Chapter 4-SPICE for Power Electronics and Electric Power-Book, Lecture notes of Power Electronics

Download Chapter 4-SPICE for Power Electronics and Electric Power-Book and more Lecture notes Power Electronics in PDF only on Docsity! 66 SPICE for Power Electronics and Electric Power, Second Edition FIGURE 4.1 Pulse waveform. TABLE 4.1 Model Parameters of Pulse Sources Name Meaning Unit Default V1 Initial voltage V None V2 Pulsed voltage V None TD Delay time sec 0 TR Rise time sec TSTEP TF Fall time sec TSTEP PW Pulse width sec TSTOP PER Period sec TSTOP FIGURE 4.2 PSpice schematic for a pulse source. (a) Symbol, (b) editing model parameters. Period v, i V2 td tr tw tf V1 0 t(s) V1 + −TD = 0 TF = 1 ns PW = 100 us PER = 200 us V1 = −220 V TR = 1 ns V2 = 220 V (a) Voltage and Current Sources 67 tions, the DC (i.e., DC=5V) and AC (AC=1V) specifications can be assigned to The symbol of a pulse source is PULSE and the general form is PULSE (V1 V2 TD TR TF PW PER) are the incrementing time and stop time, respectively, during transient (.TRAN) analysis. 4.2.1.1 Typical Statements For V1 = − 2 d r f and period = 100 nsec, the model statement is PULSE (−1 1 2NS 2NS 2NS 50NS 100NS) With V1 = 0, V2 = 1, the model becomes PULSE (0 1 2NS 2NS 2NS 50NS 100NS) With V1 = 0, V2 = −1, the model becomes PULSE (0 −1 2NS 2NS 2NS 50NS 100NS) 4.2.2 PIECEWISE LINEAR SOURCE A point in a waveform can be described by time Ti and its value Vi. Every pair of values (Ti, Vi) specifies the source value Vi at time Ti. The voltage at a time between the intermediate points is determined by PSpice by using linear interpolation. The schematic of a piecewise linear source is shown in Figure 4.3(a), and the menu for setting the model parameters are shown in Figure 4.3(b). Up to ten FIGURE 4.3 Piecewise linear source in PSpice schematics. (a) Symbol, (b) editing model parameters. V1 (a) + − 1, V = 1 V, t = 2 nsec, t = 2 nsec, t = 2 nsec, pulse width = 50 nsec, the same source. The pulse source is used for the transient analysis of a circuit. V1 and V2 must be specified by the user. TSTEP and TSTOP in Table 4.1 70 SPICE for Power Electronics and Electric Power, Second Edition 4.2.4 EXPONENTIAL SOURCE and the menu for setting the model parameters are shown in Figure 4.8(b). In addition to the transient specifications, the DC (i.e., DC = 5V) and AC (AC = 1V) specifications can be assigned to the same source. TD1 is the rise-delay time, TC1 is the rise-time constant, TD2 is the fall-delay time and TD2 is the fall-time constant. The symbol of exponential sources is EXP and the general form is EXP (V1 V2 TD1 TC1 TD2 TC2) V1 and V2 must be specified by the user. TSTEP in Table 4.4 is the incre- menting time during transient (.TRAN) analysis. In an EXP waveform, the voltage remains V1 for the first TD1 seconds. Then, the voltage rises exponentially from V1 to V2 with a rise-time constant of TC1. After a time of TD2, the voltage falls exponentially from V2 to V1 with a fall-time constant of TC2. (The values of EXP waveform as well as the values of other time-dependent waveforms at intermediate time points are determined by PSpice by means of linear interpolation.) FIGURE 4.6 Damped sinusoidal waveform. TABLE 4.4 Model Parameters of EXP Sources Name Meaning Unit Default V1 Initial voltage V None V2 Pulsed voltage V None TD1 Rise-delay time sec 0 TC1 Rise-time constant sec TSTEP TD2 Fall-delay time sec TD1 + TSTEP TC2 Fall-time constant sec TSTEP td V e−αt V0 VA t 0 The waveform and parameters of an exponential waveform are shown in Figure 4.7 and Table 4.4. The schematic of an exponential source is shown in Figure 4.8(a), Voltage and Current Sources 71 4.2.4.1 Typical Statements For V1 = 0, V2 = 1V, TD1 = 2NS, TC1 = 20NS, TD2 = 60NS, and TD2 = 30NS, the model statement is EXP (0 1 2NS 20NS 