AND8250/D Zener Macro-- Models Provide Accurate SPICE Simulations Prepared by: Jim Lepkowski ON Semiconductor http://onsemi.com APPLICATION NOTE Zener I vs. V Characteristics The current versus voltage relationship of a Zener diode is shown in Figure 1. The four operational regions are the forward, leakage, breakdown and the maximum current regions. Zener diodes are typically used as voltage regulators; thus, the reverse bias breakdown region is the normal operating area for the device. INTRODUCTION Zener macro--models provide an accurate SPICE simulation of a diode’s current versus voltage characteristics. The macro--models are created by combining standard SPICE devices into a sub--circuit. Zener macro--models offer several advantages over the standard diode model available in SPICE, including a more accurate representation of the breakdown characteristics. Current IF VZM VZ VBR VR IR Voltage VF IZK IZT IZM Current Limit Leakage Region Region Forward Region Breakdown Region IF = Forward current VF = Voltage at IF IR = Reverse leakage current VR = Voltage at IR IZK = Test current for voltage VBR VBR = Voltage at IZK ZZK = Dynamic impedance at IZK = ΔVZ / ΔIZK IZT = Test current for voltage VZ VZ = Voltage at current IZT ZZT = Dynamic impedance at IZT = ΔVZ / ΔIZT IZM = Maximum DC steady--state current VZM = Voltage at IZM (typically not defined on the data sheet) Figure 1. Zener Diode I vs. V Characteristics and Specification Definitions © Semiconductor Components Industries, LLC, 2006 January, 2006 -- Rev. 0 1 Publication Order Number: AND8250/D AND8250/D Zener Diode SPICE Model Options The three basic methods used to create Zener diode SPICE models are listed below. 1. Curve Fit Models 2. SPICE Diode Statement 3. Macro--Model Subcircuit SPICE Diode Statement Curve Fit Models * anode cathode model name D1 2 1 MD1 The majority of the Zener SPICE models available in the industry are created using the SPICE ‘D’ diode statement. Table 1 provides the variables available with the PSPICE ‘D’ diode model. An example of a ‘D’ statement is shown below. Curve fit SPICE models are an attractive modeling option in versions of SPICE that have analog behavior modeling statements. The mathematical functions and “If--Then--Else” commands can be used to perform conditional branching to accurately match the Zener’s impedance in the four operating regions. Curve fit models are not as popular as the Diode ‘D’ statement or macro--model options because the analog behavioral statements are not available in some versions of SPICE. In contrast, the SPICE statements used in the diode and macro--model are compatible with almost all versions of SPICE. Curve fit models are created using a polynomial expression in the SPICE voltage controlled current source ‘G’ command. The polynomials can be generated using the curve fit feature of a mathematical program such as MathCad or Excel to form a transfer function of the Zener’s impedance. A negative feature of the curve fit approach is that this option creates a mathematical model, while in contrast the macro--model approach produces an equivalent circuit to represent the Zener. .MODEL MD1 D IS=6.57933e--10 N=1.84949 XTI=1 +RS=1.022CJO=1.5e--10 TT=1e--08 There are several restrictions that limit the accuracy of using the diode ‘D’ statement to model a Zener. First, the diode statement does not have a provision for defining a separate series resistance for the forward and reverse bias breakdown regions. The resistances in the two regions are not equal; thus, it is not possible to accurately model the slope of the voltage versus current characteristic in both regions. Next, the ‘D’ statement does not have a variable to model the variance of the Zener voltage with temperature (T). The polarity and magnitude of ΔVZ/ΔT is a function of the breakdown voltage. If VZ is < 5.6 V, ΔVZ/ΔT ≈ --2.0 mV/_C. If VZ is > than 5.6 V, the ΔVZ/ΔT temperature coefficient is positive and increases as a function of the magnitude of VZ. Also, the diode statement does not have a variable to limit the current to a maximum value that matches the Zener’s power dissipation capability. Table 1. Default Values of the PSPICE Diode Statement ‘D’ Variables Variable Parameter SPICE Default Value ON Macro--Model Default Value Units 1 E--14 1 E--14 A IS Saturation Current RS Resistance 0 10 Ω BV Reverse Breakdown Voltage ∞ 5 V IBV Current at Reverse Breakdown Voltage 1 E--3 1 E--3 A Emission Coefficient (η) 1 1 -- Saturation Current Temp. Coefficient 3 0 -- Transit Time 0 10 nS Zero Bias Junction Capacitance 0 50 pF VJ Junction Potential 1 1 V M Grading Coefficient 0.5 0.5 -- EG Activation Energy 1.11 1.11 eV KF Flicker Noise Coefficient 0 0 -- AF Flicker Noise Exponent 1 1 -- FC Depletion Capacitance Forward Bias Coefficient 0.5 0.5 -- Nominal Temperature 27 27 _C N XT1 TT CJO TNOM 1. The values of the ON macro--model components are generated by the MODPEX software from the data sheet specifications. 