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1、46High Frequency Electronics High Frequency Design RF COMPONENT MODELS Accurate Simulation of RF Designs Requires Consistent Modeling Techniques By V. Cojocaru, TDK Electronics Ireland Ltd. and D. Markell, J. Capwell, T. Weller and L. Dunleavy, Modelithics, Inc. W ith a consistent approach, based up

2、on the use of accurate characterization techniques and advanced passive and active com- ponent models, a high level of accuracy can be achieved when simulat- ing basic RF/microwave circuit designs. This article describes the tech- niques used in a number of new or enhanced high-frequency component m

3、odels that increase the simulation prediction capability and reduce the number of design, fabrication and test cycles. It presents the general fea- tures of some novel SMT capacitor and induc- tor models, as well as those of high-frequency non-linear models for varactor and switching diodes. The acc

4、uracy of the models is thor- oughly verified against experimental data in a number of tests performed on each individual component model, as well as in a more com- plex test carried out on a typical dual-band VCO tank circuit used in some modern com- munication systems. Introduction In comparison wi

5、th active devices or even distributed and monolithically integrated pas- sive components, improved lumped passive component models for hybrid circuit design have been largely ignored. For example, in many situations designers can wrongly assume that the models provided for surface mount capacitors a

6、nd inductors in modern simulators are adequate for the purpose of their simulations. Consequently, it is common- place to focus the modeling effort on compo- nents perceived to be of more critical impor- tance. In this article we demonstrate some illustrative examples of the high level of accu- racy

7、 that can be achieved beyond 12 GHz with precise modeling of lumped passives, and com- pare the results that are obtained with com- monbut more simplisticmodels. Specifically, we will address the character- ization and modeling of surface mount capaci- tors and inductors, as well as packaged varac-

8、tors and PIN diodes. The models are based on equivalent circuit topologies utilizing sub- strate-scalable parameter values. These mod- els are extracted from TRL-calibrated S- parameter measurements on multiple sub- strates (e.g., 5, 14 and 21 mil-thick FR4) and provide a compact, versatile model fo

9、r general design purposes. The ability of the diode mod- els to track the non-linear I-V and C-V char- acteristics over a broad range of bias condi- tions has been improved relative to existing model topologies. Surface Mount LC Models In the microwave frequency range, the behavior of surface mount

10、passive compo- nents, such as ceramic multi-layer capacitors and various types of inductors (e.g., air wound and chip style) is known to depend on the sur- rounding circuit board environment. Factors that will affect the frequency response include the substrate characteristics 1, 2, 3 and the type o

11、f transmission line used as the intercon- nect 4. In certain applications the variation due to somewhat minimal substrate alter- ations can be significant. One example per- taining to a common design requirement is choosing a suitable series capacitor for a DC- block, in which case the optimum capac

12、itor With greater reliance on computer simulation of RF and microwave circuits,the accuracy of component models must be assured. This article describes the latest measurement-based modeling techniques. From September 2002 High Frequency Electronics Copyright 2002, Summit Technical Media, LLC RadioFa

13、ns.CN 收音机爱 好者资料库 48High Frequency Electronics High Frequency Design RF COMPONENT MODELS will exhibit a series resonance at the design frequency. As illustrated in Figure 1, the series resonance is strongly tied to the substrate proper- ties. In this example, the resonance shifts from 4.5 GHz down to

14、 3 GHz as the FR4 substrate thickness increas- es from 14 to 24 mils. One our goals in this article is to demonstrate that the method used to model the substrate-dependency of a surface mount LC component deter- mines the resulting versatility of the model. The results given in Figure 1 include meas

15、ured S-parameter data along with simulated results using a single, substrate-scalable equivalent circuit model 3. The substrate-scal- able model is physically motivated, in that the equations for the circuit parameters are functions of the sub- strate cross-section and component geometry. For better

16、 or worse, howev- er, there tends to exist more than one model topology that will “match” a set of measurement data when the data is of limited extent.(Data may be limited in frequency, sample size, test configuration, etc.) Some support of this statement is given in Figure 2, in which the simulated

17、 response of the substrate-scalable model from Figure 1 is compared to a very simplistic, series L-C model, where L emulates an effective series inductance and C the nominal capacitance of the part. For this limited data set (a single sub- strate) the magnitude and phase response of the two models a

