Schematic-Level Transmission Line Models For The Pyramid
Schematic-Level Transmission LineModels for the Pyramid Probe AbstractCascade Microtech’s Pyramid Probe enables customers to perform production-grade, on-die, full-speed test of RF circuits for Known-GoodDie (KGD). For some applications, it may be necessary to model the transmission lines within the thin film portion of the probe card. Modelinginformation is useful for impedance matching the device under test (DUT) to a particular load, or to predict the insertion loss of the overallassembly. This application note presents an electrical model for a microstrip Pyramid Probe transmission line. Two schematic models arepresented, utilizing Agilent’s Advanced Design System (ADS).Why Model?RF transmission lines carry an AC signal through a controlled-impedance transmission medium. This contains the EM field and minimizes lossand coupling to other nearby structures. A simple transmission line model allows the designer to estimate the electrical length of the structure,along with the path loss.There are many approaches to take when modeling a transmission line. It is important to choose the appropriate simulation model for therequired outcome. For example, two-dimensional, schematic-level models are appropriate for determining phase delay through a line. Thisis also ideal for approximating the power loss as a function of frequency and length. For this application note, Agilent’s ADS1 is used. Alternatetools, such as Ansoft Designer 2 and AWR Microwave Office 3, are also suitable for this type of simulation.The classic circuit simulator SPICE includes two transmission line models. The lossless model may be used to calculate phase delay of the line.Three-dimensional field solvers, including Ansoft’s HFSS 4, provide an alternate approach to simulating the transmission line. With this classof simulation tool, the entire 3-D structure is constructed, including the physical dimensions of the structure and all material properties. Thestructure is then meshed, and Maxwell’s equations are solved. Once a converged model has been established, RF energy may be applied to thestructure to obtain S-parameters. RF coupling between structures may be modeled and visualized.Because the application discussed within this paper involves determining only path loss and phase delay of the transmission line, 3-D modelsare not required to obtain acceptable results.Although simulations are extremely useful, they can never replace the usefulness of good measurements. It is important to back-annotate realmeasurement data into the simulation models. Choose a circuit model that covers the first-order effects without any unnecessary overhead.Otherwise, the simulation becomes the greater experiment.The approach taken in this application note is to match simple transmission line models with measurement data obtained from Pyramid Probetransmission lines. First, a generic lossy transmission line is presented. This model may be used with a variety of circuit simulators. It is suitablefor designing impedance matching networks involving the thin film transmission line. Second, a 2-D microstrip model of the transmissionline is presented. Although the generic transmission line is sufficient, some users may wish to replicate the transmission properties with amicrostrip model. The model presented reveals how the generic microstrip model is adapted to match the embedded microstrip utilized withinthe Pyramid Probe.
Examples of modeling the transmission line are provided. First, a scalar path loss estimate at 1.6 GHz is shown. Finally, a 2.4 GHz impedancematching network is provided.The models presented are designed to match actual measurement data, to replicate impedance, phase velocity and loss as a function of lengthand frequency. 3-D effects, such as crosstalk and isolation, are not accounted for with the techniques presented here.Transmission Line ModelThe ADS model TLINP may be used to represent the thin film transmission line. Parameters for this model were obtained through measurementsand are shown in Table 1.VariableValueADS ModelNotesTLINPTwo-terminal physical transmission lineZ50ΩCharacteristic impedanceLUser-DefinedmLine lengthK3.23Relative dielectric constantA86dB/mAttenuationF10GHzFrequency for scaling attenuationTanDTable 1Units0Dielectric loss tangentTransmission Line Model ParametersPhase VelocityMeasurements were performed on a Pyramid Probe microstrip transmission line.The phase velocity5 was measured to be 167µm/ps.From this, the relative dielectric constant may be determined:Example ADS schematic, using theTransmission Line Model.FIG. 1For the transmission line model TLINP, the relative dielectric constant is entered directly into the model.APP NOTE::Schematic-Level Transmission Line Models for the Cascade Microtech Pyramid Probe ::Cascade Microtech, Inc.2