2. The PSPICE diode command does not have a maximum current limit (IMAX) variable. The macro--model’s default value for IZM is 200 mA. 3. The PSPICE diode command does not have a variable to define the temperature coefficient of the breakdown voltage. The macro--model’s default value for ΔVZ/ΔT is 0 mV/_C. http://onsemi.com 2 AND8250/D Macro--Model Subcircuit A Zener diode macro--model can be created using standard SPICE components. Figure 2 shows a schematic representation of the macro--model that is used to create the majority of the ON Zener SPICE models. The netlist for the MMBZ5232’s macro--model is provided in Appendix I as an example. A summary of the operation of the model is given in Table 2. Further details on the macro--model are provided in references [5] and [6]. Alternative Zener diode macro--models are given in references [1]--[4]. Anode I D = IF + IL + IR 2 Anode + 2 ID VD -- 1 Cathode IR RZ IF IL D1 RL 3 D3 IZG RZG 4 D2 -+ EV1 1 5 EV1 = VBR = IBV x RBV IBV 6 RBV 0 + EV1 -- Cathode Figure 2. Zener Diode SPICE Macro--Model Forward Bias Region Diode D1 is the key component when the voltage VD across the Zener is greater than zero. D1’s forward bias characteristics are controlled by the saturation (IS), emission coefficient (N) and series resistance (RS) variables. The forward bias current equations are listed below. ID = IF + IL + IR V = IF_D1 + D + IS_D2 RL IL & IR ≪ IF_D1 ∴ID ≅ IF_D1 ≅ IS_D1 e ^ VD1 VD1 − 1 ≅ IS_D1 e ^ ηVT ηVT VT = kT q ≅ 26 mV @ 25˚C Leakage Region The leakage or reverse bias before breakdown region is defined when voltage VD is between 0 V and the breakdown voltage (VBR). Currents IF and IR are small in comparison to IL because diodes D1 and D2 are reverse biased. The leakage current can be approximated by the ratio of VD to RL. ID = IF + IL + IR V = IS_D1 + D − IS_D2 RL VD ∴ID ≅ RL IS_D1 & IS_D2 ≪ IL Breakdown Region (VBR), represented by EV1, is equal to the product of current source IBV and resistor RBV. The Zener voltage VZ, specified at current IZT, is equal to the sum of the voltages of EV1, RZ, D2 and D3 as shown below. The reverse bias breakdown region is modeled by the devices contained in the current path of IR. Current flows through this path when voltage VD exceeds the voltage of EV1 plus the forward voltage of D2. The breakdown voltage VD I ∴VD ≅ ηVT In D ηVT IS VZ = VBR + VD2 + VRZ − VD3 ID ≅ IS e ^ I I VZ @ IZT = EV1 + η2VT ln D2 + (IZTRZ) − η3VT ln D3 IS3 IS2 I --I IZT = (IBRRBV) + η2VT ln + (IZTRZ) − η3VT ln ZG ZT IS2 IS3 http://onsemi.com 3 AND8250/D Current Limit Region An equation that determines the ratio of the emission coefficients η2 and η3 is created by assuming that the reverse saturation currents for diodes D2 and D3 are equal. I --I η3 = η2 ln ZG ZT IZT Diode D3, current source IZG and resistor RZG are used to form a current limiting circuit. The current limiting mode occurs when ID2 increases to the value of IZG, which reverse biases D3 and limits the current. The maximum current (IZM) has a weak dependency on the magnitude of the bias voltage and RZG is used to provide a slope to the current versus voltage curve. D3’s current can be expressed by the equations listed below. The Zener impedance, or the slope of the current versus voltage curve, is equal to the derivative of the diode’s voltage equation with respect to current. The impedance equation shown below is valid for low frequencies, where the junction capacitance can be neglected. ZD = ID3 = IZG − ID2 − IRZG IRZG ≪ IZG & ID2 ηVT δVD = ID δID ∴ID3 ≅ IZG − ID2 The impedance of the Zener, defined as ZZT and ZZK, is defined at test currents IZT and IZK, respectively. The two impedance and η3 equations are used to calculate RZ, η2 and η3. The Zener impedance in the breakdown region is approximated by neglecting the parallel connected resistor RL and the reverse biased diode D1 for simplicity. Macro--Model Limitations Macro--models provide an accurate SPICE representation of a Zener’s current and voltage characteristics for most applications. The macro--models solve several of the limitations associated with the SPICE diode ‘D’ statement and the curve fit models. The accuracy of the macro--models is directly proportional to the thoroughness of the Zener’s data sheet. Macro--models are a powerful analytical design tool; however, they should not be used as a replacement