60NS 30NS) With TRD = 0, the statement becomes EXP (0 1 0 20NS 60NS 30NS) With V1 = −1V and V2 = 2V, it is EXP (−1 2 2NS 20NS 60NS 30NS) 4.2.5 SINGLE-FREQUENCY FREQUENCY MODULATION SOURCE The schematic of a single-frequency frequency modulation (SFFM) source is FIGURE 4.7 Exponential waveform. FIGURE 4.8 Exponential Source in PSpice schematic. (a) Symbol, (b) editing model parameters. t (s)td2td1 tc1 tc2 0 V1 V2 v, i V3 (a) TD1 = 2 ns V1 = 0 + − TD2 = 60 ns TC1 = 20 ns V2 = 1 TC2 = 30 ns shown in Figure 4.9(a), and the menu for setting the model parameters is shown 72 SPICE for Power Electronics and Electric Power, Second Edition in Figure 4.9(b). In addition to the transient specifications, the DC (i.e., DC = 5V) and AC (AC = 1V) specifications can be assigned to the same source. The symbol of a source with single-frequency frequency modulation is SFFM, and the general form is (see Table 4.5) SFFM (VO VA FC MOD FS) VO and VA must be specified by the user. TSTOP is the stop time during transient (.TRAN) analysis. The waveform is of the form 4.2.5.1 Typical Statements For VO = 0, VA = 1V, FC = 30MHz, MOD = 5, and FS = 5kHz, the model statement is SFFM (0 1V 30MHZ 55KHZ) With VO = 1mV and VA = 2V, the model becomes SFFM (1MV 2V 30MHZ 55KHZ) (b) FIGURE 4.9 SFFM source in PSpice schematic. (a) Symbol, (b) editing model parameters. TABLE 4.5 Model Parameters of SFFM Sources Name Meaning Unit Default VO Offset voltage V None VA Amplitude of voltage V None FC Carrier frequency Hz 1/TSTOP MOD Modulation index 0 FS Signal frequency Hz 1/TSTOP V4 (a) + − FM = 5 kHz VAMPL = 1 VOFF = 0 FC = 20 Meg MOD = 5 V V V F t M F t= + +O A C Ssin[( ) sin( )]2 2 Voltage and Current Sources 75 4.3.2.1 Typical Statements Note: IIN assumes 2 A for DC analysis, 1 A with a delay angle of 30° for AC analysis, and a sine wave of 2 A at 10kHz for transient analysis. This allows source specifications for different analyses in the same statement. 4.3.3 SCHEMATIC INDEPENDENT SOURCES current sources are shown in Figure 4.11(b) and Figure 4.11(c). The user can change the values of the sources. 4.4 DEPENDENT SOURCES There are five types of dependent sources: Polynomial source Voltage-controlled voltage source Current-controlled current source Voltage-controlled current source Current-controlled voltage source 4.4.1 POLYNOMIAL SOURCE Let us call the three controlling variables A, B, and C, and the output sources, Y. Y takes the form Y = f (A, B, C, …) where Y can be a voltage or current, and A, B, and C can be a voltage or current or any combination. The symbol of a polynomial or nonlinear source is POLY(n), where n is the number of dimensions of the polynomial. The default value of n is 1. The dimensions depend on the number of controlling sources. The general form is POLY(n) <(controlling)nodes> <(coefficient) values> The output sources or the controlling sources can be voltages or currents. For voltage-controlled sources, the number of controlling nodes must be twice the I1 15 0 2.5MA ; By default, DC specification of 2.5 mA I2 15 0 DC 2.5MA ; DC specification of 2.5 mA IAC 5 6 AC 1A ; AC specification of 1 A with 0° delay IACP 5 6 AC 1A 45DEG ; AC specification of 1 V with 45° delay IPULSE 10 0 PULSE (0 1A 2NS 2NS 2NS 50NS 100NS) ; transient pulse IIN 25 22 DC 2A AC 1A 30DEG SIN (0 2A 10KHZ) The PSpice source library source.slb is shown in Figure 4.11(a). DC voltage and Figure 4.12 shows a source Y that is controlled by A, B, and C. The output source 76 SPICE for Power Electronics and Electric Power, Second Edition FIGURE 4.11 Independent DC sources. (a) Sources menu, (b) DC voltage source, (c) DC current source. FIGURE 4.12 Polynomial source. V5 5 Vdc (b) − + l1 (c) + − NC1+ + − + − + − + − NC1− NC2+ NC2− NC3+ N+ N−NC3− A B (a) Controlling sources (b) Output source C Y Voltage