Path LossTransmission line path loss measurements were obtained:Measured transmission line path lossvs. frequency. Sample material was 5mm ofPyramid Probe embedded microstrip.FIG. 2VariableValueUnitsNotesLength5000µmMeasured distance of the thru-pathRef-Loss0.43dBMeasured thru-path lossRef-Frequency10GHzFrequency of ref-lossTable 2Transmission Line Path Loss MeasurementsThe TLINP model requires the path loss to be specified in dB/m:The reference frequency of 10 GHz was chosen to allow for loss averaging across the frequency range. A sufficiently long length of transmissionline (5mm) was chosen in order to minimize effects of the probe interfaces. The loss tangent (TanD) is set to 0, as all of the loss is modeledthrough A, the attenuation factor.This model allows the designer to predict the phase velocity (delay), and path loss of any 50Ω Pyramid Probe microstrip transmission line. Itwill yield adequate results through 12 GHz.APP NOTE::Schematic-Level Transmission Line Models for the Cascade Microtech Pyramid Probe ::Cascade Microtech, Inc.3
Microstrip ModelA microstrip model has been constructed which matches the characteristics of the Pyramid Probe embedded microstrip transmission line.Parameters for the ADS model MLIN were matched to actual measurement data. Tables 3 and 4 show the parameters of this model.First, the material substrate must be defined:VariableNameValueUnitsNotesPyramid Embedded MicrostripH20Substrate nameµmSubstrate thicknessEr4.4Cond5.8 e 07S/mT5µmRelative dielectric constant,. Adjusted tomatch measured phase velocity. See text.Conductor conductivity. (Copper)Conductor thicknessTanD0.015Table 3Dielectric loss tangent. Adjusted tomatch transmission loss. See text.Defining the material substrateThe transmission line references the substrate:VariableADS ModelSubstTable 4ValueUnitsNotesMLINMicrostrip linePyramid Embedded Microstrip(See Below)W34µmLine width. Adjusted to match impedance. See text.LUser-Definedmil (default)Line lengthThe transmission line references the substrateEffective Dielectric ConstantThe microstrip model within ADS assumes the signal trace ison the surface of the substrate. A great portion of the RF fieldis actually in air. For Pyramid Probe, the microstrip signal traceis embedded within the dielectric. Most of the field is containedwithin the dielectric in this case.In order to use the microstrip model properly, the “effectivedielectric constant” for the model must be determined. A modelwas constructed where two transmission lines of differinglength were created. For a time-domain simulation, the delaythrough each transmission line is compared to determine thephase velocity.As a result of this experiment, an effective dielectric constantof 4.4 was determined. This value, used in conjunction with themicrostrip model MLIN, produces a phase velocity of 167µm/ps,which matches the measured data. It is vital to remember that thisvalue does not imply the dielectric constant of the material. It isonly used to enable use of the simplified microstrip model.APP NOTE::Example ADS Model, using MLIN to emulate the thin film microstriptransmission line. Physical dimensions listed have been adjusted to match theelectrical characteristics to the model.FIG. 3Schematic-Level Transmission Line Models for the Cascade Microtech Pyramid Probe ::Cascade Microtech, Inc.4
FIG. 4Comparison of Microstrip model and Pyramid Probe embedded microstrip. Although more of the field is contained within the dielectric with this process,the microstrip model can still be used for determining electrical length and path loss.ImpedanceADS provides a transmission line calculator, LineCalc6, as a part of the ADS product package. Physical parameters of the model were enteredinto LineCalc. The width of the signal trace W was adjusted in order to obtain a 50Ω impedance in the model. Because of the differences withthe MLIN model to the Pyramid Probe, the width of the trace is not identical to the actual width of the trace within the probe.Similar transmission line calculators are readily available, including AWR TXline7. It is important to remember that each tool will generateslightly different results for the parameters entered. This is due to the unique implementation of each model, and is not an error on the part ofeither product. For this model, AWR TXline will reveal a trace width approximately 2µm wider than the ADS model.FIG. 5APP NOTE::Agilent’s LineCalc tool. Parameters listed were used to obtain 50Ω impedance.Schematic-Level Transmission Line Models for the Cascade Microtech Pyramid Probe ::Cascade Microtech, Inc.5