18、re near- ly identical up to the first resonant frequency. The importance of the physically based model becomes clear when the model is applied in a configuration that differs from that used for model extraction. Figure 3 shows a capaci- tor configuration that is frequently used to obtain non-standar

19、d part val- ues. Measured S-parameter data for this dual shunt capacitor arrange- ment, on a 14 mil-thick FR4 sub- strate, is shown along with various simulation results in Figure 4. The simulation using the substrate-scal- able models, with the input parame- ters for the substrate properly defined,

20、 faithfully reproduces the measurement data across the fre- quency range.There is also a curve in the figure that is generated using the substrate scalable models, but with the substrate height input parameter set to 24 mils; these results corre- spond to what might be obtained with a fairly robust

21、equivalent circuit topology extracted using measure- ment data from a substrate differing from the application substrate. The shift in the frequency response is comparable to that seen previously in Figure 1. The last curve in the figure is obtained by replacing the accurate capacitor models with th

22、eir simple LC counterparts. While the simple topology provided very accurate S- parameter representation for the series 2-port configuration, the same models used in the dual shunt config- uration provide completely miss the resonance near 6 GHz. Chip inductors exhibit substrate- dependent behavior

23、that is similar to that of capacitors,although the inductors present a somewhat more complicated modeling problem at higher frequencies. In Figure 5, the measured and model S21responses for a 15 nH, 0402 chip inductor are shown for test fixtures on 5 and 31 Figure 1 Measured (dashed lines) and model

24、ed (solid lines with markers) S11response for a 4.7 pF surface mount capacitor in a series 2-port configuration. Results are shown for test fixtures on 14 mil-thick FR4 (circles) and 24 mil-thick FR4 (squares). Figure 2 Modeled S11 for a 4.7 pF surface mount capacitor on 14 mil-thick FR4 in a series

25、 2-port config- uration. Results are shown for an accurate, substrate- scalable modelsolid line with circles (magnitude) and squares (phase)and a simplified series L-C equivalent circuit (lines). Figure 3 Dual shunt capacitor con- figuration. RadioFans.CN 收音机爱 好者资料库 September 200249 mil-thick FR4 su

26、bstrates. As with capacitors, a decrease in the substrate thickness pushes the resonant behavior higher in frequency; the frequency shift applies to the fundamental (parallel) resonance as well as the higher- order resonances found near 11-12 GHz. One of the diffi- culties associated with the modeli

27、ng solution is the asym- metric response near these higher-order resonances. The asymmetry is easily identified in a comparison of the for- ward (1|S11|2 |S21|2) and reverse (1|S22|2|S21|2) loss factors, as shown in Figure 6. On both the 5 and 31 mil-thick FR4 substrates the forward loss factor is v

28、ery highindicating that 70-80 percent of the incident power is lost through dissipation and radiationwhile the peaks in the reverse loss factor are much lower. The asymmetry forces a decision as to whether to employ a suitably asymmetric equivalent circuit topology to emu- late the response, or a mo

29、re standard symmetric model that averages through the forward and reverse responses. Generally, the better choice is a symmetric model since the orientation of the part often cannot be predicted or controlled once in the production environment. Varactor and PIN Diode Modeling Varactor diodes are key

30、 components in the design of any VCO circuit. The performance of the model used to describe the varactor diode is of prime importance for the simulation of certain crucial VCO characteristics, such as tuning range, tuning sensitivity, phase noise and har- monic generation.The large-signal nature of

31、the VCO cir- cuit means that the forward operating region of the var- actor cannot be neglected, despite the fact that typically they are operated well into the reverse bias region. A robust and very accurate varactor model has been developed and employed in our recent designs. Proper cal- ibration

32、and de-embedding techniques are of crucial importance as a starting point. Important enhanced char- acteristics of the modeling methodology include: precise characterization of the packaged varactor through the use of a high performance microwave test fixture, up to at least the fourth harmonic of t

33、he maxi- mum intended oscillation frequency.Proper calibra- tion and de-embedding techniques are of crucial impor- tance all around. improved non-linear model of the I-V characteristics in the low-forward bias region improved non-linear model of the C-V characteristic over an extended tuning range F

34、igure 4 Measured and modeled S21response for the dual shunt capacitor configuration on 14 mil-thick FR4. Results include measurement data (blue line), model response using substrate-scalable model set-up for the 14 mil-thick substrate (red circles), model response using substrate-scalable model set-