and Current Sources 77 number of dimensions. For current-controlled sources, the number of controlling sources must be equal to the number of dimensions. The number of dimensions and the number of coefficients are arbitrary. For a polynomial of n = 1 with A as the only controlling variable, the source function takes the form where P0, P1, …, Pn are the coefficient values, and this is written in PSpice as POLY NC1+ NC1− P0 P1 P2 P3 P4 P5 … Pn where NC1+ and NC1− are the positive and negative nodes, respectively, of controlling source A. For a polynomial of n = 2 with A and B as the controlling sources, the source function Y takes the form and this is described in PSpice as POLY(2) NC1+ NC1− NC2+ NC2− P0 P1 P2 P3 P4 P5 … Pn where NC1+, NC2+ and NC1−, NC2− are the positive and negative nodes, respectively, of the controlling soruces. For a polynomial of n = 3 with A, B, and C as the controlling sources, the source function Y takes the form and this is written in PSpice as POLY(3) NC1+ NC1− NC2+ NC2− NC3+ NC3− P0 P1 P2 P3 P4 P5 … Pn where NC1+, NC2+, NC3+ and NC1−, NC2−, NC3− are the positive and negative nodes, respectively, of the controlling sources. Y P P A P A P A P A P An n= + + + + + +0 1 2 2 3 3 4 4
Y P P A P B P A P AB P B P A P A B P AB = + + + + + + + + 0 1 2 3 2 4 5 2 6 3 7 2 8 2 9 3+ +P B
Y P P A P B P C P A P AB P AC P B P BC P= + + + + + + + + +0 1 2 3 4 2 5 6 7 2 8 9 2 10 3 11 2 12 2 13 2 14 15 C P A P A B P A C P AB P ABC P A+ + + + + + C P B P B C P BC P C P A 2 16 3 17 2 18 2 19 3 20 4 + + + + + +
80 SPICE for Power Electronics and Electric Power, Second Edition voltage source VN, to the negative node of VN. The current through the control- ling voltage source, I(VN), determines the output current. The voltage source VN that monitors the controlling current must be an independent voltage source, and it can have a finite value or zero. If the current through a resistor controls the source, a dummy voltage source of 0 V should be connected in series with the resistor to monitor the controlling current. The nonlinear form is F<name> N+ N− [POLY (polynomial specifications)] The POLY source is described in Subsection 4.4.1. The number of controlling current sources for the POLY must be equal to the number of dimensions. 4.4.3.1 Typical Statements FAB 1 2 VIN 10 ; Current gain of 10 FAMP 13 4 VCC 50 ; Current gain of 50 FNONLIN, which is connected between nodes 25 and 40, is controlled by the current through voltage source VN. Its value is given by the polynomial I = I(VN) + 1.5[I(VN)]2 + 1.2[I(VN)]3 + 1.7[I(VN)]4, and the PSpice model becomes FNONLIN 25 40 POLY VN 0.0 1.0 1.5 1.2 1.7 4.4.4 VOLTAGE-CONTROLLED CURRENT SOURCE G, and it takes the linear form G<name> N+ N− NC+ NC− <(transconductance) value> N+ and N− are the positive and negative output nodes, respectively, and NC+ and NC− are the positive and negative nodes, respectively, of the controlling voltage. The nonlinear form is G<name> N+ N− [POLY (polynomial specifications)] + [VALUE (expression)] [TABLE (expression)] + [LAPLACE (expression)] [FREQ (expression)] The POLY description is described in Subsection 4.4.1. The VALUE, TABLE, LAPLACE, and FREQ descriptions of sources are available only with the analog behavioral modeling option of PSpice. These are discussed in Section 4.5. 