Varactor SPICE Models for RF VCO Applications Application Note Varactor Equivalent Circuit Model Definitions A simplified equivalent circuit of varactor is shown in Figure 1. This varactor model is useful for RF VCO applications although it neglects some parasitic components often needed for higher frequency microwave applications, such as the distributed line package model and some capacitance due to ground proximity. For most RF VCO applications, to about 2.5 GHz, these parasitic components would not be important unless higher harmonics generated by the varactor affects performance of the VCO. In this case, a more detailed equivalent circuit model is needed. The technique used should be based on the varactor model extraction procedure from S-parameter data. A SPICE model, defined for the Libra IV environment, is shown in Figure 2, with the description of the parameters employed. It neglects the package capacitance, C P, its typical 0.10 pf value is absorbed within the junction capacitance C V. C V Junction Capacitance Cathode R S L S Anode D Junction Diode Series Resistance C P Series Inductance Parallel Capacitance Figure 1. Simplified Equivalent Circuit of Varactor Figure 2. Libra IV SPICE Model Alpha Industries, Inc. [781] 935-5150 Fax [617] 824-4579 Email sales@alphaind.com www.alphaind.com 1
Varactor SPICE Models for RF VCO Applications Parameter Description Unit Default IS Saturation current (with N, determine the DC characteristics of the diode) A 1e-14 R S Series resistance Ω 0 N Emission coefficient (with IS, determines the DC characteristics of the diode) - 1 TT Transit time S 0 C JO Zero-bias junction capacitance (with V J and M define nonlinear junction capacitance of the diode) F 0 V J Junction potential (with V J and M define nonlinear junction capacitance of the diode) V 1 M Grading coefficient (with V J and M define nonlinear junction capacitance of the diode) - 0.5 E G Energy gap (with XTI, helps define the dependence of IS on temperature) EV 1.11 XTI Saturation current temperature exponent (with E G, helps define the dependence of IS on temperature) - 3 KF Flicker noise coefficient - 0 AF Flicker noise exponent - 1 FC Forward-bias depletion capacitance coefficient - 0.5 B V Reverse breakdown voltage V Infinity I BV Current at reverse breakdown voltage A 1e-3 ISR Recombination current parameter A 0 NR Emission coefficient for ISR - 2 IKF High-injection knee current A Infinity NBV Reverse breakdown ideality factor - 1 IBVL Low-level reverse breakdown knee current A 0 NBVL Low-level reverse breakdown ideality factor - 1 T NOM Nominal ambient temperature at which these model parameters were derived C 27 FFE Flicker noise frequency exponent - 1 Table 1. SPICE Model Parameters Table 1 describes the model parameters. It shows default values appropriate for silicon varactor diodes, which may be used by the Libra IV simulator unless others are specifically defined. The effect of the diode junction is ignored in this model. This simplification ignores the rectifying effect of diode during a positive voltage swing. However, for most RF VCO applications, the lowest practical DC control voltage value is 0.5 V and the magnitude of RF voltage rarely exceeds 0.2 V peak. Therefore, the varactor is maintained in its reverse bias state. However, in a large signal application where it is necessary to consider the diode s rectifying properties, it may be done by entering the additional diode parameters in the SPICE model defined for the LIBRA IV environment. According to the SPICE model in Table 1, the varactor capacitance, C V, is a function of the applied reverse DC voltage, V R, and may be expressed as follows: This equation is a mathematical simulation of the capacitance characteristic. The model is accurate for abrupt junction varactors (SMV1400 Series); for hyperabrupt junction varactors the model is less accurate but very reliable. The form is similar to the traditional varactor equation but uses values for V J, M and C P, that were extracted individually from measured C V (V R ) data for each varactor part number. Series resistance, R S, is a function of applied voltage and operating frequency and may be considered constant. The value used should be taken from the specified maximum value or derived from its Q specification. Series inductance, L S, is also considered constant at a value of 1.7 nh. This incorporates the 1.5 nh package inductance with some insertion inductance typical for PC boards in RF wireless applications. C V = C JO M ( 1 + V R ) V J + C P 2 Alpha Industries, Inc. [781] 935-5150 Fax [617] 824-4579 Email sales@alphaind.com www.alphaind.com
