Varactor SPICE Models for RF VCO ApplicationsAPN1004Varactor Equivalent Circuit Model DefinitionsA 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 parasiticcomponents 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 .Application NoteParallel CapacitanceFigure 1.Simplified Equivalent Circuit of VaractorFigure 2.Libra IV SPICE ModelParameterDescriptionUnit Default IS Saturation current (with N, determine the DC characteristics of the diode)A 1e-14R S Series resistanceΩ0N Emission coefficient (with IS, determines the DC characteristics of the diode)-1TT Transit timeS 0C JO Zero-bias junction capacitance (with V J and M define nonlinear junction capacitance of the diode)F 0V J Junction potential (with V J and M define nonlinear junction capacitance of the diode)V 1M Grading coefficient (with V J and M define nonlinear junction capacitance of the diode)-0.5E G Energy gap (with XTI, helps define the dependence of IS on temperature)EV 1.11XTI Saturation current temperature exponent (with E G , helps define the dependence of IS on temperature)-3KF Flicker noise coefficient -0AF Flicker noise exponent-1FC Forward-bias depletion capacitance coefficient -0.5B V Reverse breakdown voltageV Infinity I BV Current at reverse breakdown voltage A 1e-3ISR Recombination current parameter A 0NR Emission coefficient for ISR -2IKF High-injection knee current A Infinity NBV Reverse breakdown ideality factor -1IBVL Low-level reverse breakdown knee current A 0NBVL Low-level reverse breakdown ideality factor-1T NOM Nominal ambient temperature at which these model parameters were derived °C 27FFEFlicker noise frequency exponent-1Table 1.SPICE Model ParametersT able 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 T able 1, the varactor capacitance, C V , is a function of the applied reverse DC voltage, V R , and may be expressed as follows:C V =+ C P1 +C JOMV R V J()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.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 SPart Number(pF)(V)M(pF)(Ω)(nH)C0.5/C2.5 SMV112723.9 2.2100.5 1.7 1.68 SMV112927.5 2.8 1.100.4 1.7 1.73 SMV11398 1.20.6500.6 1.7 1.68 SMV114070.44 3.5 1.400.3 1.7 1.68 SMV11417.32 2.2100.7 1.7 1.66 SMV114213.38 2.2100.7 1.7 1.67 SMV114318.99 2.2100.65 1.7 1.67 SMV114424.01 2.2100.65 1.7 1.67 SMV114541.8 2.5 1.100.6 1.7 1.68 SMV114661.13 2.5 1.100.6 1.7 1.68 SMV114789.52 2.5 1.100.55 1.7 1.68 SMV1148104.7 2.25 1.100.5 1.7 1.7 SMV117513.433 1.150 1.0 1.7 1.68 SMV120626.114 1.450.30.7 1.7 1.69 SMV120759.4 6.5 2.320.4 1.7 1.73 SMV121272.4711067 4.50.45 1.7 2.82 SMV121328.9190105 2.20.8 1.7 2.53 SMV121422.74190106 1.50.7 1.7 2.60 SMV121514.36190115 1.1 1.0 1.7 2.73 SMV122325.1910045 2.5 1.5 1.7 2.10 SMV122425.1910045 2.5 1.5 1.7 2.10 SMV122517.4611047 1.6 1.8 1.7 2.05 SMV122752.465 1.800.55 1.7 1.75 SMV1228130.15 1.800.32 1.7 1.75 SMV1229271.725 1.800.25 1.7 1.75 SMV1232 4.2 1.70.90 1.5 1.7 1.87 SMV1233 4.12 1.70.90.7 1.2 1.7 1.71 SMV12348.75 2.3 1.1 1.20.8 1.7 1.82 SMV123516.138420.6 1.7 1.84 SMV123621.638 4.2 3.20.5 1.7 1.86 SMV123766.1610 5.390.13 1.7 2.05 SMV1245 6.9 3.5 1.70.472 1.7 1.82 SMV12479.221001000.552 1.7 2.15 SMV124821.541310.50 1.8 1.7 6.2 SMV12493917140 1.5 1.7 6.75 SMV12504717140 1.5 1.7 5.41 SMV12516017140 1.3 1.7 5.86Table 2.Plastic Packaged Varactor Values for SPICE Model Simulation EquationC JO V J C P R S L S Part Number (pF)(V)M (pF)(Ω)(nH)C0.5/C2.5SMV12537017140 1.2 1.7 5.88SMV125582171401 1.7 4.42SMV129913.73190110 1.1 2.5 1.7 2.61SMV1405 2.920.680.410.050.8 1.7 1.41SMV1408 3.70.80.430.130.6 1.7 1.5SMV1409 5.20.80.450.130.5 1.7 1.51SMV1410 5.540.80.450.130.45 1.7 1.52SMV14117.5750.80.450.130.40 1.7 1.52SMV14139.20.790.450.130.35 1.7 1.52SMV141411.20.780.460.130.3 1.7 1.54SMV141512.80.780.460.130.27 1.7 1.55SMV141616.040.840.480.130.24 1.7 1.54SMV141719.20.840.480.130.221.7 1.54SMV141921.40.870.540.130.2 1.7 1.61SMV142030.20.80.470.130.19 1.71.59SMV142136.10.80.470.130.18 1.7 1.57SMV1493290.630.4700.25 1.7 1.63SMV20227.0872.30.4 2.1 1.7 1.65SMV202325.792501102.41.31.72.09ExamplesFigure 3shows the SPICE model calculated capacitance Alpha abrupt junction varactor SMV1493-011 with measured capacitance values.Figure 4 shows the SPICE model calculated capacitance for Alpha hyperabrupt junction varactor SMV1235-011 with measured capacitance values.24681012Varactor VoltageC a p a c i t a n c e (p F )05101520Table 2.Plastic Packaged Varactor Values for SPICE Model Simulation Equation (Continued)Figure 4.SMV1235 7.575/(1-V V /0.8)^0.45专注于微波、射频、天线设计人才的培养易迪拓培训网址：A D S视 频 培 训 课 程 推 荐ADS–Advanced Design System是由原美国安捷伦科技（现更名为是德科技）推出的微波射频电路、通信系统和MMIC/RFIC仿真设计软件，其功能强大、应用广泛，被国内高校、科研院所和大型科技公司使用广为使用。