Anritsu HFE1103_Stauffer 电路图.pdf

22High Frequency Electronics High Frequency Design VARACTOR MODEL Finding the Lumped Element Varactor Diode Model By George H. Stauffer Rockwell Collins A n accurate model for the varactor diode is necessary when designing a voltage controlled oscillator (VCO) using CAD simula- tion. In order to predict tuning range, start up gain, and phase noise, the resonator must be accu- rately modeled over the frequency range of the oscillations. The varactor diode used for tun- ing has a predominant effect on the Q, phase noise and tuning range of the resonator. If the varactor model is inaccurate, the results of the most elaborate computer simulation will be misleading and the oscillator, when built, may have disappointing performance. Varactor Diode Model Figure 1 shows a commonly used lumped element varactor diode model. The values for package inductance and capacitance, Lpand Cpshown are typical for an 0805 surface mount part. The values for junction capaci- tance, Cjand Q are supplied by the manufac- turer and are almost always specified at a low frequency, usually 50 MHz, and a bias voltage of 4 Volts. Q is defined by Q = 1/CjRs. This formula can be used to calculate the series resistance Rsof the varactor model at the measured frequency, however at microwave frequencies additional losses often result in a significantly higher value for Rs. Also, Rs decreases with increasing bias voltage as the width of the depletion region around the PN junction increases, reducing the length of the conductive path through the bulk semiconduc- tor material surrounding the junction. Rsis sometimes assumed to be constant with reverse voltage and frequency in order to simplify use of the model. A much more accu- rate picture can be had by measuring the diode close to operating conditions and then choosing values for the lumped element model based on these measurements. Two important operating conditions are the frequency at which the diode is to be used and mounting method. One way would be to simply mount the diode at the end of a 50 ohm transmission line and measure S11of the two-terminal diode using a network analyzer. However, unless extreme care is taken to make a very accurate S11calibration at the point where the diode is mounted, the calculated real part of the diode impedance, Rsmay have a large error because the impedance of the diode is close to the edge of the Smith chart. A more accurate network analyzer measurement is made by first matching the diode to 50 ohms Here is a method for using measured data to accurately describe the behavior of a varactor diode, providing the CAD simulator with a model that corresponds to actual device performance Figure 1 Lumped element model of varac- tor diode using manufacturers specifica- tions. Rsis calculated from Q= 1/ CjRsat 50 MHz. From November 2003 High Frequency Electronics Copyright 2003 Summit Technical Media, LLC RadioFans.CN 收音机爱 好者资料库 24High Frequency Electronics High Frequency Design VARACTOR MODEL at the frequency of interest. A match- ing structure which uses only microstrip elements is preferable because it can be analyzed quite accurately using an EM simulator and its effect in the circuit can then be accounted for when calculating the model parameters. An Accurate Model is Required for VCO Design A recent 3 GHz VCO design required that the resonator circuit be optimized for best phase noise and tuning range, yet also allow for ade- quate production margin. A suitable varactor diode was selected based on the required range of capacitance variation. In order to begin to accu- rately characterize the diode, the model with values supplied by the manufacturer was matched at 3 GHz using a microstrip network as shown in Figure 2a. The swept frequency response from 2 to 4 GHz describes a loop on the Smith chart as shown in Figure 2b. At 3 GHz the resonance loop passes through the center of the Smith chart indicating critical cou- pling. From this point it is a simple mat- ter to add microstrip elements to pro- duce a practical circuit to be used as a test fixture. The layout is shown in Figure 3 and includes a biasing net- work consisting of a radial stub and a high impedance quarter wave line.At 3 GHz the bias network is an RF short at the cathode terminal. The S-parameters of the bias net- work and the tapped line are calcu- lated individually using an EM simu- lation program and the results are used in the measurement fixture schematic in Figure 4. This layout was reproduced on 20 mil Rogers 4003 board, and this 2 x 2 inch board was mounted on a test fix- ture block, shown in Figure 5. The network