PB FM 1990-2009 AN-01 DWS APPLICATIONS PASSIVE COMPONENT MODELING BASED ON REFLECTOMETER MEASUREMENTThe speed of digital systems is is a partial modeling of skin effect circuit, that means that the inputshowing up the limits of thestandard modeling based onlumped circuit parameters.Interconnections few centimeterslong can be critical for the integrityof signals if the rise time is smaller a) b)than a nanosecond because ofreflections, dispersion and skineffect. For example, a signal with asubnanosecond rise time, and abad-designed board c)interconnection few centimeterslong can invalidate the correctperformance of the design. Z0 Td Z0 TdThese problems require the S11,S21introduction of new concepts about (S22,S12)modeling techniques, based ondistributed models that can take all d) e)the undesirable effects intoaccount. Fig. 1: Interconnection models: a) lumped LC, b) lossy lumped, c) distributed LC, d) Distributed lossy TLM, e) behavioral.According to the problem, severalmodels are available, with and dispersion phenomena during waveform is transferred to thedifferent complexity: the propagation of the signal. output after the delay Td without1) Lumped LC model. Losses are modeled through series modifications1. Losses can beThis model (Fig.1a) is the simplest and parallel resistors distributed in modeled using resistors, asone and takes only the each cell of the chain. Drawbacks discussed before2. As well as thecharacteristic impedance and the of this model are the large number previous model, the number ofpropagation delay into account, of cells that are necessary in order elements required to model a lossywhile losses can be modeled to model the interconnection with interconnection with accuracy canthrough series or parallel resistors accuracy and the simulation time increase very fast and the relatively(Fig.1b). This model cannot take that increases considerably. small propagation time of theskin effect and dispersion 3) Transmission line model. single pieces of transmission linephenomena into account and may This model (Fig.1d) is similar to complicates the problem so that,be only used when the propagation the previous one, where a very often, the problem is not yetdelay is shorter than the transition transmission line characterized bytime of the signal. Z0 (characteristic impedance) and 2) Distributed LC model. Td (propagation time) replaces theIn this case (Fig.1c), if the delay of LC element. A transmission line 1 If the line is terminated on itsa single cell is smaller than the is, for definition, a wide-band characteristic impedance.transition time of the signal, there 2 Or ladder RL for skin effect modeling.
PB 1990-2009 [mrho] (DWS Waveform Viewer). This 40 A C methodology is also usable after 20 D the prototyping phase in order to verify the behavior of the S11 0 E prototype in all the situations by replacing the pre-layout models -20 B (with lumped or distributed -40 parameters) with the measure- based models. As a consequence it 0 10 20 30 40 50 60 70 80 90 100 is possible to use the simulation TIME[nS] tool for investigating the signal Fig. 2: Measured TDR response of the parameter S11 for a coaxial cable waveform where it is not possible to measure it, for example insidesolvable with conventional SPICE- simulations a high degree of the package.derived simulators. realism. Standard componentThe DWS simulation engine, not libraries are already available, andonly allows designers to simulate the user can easily create newthe models already presented, but models with the utilities offered byalso, thanks to a new the graphic environment DWVmethodology, allows them touse both standard models [mrho]and behavioral descriptions 40 3based on REFLECTOMETER 20 4 5MEASUREMENTS in time 6 S11 7 0domain (BTM - Behavioral Time 2Modeling). -20Using a reflectometer (TDR - -40 1Time Domain Reflectometer) it ispossible to make a wide-band 0 10 20 30 40 50 60 70 80 90 100 TIME[nS]characterization of one or two a)port3 devices by means of the [rho] 1.0 4 7measure of their scattering 5 6 0.8parameters S11, S22, S21 e S12. 