Varactor SPICE Models for RF VCO Applications Table 2 gives values for Alpha s plastic packaged varactors that may be used for SPICE model simulation equation. It may be employed for each varactor junction in the SOD-323 and SOT-23 package. It also gives calculated values for the capacitance ratio between 0.5 2.5 V for each diode that is a typical voltage range for battery operated wireless VCO circuits. Note: The values listed for V J, M and C P in the table were empirically determined and do not represent the precise physical or electronic properties of the semiconductor or the package. C JO V J C P R S L S Part Number (pf) (V) M (pf) (Ω) (nh) C0.5/C2.5 SMV1127 23.9 2.2 1 0 0.5 1.7 1.68 SMV1129 27.5 2.8 1.1 0 0.4 1.7 1.73 SMV1139 8 1.2 0.65 0 0.6 1.7 1.68 SMV1140 70.44 3.5 1.4 0 0.3 1.7 1.68 SMV1141 7.32 2.2 1 0 0.7 1.7 1.66 SMV1142 13.38 2.2 1 0 0.7 1.7 1.67 SMV1143 18.99 2.2 1 0 0.65 1.7 1.67 SMV1144 24.01 2.2 1 0 0.65 1.7 1.67 SMV1145 41.8 2.5 1.1 0 0.6 1.7 1.68 SMV1146 61.13 2.5 1.1 0 0.6 1.7 1.68 SMV1147 89.52 2.5 1.1 0 0.55 1.7 1.68 SMV1148 104.7 2.25 1.1 0 0.5 1.7 1.7 SMV1175 13.43 3 1.15 0 1.0 1.7 1.68 SMV1206 26.11 4 1.45 0.3 0.7 1.7 1.69 SMV1207 59.4 6.5 2.3 2 0.4 1.7 1.73 SMV1212 72.47 110 67 4.5 0.45 1.7 2.82 SMV1213 28.9 190 105 2.2 0.8 1.7 2.53 SMV1214 22.74 190 106 1.5 0.7 1.7 2.60 SMV1215 14.36 190 115 1.1 1.0 1.7 2.73 SMV1223 25.19 100 45 2.5 1.5 1.7 2.10 SMV1224 25.19 100 45 2.5 1.5 1.7 2.10 SMV1225 17.46 110 47 1.6 1.8 1.7 2.05 SMV1227 52.46 5 1.8 0 0.55 1.7 1.75 SMV1228 130.1 5 1.8 0 0.32 1.7 1.75 SMV1229 271.72 5 1.8 0 0.25 1.7 1.75 SMV1232 4.2 1.7 0.9 0 1.5 1.7 1.87 SMV1233 4.12 1.7 0.9 0.7 1.2 1.7 1.71 SMV1234 8.75 2.3 1.1 1.2 0.8 1.7 1.82 SMV1235 16.13 8 4 2 0.6 1.7 1.84 SMV1236 21.63 8 4.2 3.2 0.5 1.7 1.86 SMV1237 66.16 10 5.3 9 0.13 1.7 2.05 SMV1245 6.9 3.5 1.7 0.47 2 1.7 1.82 SMV1247 9.22 100 100 0.55 2 1.7 2.15 SMV1248 21.54 13 10.5 0 1.8 1.7 6.2 SMV1249 39 17 14 0 1.5 1.7 6.75 SMV1250 47 17 14 0 1.5 1.7 5.41 SMV1251 60 17 14 0 1.3 1.7 5.86 Table 2. Plastic Packaged Varactor Values for SPICE Model Simulation Equation Alpha Industries, Inc. [781] 935-5150 Fax [617] 824-4579 Email sales@alphaind.com www.alphaind.com 3
Varactor SPICE Models for RF VCO Applications C JO V J C P R S L S Part Number (pf) (V) M (pf) (Ω) (nh) C0.5/C2.5 SMV1253 70 17 14 0 1.2 1.7 5.88 SMV1255 82 17 14 0 1 1.7 4.42 SMV1299 13.73 190 110 1.1 2.5 1.7 2.61 SMV1405 2.92 0.68 0.41 0.05 0.8 1.7 1.41 SMV1408 3.7 0.8 0.43 0.13 0.6 1.7 1.5 SMV1409 5.2 0.8 0.45 0.13 0.5 1.7 1.51 SMV1410 5.54 0.8 0.45 0.13 0.45 1.7 1.52 SMV1411 7.575 0.8 0.45 0.13 0.40 1.7 1.52 SMV1413 9.2 0.79 0.45 0.13 0.35 1.7 1.52 SMV1414 11.2 0.78 0.46 0.13 0.3 1.7 1.54 SMV1415 12.8 0.78 0.46 0.13 0.27 1.7 1.55 SMV1416 16.04 0.84 0.48 0.13 0.24 1.7 1.54 SMV1417 19.2 0.84 0.48 0.13 0.22 1.7 1.54 SMV1419 21.4 0.87 0.54 0.13 0.2 1.7 1.61 SMV1420 30.2 0.8 0.47 0.13 0.19 1.7 1.59 SMV1421 36.1 0.8 0.47 0.13 0.18 1.7 1.57 SMV1493 29 0.63 0.47 0 0.25 1.7 1.63 SMV2022 7.08 7 2.3 0.4 2.1 1.7 1.65 SMV2023 25.79 250 110 2.4 1.3 1.7 2.09 Table 2. Plastic Packaged Varactor Values for SPICE Model Simulation Equation (Continued) Examples Figure 3 shows the SPICE model calculated capacitance Alpha abrupt junction varactor SMV1493-011 with measured capacitance values. 35 Figure 4 shows the SPICE model calculated capacitance for Alpha hyperabrupt junction varactor SMV1235-011 with measured capacitance values. 20 Capacitance (pf) 30 25 20 15 Approximation 10 SMV1493-011 5 0 1 2 3 4 5 6 Varactor Voltage Capacitance (pf) 15 10 5 SMV1235 0 Approximation 0 2 4 6 8 10 12 Varactor Voltage Figure 3. SMV1493-011 C V = 29/(1-V VAR /0.63)^0.47 Figure 4. SMV1235 7.575/(1-V V /0.8)^0.45 4 Alpha Industries, Inc. [781] 935-5150 Fax [617] 824-4579 Email sales@alphaind.com www.alphaind.com
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