35、up for a 24 mil- thick substrate (black squares) and response using simple series L-C equivalent circuit (green triangles). Figure 5 Measured (lines) and model (lines+markers) S21response for a 15 nH surface mount 0402 inductor in a series 2-port configuration. Results are shown for test fixtures on

36、 5 mil-thick FR4 (red circles) and 31 mil-thick FR4 (black squares). Figure 6 Measured forward loss factor (1|S11|2 |S21|2) and reverse loss factor (1|S22|2 |S21|2) for a 15 nH surface mount inductor. Results are shown for test fixtures on 5 mil-thick FR4 red lines) and 31 mil- thick FR4 (black line

37、s). The thick lines correspond to the forward loss factor. RadioFans.CN 收音机爱 好者资料库 50High Frequency Electronics High Frequency Design RF COMPONENT MODELS consistent model parameter extraction of the package related parasitic elements of the model. Packaged switching diodes are also very common devic

38、es used in modern communication applications. Among those, PIN diodes are often preferred for their unrivaled switch- ing and power handling perfor- mances in the microwave range. Similar type of improvements have been employed in relation to the non- linear PIN diode model, resulting in some excell

39、ent performance in describing both the ON and the OFF state of the device, as well as the transition between these states. Prediction accuracy of the non-linear model for important characteristics such as the insertion loss has been brought down to values of around 0.1 dB, within the relevant operat

40、ing ranges. A comparison between measure- ment and simulation results for I-V, C-V and small-signal S-parameters of a commercial, packaged varactor diode is shown in Figure 7. The broadband S-parameters are mea- sured and simulated at a number of tuning voltages across the relevant tuning range. As

41、illustrated in Figure 8, the need to account for substrate-related effects is as critical in packaged var- actor diodes as it is for passive RLC- type components.This diode (a differ- ent part than that discussed above) was characterized using test fixtures printed on 5 and 59 mil-thick FR4. A non-l

42、inear, substrate-scalable model, utilizing physically-motivated equiv- alent circuit parameter equations similar to those for the inductor and capacitor, was then extracted using S-parameter data from both sub- strates at multiple bias conditions. The resulting model becomes a versa- tile tool for g

43、eneral circuit simulation in a variety of substrate environ- ments. Characterization and Simulation of the Test Circuits Simple series and shunt tank cir- cuits,commonly used in VCO designs, have been designed on FR4 boards to test the characterization, modeling and simulation methodolo- gy employed

44、. Circuits have been spe- cially designed for accurate probed characterization, by adding probing pads and appropriate de-embedding structures.Measurements were taken at a number of tuning voltage values. Finally, the circuits were implemented in the circuit simulator (ADS), with all the circuit com

45、po- nents (SMT capacitors and inductors, packaged varactor and switching diodes, microstrip resonators and all other incidental layout structures) being consistently modeled and implemented in the final simulated circuit. A simplified ADS schematic of one of the tank circuits analyzed, includ- ing s

46、ome of the relevant new models is presented in Figure 9. Comparative results between the measurement and simulation data at two different tuning voltages are shown in Figures 10(a) and (b). The Figure 7 I-V (a) and C-V (b) models for varactor diodes. Measurement (circles) vs simulated (thick continu

47、ous line) small-signal characteristics (c) at different tuning voltages (Vtune = -0.5, 1.5, 2.5V). Figure 8 Measured (markers only) and simulated (lines only) S11for a sur- face mount varactor diode on 5 mil-thick FR4 (red) and 59 mil-thick (black) substrates. (2 V reverse bias shown on the left; +0

48、.5 V forward bias shown on the right.) September 200251 accuracy of the present simulations as well as the marked improvement from the situation when existing models for various components are used, are evident from these graphs. Similar results have been obtained for other types of tank configurati

49、ons, and the methodology is currently extended to the characterization and simulation of other sub-circuits such as the oscillator and buffer circuits. Summary This paper has presented a rela- tively broad discussion on general considerations of surface mount LC and diode modeling. The main pur- pose was to demonstrate the high degree of simulation accuracy that is possible over a broad frequency range when careful characterization and modeling techniques are used. Some circuit examples, both simple and somewhat complex, pointed out the errors that can occur when less accu- r