3 0.6These models are very useful S21where sections of interconnection, 0.4pieces of coaxial cable, packages, 0.2etc. can be characterized 2experimentally. Usually, an 0.0 1accurate electrical modeling of 10 12 14 16 18 20 22 24 26 28 30 TIME[nS]passive devices is not possible, b)because of their complicated Fig. 3: Measure and PWL extraction of the S11(a) and S21(b). * Coaxial cable: TDR and TDT simulation for model validation * ******************************************************************geometries. The utilization of field * * * Coaxial cable description using S-parameters with PWL extractionsimulators for the extraction of the * BCOAX 20 0 30 0 S11=PWL ( 0.0NS -3.26e-02 18.6NS -1.99e-03 19.2NS 3.23e-02parameters of the cross section + 20.4NS 2.49e-02 25.8NS 1.7e-02 47.2NS 8.42e-03 96.6NS 2.5e-03) Z0=50 TD=0 + S21=PWL ( 0.0NS -1.53e-03 0.2NS 1.33e-01 .44NS 6.6e-01 .64NS 8.19e-01shows a lot of troubles (first of all + 1.12NS 8.99e-01 2.2NS 9.42e-01 17.6NS 9.975e-01) Z0=50 TD=9.15NS *the input description) and cant * * termination resistor *take into account the RLOAD 30 0 50 *discontinuities that sometimes are * * * TDR step generator: a 2V step shows the result equivalent in RHO scale.present along the device (for * VTDR 20 0 PWL ( 0.0PS 0.0 3.25NS 0.0 3.28NS 2 ) 50 *example connectors). The * * analysismeasures are directly utilizable * .TRAN TSTEP=30P TSTOP=100N A(VTDR, 20) V(30) LIMPTS=1000 .ENDby the simulator giving the Fig. 4: Simulation file (DWS syntax) used for model validation.3Models with more than two ports will besoon available.
PB 1990-2009 [mrho] 40SCATTERING PARAMETERS 20 S11 0The measurement of the time- measure -20domain scattering parameters (or S-parameters) during the -40 modelcharacterization of circuital parts 0 10 20 30 40 50 60 70 80 90 100allows the user to quickly define TIME[nS]accurate models, also for high a)frequency applications. One of the [rho] 1.0advantages of this technique is the 0.8wide band of the measure (10-20GHz) and the termination 0.6required at the ports of the network S21 0.4under test, usually 50 . Othermeasurement techniques require 0.2sometimes creating shorts or open 0.0circuits in the network, that are 10 12 14 16 18 20 22 24 26 28 30conditions usually difficult to b) TIME[nS]realize for high frequency. Fig. 5: Comparison between simulations and actual responses: a) S11, b) S21.The S-parameter technique is basedon the measurement of reflected b(t) = S(t) * a(t) or only three in the case the deviceor transmitted voltage waves when is not symmetrical. Somethe device is stimulated by an where S(t) is the impulse response applications are presented in theincident wave. Simple bipoles, of the one-port device obtainable following.whose model presents only one from TDR measure and the symbolport, are modeled by only one * means time-convolution operator. COAXIAL CABLEscattering parameter S(t). Two-port devices require fourThe relationship between the scattering parameters but only two One of the characteristics of coaxialreflected wave b and the incident measures are enough if the device is cables is the uniformity of thewave a is: both symmetrical and reciprocal electrical parameters along it: for (because the others are identical), this reason the cable may be modeled by a reciprocal (S21 = S12) and symmetrical (S22 = S11) two-port element. Fig. 2 shows a typical measured TDR response of the parameter S11 for a section of a) micro coaxial cable 2 meters long with a characteristic impedance of 50 . The response is displayed with the graphic environment DWV after the measure has been captured from the measure set-up. The vertical scale is expressed in m (it is reminded that = 0 is equivalent to a 50 resistance, = 1 an b) open circuit and = -1 a short). The peak A is a parasitic effect due to the end of the launch cable, in the point where it is jointed with the device under test. The section B shows the reflection during the Fig. 6: PWL extraction of the scattering parameters S11(a) and S22(b).