analyzer was calibrated at the coax connector, with the reference plane brought to the edge of the board using a 16.7 ps port extension. The S11measurements were then made at bias voltages over a 0-20 V range while sweeping from 2 to 4 GHz. The S11measurements were saved and imported into the CAD program. After these measurements, all that remains to be done is to adjust Cjand Rsof the model of Figure 4 so that the measured S11 agrees with S11calculated from Figure 4 over the entire 2 to 4 GHz frequency range for each value of bias Figure 3 Microstrip test fixture with tapped line and bias circuit. Figure 2 Varactor diode model matched to 50 ohms using microstrip tapped line (a); S11from 2 to 4 GHz (b). Figure 4 Tapped line and bias network models from EM simulation connected to diode model. (a) (b) RadioFans.CN 收音机爱 好者资料库 26High Frequency Electronics High Frequency Design VARACTOR MODEL voltage. The CAD program employs a built in optimizer to accomplish this task. The results of one such opti- mization for a bias voltage of 4 V are shown in Figure 6 where the mea- sured and modeled values are seen to match closely. A graph of the results after opti- mizing the model to the measured data at all bias voltages is shown in Figure 7. Here Cjand Rsare plotted versus bias voltage. Also shown is the capacitance variation computed using the equation for the junction capaci- tance of an abrupt junction diode : (1) Q of the varactor at 3 GHz calcu- lated from measured values of Rsand Cjusing Q = 1/CjRsis shown plotted versus bias voltage in Figure 8. Figure 9 shows the model derived from the measured data. Cjis deter- mined from equation (1) and Rscalcu- lated from equation (2), a polynomial with coefficients chosen to fit the Rs vs. bias voltage curve in Figure 7: (2) Resonator Design with the Accurate Diode Model The actual resonator used in the 3 GHz VCO is a shorted microstrip line shunted at the input by the var- Rvv vv s= + 4 025101 8410 0292052 056 5433 2 . . CV C V j j ( )= ( ) + 0 1 75 0 5 . . Figure 5 Test fixture with diode mounted for S11mea- surement. Figure 6 Measured and modeled response at V = 4 V. Figure 7 Cjand Rscomputed from model and the cal- culated value of C(v). Figure 8 Varactor Qversus bias voltage at 3 GHz. RadioFans.CN 收音机爱 好者资料库 28High Frequency Electronics High Frequency Design VARACTOR MODEL actor diode and coupled to the active device of the VCO by a small value series capacitor, as diagrammed in Figure 10a. As shown in Figure 10b, the calculated res- onator loss using the derived model from Figure 9 is low enough at resonance for oscillations to start when con- nected to one port of an unstable active device having a reflection gain of 6 dB or more over the frequency range from 2.8 to 3.2 GHz. Conclusion At a bias voltage of 4 VDC, Rsfirst calculated from Q = 1/CjRsusing the manufacturers value of Q at 50 MHz was 0.67 ohms. Compare this optimistic value to the more realistic value of Rs= 1.64 ohms derived from the mea- surements described at 3 GHz.The first value would have resulted in an overly optimistic design and the engineer would have been left wondering where it had all gone wrong. A model that accurately behaves like the actual device gives much more confidence in the simulated results and may avoid disappointment when the hard- ware is built and tested. References 1. D. Johnson, “Tuning Diode Design Techniques,” Motorola Application Note AN551. 2. “Varactor SPICE Models for RF VCO Applications,” Application Note APN1004, Alpha Industries. Author Information George Stauffer is a Principal Engineer at Rockwell Collins Government Systems, Germantown, MD. His pri- mary interest is microwave synthesizer design. He can be reached by e-mail at: Figure 9 Derived model at 3 GHz with equations for Cj and Rsas functions of V. Figure 10 Layout of 2.8-3.2 GHz resonator with require- ments for start-up and steady state oscillations (a), and the resonance loops at 0 and 20 VDC tuning voltages calculated from the improved diode model (b). (a) (b) CALL FOR TUTORIAL ARTICLES High Frequency Electronicsincludes a tutorial article in each issue. These are targeted to both new engineers and those who have been work- ing in other areas of specialization. We are accepting proposals for articles on following topics for publication in these 2004 issues: March:Personal Area Networks (PANs) April:Power Amplifier Linearization May:Filter Specifications September: Balanced Circuits October: Optical Detectors and Preamps Send an abstract or outline by e-mail to: editor . If you have questions, send them by e-mail or telephone to Gary Breed, Editorial Director, at 608-845-3965.