for hardware development tests. A summary of the limitations of the macro--models is shown in Table 3. ZZ ≅ RZ + ZD2 + ZD3 ZZT ≅ RZ + η2VT η3VT + (IZG --IZT) IZT ZZK ≅ RZ + η2VT η3VT + (IZG --IZK) IZK Table 2. Key Design Equations and Features of the Zener Diode Macro--Model Region Forward Bias Voltage Boundaries VD > 0 Macro--Model Components Key Design Equations ID ≅ IF_D1 ≅ IS_D1 e ^ D1 VD1 ηVT Comments • ID is defined by the Ebers--Moll equation • D1’s RS variable models the ΔI/ΔV slope Leakage Region VBR < VD ≤ 0 V ID ≅ IL ≅ D RL RL • RL’s temperature coefficients model ΔIL/ΔT Breakdown VZM < VD ≤ VBR VZ ≅ VZT + ZZTID VZT = VZ @ IZT ZZT ≅ RZ + RSD2 + RSD3 EV1, D2, RZ IBV, RBV • The recommended bias current for a voltage regulator application is IZM < ID ≤ IZT • • Current Limit VD ≤ VZM D3, IZG, RZG IZM ≅ IZG http://onsemi.com 4 • • RBV’s temperature coefficients model ΔVZ/ΔT RZ models the ΔI/ΔV slope IZM is a function of the IC package RZG models the ΔI/ΔV slope AND8250/D Table 3. Simulation Limits of Zener Macro--Models Region Key Design Parameter Forward Forward Voltage (VF) Leakage Breakdown Current Limit Leakage Current (IL) Zener Voltage (VZ) Maximum Current (IMAX) Model Limitation • VF is typically specified as a maximum value at a single current point in the data sheet • The simulation accuracy is enhanced if two typical current points are used by the modeling algorithm • • IL is modeled as a linear function of the bias voltage • • VZ tolerance (typ. 5%) is not modeled • • • Voltage surge suppression capability beyond IMAX is not modeled IL actually varies as an exponential function of the bias voltage Monte--Carlo simulations can provide tolerance and worst case analysis Thermal self--heating produced when ID is large is not modeled Device overcurrent failures are not modeled. At the device’s destruction point, VZ ‘collapses’ or decreases to a low value, which increases the current through the device to a level that damages the device References 1. Antognetti, P. and Massobrio, G., “Semiconductor Device Modeling with Spice”, McGraw--Hill, New York, 1990. 2. Deveney, M., “A Temperature Dependent SPICE Macro--Model for Zener and Avalanche Diodes”, IEEE Circuits and Systems Midwest Symposium, May, 1991. 3. Pawlikiewicz, A. and Zack, G., “A New Macro--Model for Zeners”, IEEE Circuits and Devices Magazine, Volume 9, Issue 2, March, 1993. 4. Sandler, S., “SPICE Subcircuit Accurately Models Zener Characteristics”, Personal Engineering, November, 1998. 5. Wong, S. and Hu, C., “SPICE Macro--Model for the Simulation of Zener Diode I--V Characteristics”, IEEE Circuits and Devices Magazine, Volume 7, Issue 4, July, 1991. 6. Wong, S., Hu, C. and Chan, S., “SPICE Macro--Model for the Simulation of Zener Diode Current--Voltage Characteristics”, International Journal of Electronics, Volume 71, No. 24, August, 1991. http://onsemi.com 5 AND8250/D Appendix I: MMBZ5232B Zener Diode Macro--Model SPICE Netlist ********************************************************************************** * MMBZ5232B Macro--Model SPICE Model * Model Generated by MODPEX * Copyright(c) Symmetry Design Systems * All Rights Reserved * MODEL FORMAT: PSPICE **************************************************************************** * node: anode cathode .SUBCKT mmbz5232blt1 2 1 ********************************************************************************** * Forward Region * D1’s CJO term models the Zener’s capacitance D1 2 1 MD1 .MODEL MD1 D IS=7.58703e--07 N=3.10159 XTI=1 RS=0.856 + CJO=1.5e--10 TT=1e--08 **************************************************************************** * Leakage Region * RL models leakage current (IL) * MDR temp. coef. model ∆IL / ∆T RL 1 2 MDR 1.5e+09 .MODEL MDR RES TC1=0 TC2=0 **************************************************************************** * Reverse Breakdown Region * RZ models the ∆I / ∆V slope RZ 2 3 0.862776 D2 5 4 MD2 .MODEL MD2 D IS=2.5e--12 N=0.475376 XTI=0 EG=0.1 EV1 1 5 6 0 1 * Breakdown Voltage (VBR) = IBV x RBV * MDRBV temp. coef. model ∆VBR / ∆T IBV 0 6 0.001 RBV 6 0 MDRBV 5431.8 .MODEL MDRBV RES TC1=0.000368055 **************************************************************************** * Current Limit Region * Maximum current (IZM) is set to magnitude of IZG * RZG models the ∆I / ∆V slope IZG 4 3 0.24 RZG 4 3 75 D3 3 4 MD3 .MODEL MD3 D IS=2.5e--12 N=0.198247 XTI=0 EG=0.1 * .ENDS mmbz5232blt1 **************************************************************************** http://onsemi.com 6 AND8250/D ON Semiconductor and are registered trademarks of Semiconductor Components Industries, LLC (SCILLC). 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