4.4.4.1 Typical Statements GAB 1 2 4 6 1.0 ; Transconductance of 1 GVOLT 4 7 20 22 2E5 ; Transconductance of 2E5 The symbol of the voltage-controlled current source shown in Figure 4.13(c) is Voltage and Current Sources 81 GNONLIN, which is connected between nodes 25 and 40, is controlled by V(3) and V(5). Its value is given by the polynomial Y = V(3) + 1.5V(5) + 1.2[V(3)]2 + 1.7V(3)V(5), and the model becomes GNONLIN 25 40 POLY(2) 3 0 5 0 0.0 1.0 1.5 1.2 1.7; POLY source G2, which is connected between nodes 10 and 12, is controlled by V(5), and its value is given by the polynomial Y = V(5) + 1.5[V(5)]2 + 1.2[V(5)]3 + 1.7 [V(5)]4, and the model becomes G2 10 12 POLY 5 0 0.0 1.0 1.5 1.2 1.7 ; POLY source A voltage-controlled current source can be used to simulate conductance if the controlling nodes are the same as the output nodes. This is shown in Figure 4.14(a). For example, the PSpice statement GRES 4 6 4 6 0.1 ; transconductance of 0.1 is a linear conductance of 0.1 seimens (Ω−1 or mhos) with a resistance of 1/0.1 = 10 Ω. The PSpice statement GMHO 1 2 POLY 1 2 0.0 1.5M 1.7M ; POLY source represents a nonlinear conductance (Ω−1) of the polynomial form I = 1.5 × 1−3V(1,2) + 1.7 × 10−3[V(1,2)]2 4.4.5 CURRENT-CONTROLLED VOLTAGE SOURCE H, and it takes the linear form H<name> N+ N− VN <(transresistance) value> N+ and N− are the positive and negative nodes, respectively, of the voltage source. VN is a voltage source through which the controlling current flows, and its specifications are similar to those for a current-controlled current source. FIGURE 4.14 (a) Conductance, (b) resistance. + − + − l0 = P1 V(1,2) E = P1 l(Vsense) +.. 1 N+ N−2 1 R (a) Conductance (b) Resistance R 1 0 V I Vsense 2 The symbol of the current-controlled voltage source shown in Figure 4.13(d) is 82 SPICE for Power Electronics and Electric Power, Second Edition The nonlinear form is H<name> N+ N− [POLY (polynomial specifications)] The POLY source is described in Subsection 4.4.1. The number of controlling current sources for the POLY must be equal to the number of dimensions. 4.4.5.1 Typical Statements HAB 1 2 VIN 10 HAMP 13 4 VCC 50 HNONLIN, which is connected between nodes 25 and 40, is controlled by I(VN). Its value is given by the polynomial V = I(VN) + 1.5[I(VN)]2 + 1.2[I(VN)]3 + 1.7[I(VN)]4, and the model becomes HNONLIN 25 40 POLY VN 0.0 1.0 1.5 1.2 1.7 ; POLY source A voltage-controlled current source can be applied to simulate resistance if the controlling current is the same as the current through the voltage between the HRES 4 6 VN 0.1 ; Transresistance of 0.1 is a linear resistance of 10 Ω. The PSpice statement HOHM 1 2 POLY VN 0.0 1.5M 1.7M ; POLY source represents a nonlinear resistance in ohms of the polynomial form H = 1.5 × 1−3I(VN) + 1.7 × 10−3[I (VN)]2 4.4.6 SCHEMATIC DEPENDENT SOURCES controlled voltage source (E), the current-controlled current source (F), the voltage-controlled current source (G), and the current-controlled voltage source 4.5 BEHAVIORAL DEVICE MODELING PSpice allows characterization of devices in terms of the relation between their inputs and outputs. This relation is instantaneous. At each moment in time, there is an output for each value of the input. This representation, known as behavioral modeling, is available only with the analog behavioral modeling option of PSpice. output nodes. This is shown in Figure 4.8. For example, the PSpice statement The PSpice analog library analog.slb is shown in Figure 4.15. The voltage- (H) of the PSpice library are shown in Figure 4.16(a) to Figure 4.16(d). Voltage and Current Sources 85 The <expression> itself is enclosed in braces ({ }). It can contain the arith- metical operators (“+”, “−”, “*”, and “/”) along with parentheses and the following functions: 4.5.1.1 Typical Statements ESQROOT 2 3 VALUE = {4V*SQRT (V(5))} ; Square roots EPWR 1 2 VALUE = {V(4.3)*I(VSENSE)} ; Product of v and i ELOG 3 0 VALUE = {10V*LOG (I (VS)/10mA)} ; Log of current ratio GVCO 4 5 VALUE = {15MA*SIN (6.28*10kHz*TIME* (10V*V(7)))} GRATIO 3 6 VALUE = {V (8, 2)/V(9)} ; Voltage ratio VALUE can be used to simulate linear and nonlinear resistances (or conduc- tances) if appropriate functions are used. A resistance is a current-controlled voltage source. For example, the statement ERES 2 3 VALUE = {I (VSENSE)*5K} is