Varactor SPICE Models for RF VCO Applications Parameter Description Unit Default IS Saturation current (with N, determine the DC characteristics of th

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1 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] Fax [617] [email protected] 1

2 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) 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 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] Fax [617] [email protected]

3 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 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 SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV Table 2. Plastic Packaged Varactor Values for SPICE Model Simulation Equation Alpha Industries, Inc. [781] Fax [617] [email protected] 3

4 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 SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV SMV 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 SMV with measured capacitance values. 35 Figure 4 shows the SPICE model calculated capacitance for Alpha hyperabrupt junction varactor SMV with measured capacitance values. 20 Capacitance (pf) Approximation 10 SMV Varactor Voltage Capacitance (pf) SMV Approximation Varactor Voltage Figure 3. SMV C V = 29/(1-V VAR /0.63)^0.47 Figure 4. SMV /(1-V V /0.8)^ Alpha Industries, Inc. [781] Fax [617] [email protected]

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