19 10 43 1998 Performing Pole Zero Analysis RITOL Using Pole Zero Analysis sets the minimum ratio value for real imaginary or imaginary real parts of the poles or zeros Default1 0e 6 RITOL is used as follows If X imag RITOL X real then X imag 0 If X real RITOL X imag then X real 0 X0R X0I x1R X1I X2R X21 the three complex starting trial points in the Muller algorithm for pole zero analysis Defaults X0R 1 23456e6 X0I 0 0 X1R 1 23456e5 X1I 0 0 X2R 1 23456e6 X21 0 0 These initial points are multiplied by FSCAL Pole Zero Analysis Examples Pole Zero Example 1 Low Pass Filter The following is an HSPICE input file for a low pass prototype filter for pole zero and AC analysis8 This file can be found in installdir demo hspice filters flp5th sp Fifth Order Low Pass Filter HSPICE File FILE FLP5TH SP 5TH ORDER LOW PASS FILTER T I R2 IIN 0 113 S 2 1 6543 S 2 0 2632 S 5 0 9206 S 4 1 26123 S 3 0 74556 S 2 0 2705 S 0 09836 OPTIONS POST PZ I R2 IN AC DEC 100 001HZ 10HZ PLOT AC IDB R2 IP R2 IN 0 1 R1 1 1 00 AC 0 1 0 1 Star Hspice Manual Release 1998 2 24 5 hspice book hspice ch25 6 Thu Jul 23 19 10 43 1998 Using Pole Zero Analysis C3 C4 C5 C1 L1 C2 L2 R2 END 1 2 3 1 1 2 2 3 0 0 0 2 2 3 3 0 Performing Pole Zero Analysis 1 52 1 50 0 83 0 93 0 65 3 80 …