a linear resistance with a value of 5 kΩ. VSENSE, which is connected in series with ERES, is needed to measure the current through ERES. A conductance is a voltage-controlled current source. For example, the statement GCOND 2 3 VALUE = {V(2,3)*1M} is a linear conductance with a value of 1 mΩ−1. The controlling nodes are the same as the output nodes. Function Meaning ABS(x) |x| (absolute value) SQRT(x) Function Meaning EXP(x) ex LOG(x) ln(x) (log of base e) LOG10(x) Log(x) (log of base 10) PWR(x,y) |x|y PWRS(x,y) +|x|y (if x > 0), −|x|y (if x < 0) SIN(x) sin(x) (x in radians) COS(x) cos(x) (x in radians) TAN(x) tan(x) (x in radians) ARCTAN(x) tan−1(x) (result in radians) x 86 SPICE for Power Electronics and Electric Power, Second Edition Note the following: 1. VALUE should be followed by a space. 2. <expression> must fit on one line. 4.5.2 TABLE The TABLE extension to the controlled sources of the PSpice library allows an instantaneous transfer function to be described by a table. This form is well suited for use with, for example, measured data. The general forms are: E<name> N+ N− TABLE {<expression>} = + <<(input)value>, <(output)value>>* G<name> N+ N− TABLE {<expression>} = + <<(input)value>, <(output)value>>* The <expression> is evaluated, and that value is used to look up an entry in the table. The table itself consists of pairs of values. The first value in each pair is an input, and the second value is the corresponding output. Linear interpolation is done between entries. For values of <expression> outside the table’s range, the device’s output is a constant with value equal to the entry with the smallest (or largest) input. 4.5.2.1 Typical Statements TABLE can be used to represent the voltage current characteristics of a diode as EDIODE 5 6 TABLE{I (VSENSE)} = + (0.0,0.5) (10E-3,0.870) (20E-3,0.98) (30E-3,1.058) + (40E-3,1.115) (50E-3,1.173) (60E-3,1.212) (70E-3,1.250) TABLE can be used to represent a constant power load P = 400 W with a voltage-controlled current source as GCONST 2 3 TABLE {400/V(2, 3)} = (−400, −400) (400, 400) GCONST tries to dissipate 400 W of power regardless of the voltage across it. But for a very small voltage, the formula 400/V(2,3) can lead to unreasonable values of current. TABLE limits the currents to between −400 and +400 A. Note the following: 1. TABLE must be followed by a space. 2. The input to the table is <expression>, which must fit in one line. 3. TABLE’s input must be in order from the lowest to the highest. Voltage and Current Sources 87 4.5.3 LAPLACE The LAPLACE extension to the controlled sources of the PSpice library allows a transfer function to be described by a Laplace transform function. The general forms are: E<name> N+ N− LAPLACE {<expression>} = {<transform>} G<name> N+ N− LAPLACE {<expression>} = {<transform>} The input to the transform is the value of <expression>, which follows the same rules as in Subsection 4.5.1. The <transform> is an expression in the Laplace variable, s. 4.5.3.1 Typical Statements The output voltage of a lossless integrator with a time constant of 1 msec and an input voltage V(5) can be described by ERC 4 0 LAPLACE {V(5)} = {1/(1 + 0.001*sec)} Frequency-dependent impedances can be simulated with a capacitor, which can be written as GCAP 5 4 LAPLACE {V(5,4)} = {s} Note the following: 1. LAPLACE must be followed by a space. 2. <expression> and <transform> must each fit on one line. 3. Voltages, currents, and TIME must not appear in a Laplace transform. 4. The LAPLACE device uses much more computer memory than does the built-in capacitor (C) device and should be avoided if possible. 