PB 1990-2009 ********************************************************** *** CONNECTOR MODEL *** the most significant portion of the ********************************************************** measure. The approximation starts .SUBCKT CONCTOR 1 2 after the first peak that is a parasitic * 1=backpanel side, 2=board side effect due to the end of the launch * cable, in the point where it is * behavioural description BCON 1 0 2 0 jointed with the device under test, + S11=PWL(0 -1.53e-03 50PS 3.72e-01 160PS -3.78e-01 240PS -2.61e-01 and must be ignored. It is possible + 280PS -9.34e-02 340PS -2.22e-01 400PS -1.67e-01 430PS -8.73e-02 to note the strong discontinuities + 560PS -1.53e-03) Z0=50 TD=0 present in the device that are + S21=PWL(0 0 50PS 1) Z0=50 TD=230PS detected as Z0 changes. Fig. 6b + S22=PWL(0 2.91e-04 60PS -1.07e-01 110PS -7.93e-02 190PS -2.74e-01 + 220PS -2.74e-01 280PS -1.23e-01 330PS -3.48e-01 400PS -3.48e-01 shows the measure and its related + 510PS 2.7e-01 550PS 3.11e-02 560PS -2.69e-03) Z0=50 TD=0 PWL extraction of the S22 * parameter (board side). .END CONCTOR The descriptions of the two Fig. 7: Connector model description (DWS syntax). parameters plus a simple description of the S21 parameterpropagation of the incident wave4 the interconnection. It is possible are then combined in a single DWSalong the cable. now to validate the model by means statement representing the model ofThe vertical step is due to the of a simulation, for example, of the the connector. Fig. 7 shows a listingmismatch between the impedance same measure scheme. The listing of the model. It is possible now toof the micro coaxial cable and the of the input file used for the validate the model by means of areference impedance at the port 1 simulation is shown in Fig.4 and the simulation, for example, of the(50 ) and its value is about-30m correspondent results are shown in same measure scheme used for the(corresponding to a Z0 of about Fig. 5a e 5b: it is possible to point S11 characterization.47.1 ). The slope of the B section out the good correspondenceis a typical effect of the skin effect. between the simulation responses CONCLUSIONIt is possible to note the versus the actual measure. Thediscontinuities due to small changes models can be used in chains or sub A very accurate and easy-to-doof geometry that are detected as Z0 circuits, for modeling longer modeling approach has beenchanges. The point C shows the sections of cable. presented. The methodology is welldiscontinuity at the far end of the applicable for both passive andcable and the E amplitude at the BACKPLANE CONNECTOR active (see AN-02) devices. Theend of the D section (constituted by models are extracted fromthe multiple reflections inside the This example shows a connector as measurements using the utilities ofcable for skin effect) corresponds to a typical asymmetrical device, the graphic environment DWV andthe ohmic resistance of the cable whose structure is very difficult to allow the DWS simulator to achieve(about 250 m in this example). model in terms of lumped result accuracy, otherwiseDWS is able to directly utilize the parameters because of its electrical impossible, still maintaining runsamples captured from the measure, discontinuities. For this reason a times orders of magnitude shorterbut in order to avoid useless behavioral model is more accurate than those of traditional products.increase of the simulation time, it is and easy to build.useful to extract the most The model we are going to proposesignificant part of the measure takes the asymmetry of the deviceusing the PWLEXTRACT utility of (S22 not equal to S11) into account.DWV: Fig.3a shows an example of In this example, the device ispiecewise linear extraction with reciprocal (S21 = S12) so only aonly 7 samples. transmitting measure is required.Fig.3b shows the measure of the Fig.6a shows a typical TDRS21 and its related PWL extraction. response during the measurement ofThe two-parameter descriptions are the parameter S11 (backplane side).then combined in a single DWS The response is displayed using thestatement representing the model of graphic environment DWV after the measure has been captured from the4 In this case, the incident wave is a voltage measure set-up. The same picturestep with a rise time of 25ps. reports also the PWL extraction of