4.5.4 FREQ The FREQ extension to the controlled sources of the PSpice library allows a transfer function to be described by a frequency response table. The general forms are: E<name> N+ N− FREQ {<expression>} = + <<(frequency)value>, <(magnitude in dB)value>, <(phase)value>>* G<name> N+ N− FREQ {<expression>} = + <<(frequency)value>, <(magnitude in dB)value>, <(phase)value>>* The input to the table is the value of <expression>, which follows the same rules as those mentioned in Subsection 4.5.1. The table contains the magnitude 90 SPICE for Power Electronics and Electric Power, Second Edition PROBLEMS Write PSpice statements for the following circuits. Assume that the first node is the positive terminal, and the second node is the negative terminal. 4.1 The various voltage or current waveforms that are connected between nodes 4 4.2 A voltage source that is connected between nodes 10 and 0 has a DC voltage of 12 V for DC analysis, a peak voltage of 2 V with a 60° phase shift for AC analysis, and a sinusoidal peak voltage of 0.1 V at 1 MHz for transient analysis. FIGURE P4.1 v, i 10 V 0 v, i 10 0 1 2 3 4 t (ms) (a) 0.5 1 1.5 t (ms) (a) v, i 10 V 0 0.5 1 1.5 t (ms) t (ms) (b) v, i 5 0 80 100 180 t (µs) (d) v, i 10 0 v, i 20 0 5 5 5 10 20 25 35 t (µs) (f ) (h) v, i 50 0 5 107105 t (ms) (e) v, i 10 0 –10 10 sin (2π × 5000t) (g) 5 ms 5 ms and 5 are shown in Figure P4.1. Voltage and Current Sources 91 4.3 A current source that is connected between nodes 5 and 0 has a DC current of 0.1 A for DC analysis, a peak current of 1 A with 60° phase shift for AC analysis, and a sinusoidal current of 0.1 A at 1 kHz for transient analysis. 4.4 A voltage source that is connected between nodes 4 and 5 is given by 4.5 A polynomial voltage source Y that is connected between nodes 1 and 2 is controlled by a voltage source V1 connected between nodes 4 and 5. The source is given by 4.6 A polynomial current source I that is connected between nodes 1 and 2 is controlled by a voltage source V1 connected between nodes 4 and 5. The source is given by 4.7 A voltage source V0 that is connected between nodes 5 and 6 is controlled by a voltage source V1 and has a voltage gain of 25. The controlling voltage is con- nected between nodes 10 and 12. The source is expressed as V0 = 25V1. 4.8 A current source I0 that is connected between nodes 5 and 6 is controlled by a current source I1 and has a current gain of 10. The voltage through which the controlling current flows is VC. The current source is given by I0 = 10I1. 4.9 A current source I0 that is connected between nodes 5 and 6 is controlled by a voltage source V1 between nodes 8 and 9. The transconductance is 0.05 Ω−1. The current source is given by I0 = 0.051V1. v t t= × + ×2 2 50 000 5 2 1000sin[( , ) sin( )] Y V V V= + +0 1 0 2 0 051 1 2 1 2. . . Y V V V= + +0 1 0 2 0 051 1 2 1 2. . . 92 SPICE for Power Electronics and Electric Power, Second Edition 4.10 A voltage source V0 that is connected between nodes 5 and 6 is controlled by a current source I1 and has a transresistance of 150 Ω. The voltage through which the controlling current flows is VC. The voltage source is expressed as V0 = 150I1. 4.11 A nonlinear resistance R that is connected between nodes 4 and 6 is controlled by a voltage source V1 and has a resistance of the form 4.12 A nonlinear transconductance Gm that is connected between nodes 4 and 6 is controlled by a current source. The voltage through the controlling current flows is V1. The transconductance has the form 4.13 The V–I characteristic of a diode is described by where IS = 2.2 × 10−15 A, n = 1, and VT = 26.8 mV. Use VALUE to simulate the diode voltage between nodes 3 and 4 as a function of diode current. 4.14 The V–I characteristic of a diode is described by where IS = 2.2 × 10−15 A, n = 1, and VT = 26.8 mV. Use VALUE to simulate the diode current between nodes 3 and 4 as a function of diode voltage. R V V= +1 1 20 2. G V Vm = +1 1 20 2. I I ev nVD S /D T= I I ev nVD S /D T=