Path LossActual path loss depends upon numerous factors,including the topology of the probe tips on the DUT, andthe complexity of the membrane-to-PCB interface. Thehighest precision loss measurement should includethe combination of the membrane and matching PCB.With the TLINP model revealed earlier, the measuredtransmission loss could be entered directly. For theMLIN model, the loss needs to be matched against themeasured data.To match the loss of the transmission line, theconductivity of the material and the loss tangent wereadjusted from ideal values until the loss matched themeasured data. For the conductivity, copper was used,as the ground plane of the microstrip in the thin filmis copper. The loss tangent was adjusted to align theremaining loss through the measured data. This isshown in Figure 6.FIG. 6Transmission Loss, Measured vs. Model. Example 5mm Pyramid Embedded Microstrip.Example: Path Loss EstimateAs an example, determine the scalar path loss of a microstrip transmission line for a GPS application. The operating frequency is 1.575 GHz.For this example, the transmission line is 16,000µm.From the transmission line model, the loss of the transmission line is 86dB/m @ 10 GHz. A simulation is not necessary to determine thescalar loss:This means that any signal presented at the board-to-core interface of the core will be attenuated by 0.22dB at the probe tip.Example: Impedance Matching NetworkWhen designing a lumped-element impedance matching network, thelocation of the network on the transmission line must be known. Beforedesigning the matching network, the impedance of the device includingthe transmission line needs to be calculated.Consider the example of a 2.4 GHz Bluetooth receiver, with an inputimpedance of 10 j15Ω. Determine the type of network required tomatch to 50Ω. The placement of lumped elements will be 6000µm fromthe complex load.FIG.7Building the Impedance Matching NetworkThe impedance of the load is:APP NOTE::Schematic-Level Transmission Line Models for the Cascade Microtech Pyramid Probe ::Cascade Microtech, Inc.6
The reflection coefficient at the load is:This is expressed as point “A” in Figures 7-9.At 2.4 GHz, one wavelength of transmission line is:Neglecting the loss of the transmission line momentarily, the reflection coefficientrotates as a function of the length x of the transmission line8:SoOn the Smith chart, the phase rotation of the transmission line is approximately 62 .Through simulation, we observe the reflection coefficient of 0.654 83 , whichcorresponds to an impedance of 22.5 j51.2Ω. This is noted as point “B” on theSmith chart. The difference in magnitude accounts for the slight path loss of thetransmission line.sweep AB (S11)FIG. 8sweep BC (S11)sweep CD (S11)Tracking the Impedance through the Matching NetworkAt this location on the transmission line, lumped elements are used to complete the impedance match. First, a capacitor of 1.7pF provides ashunt reactance of -39Ω. The impedance (at point “C”) is now at 52.3 -j67.2Ω.Because the real component of the impedance is now essentially 50Ω, the only thing left is to add 67Ω of inductive reactance (in series) to thecircuit. The final impedance is 52.3 j0.85Ω. The reflection coefficient of 0.02 corresponds to 32dB return loss. In other words, instrumentslooking into the network will see a real 50Ω load.This exercise may be replicated in tools such as Agilent ADS 2008. Setthe frequency sweep to a single point at 2.4 GHz. Disable all lumpedelements as well as the transmission line by using the deactivate feature.Verify your S11 measurement reveals the device impedance on the Smithchart. From there, enable each element of the circuit from right to left.Use the parameter sweep or tuning functions to sweep the length ofthe transmission line, or the value of the components, to see how theimpedance changes.The complete matching network. 6000µm of the transmission line materialbecomes an integral part of the match.FIG. 9APP NOTE::Schematic-Level Transmission Line Models for the Cascade Microtech Pyramid Probe ::Cascade Microtech, Inc.7
Simulation ChallengesThis paper presented two transmission line models that match the characteristics of Cascade Microtech’s Pyramid Probe microstriptransmission line. These models provide a useful tool for predicting the scalar loss of a probe prior to receiving the first article from the factory.Phase information may be used to assist with the design of impedance matching networks.Here are a few key points regarding this exercise to remember: The models are only an estimate, and they should be treated as such. Parameters associated with the models should not be quoted asexact physical values. Some parameters have been adjusted slightly, to match the model to actual measured data. These models do not account for the PC board to membrane interface characteristics. The models do not account for the possibilitythat one or more transmission line types may be utilized in the transmission path. Although these considerations are small, it may skewyour delay computations slightly. Impedance scaling from this model is not possible. When the impedance of the transmission line increases, the phase velocity willincrease (as a function of the varying geometries). For high impedance lines (example, 100Ω), a new model would need to be derived. When designing a network for impedance matching, design the network to prepare for slight variations in phase and amplitude.Variations in probe tip configuration and transitions from one transmission line will cause slight variations in overall velocity and loss thatmay not be fully accounted for with such a simple model. Set your expectations accordingly. It is always important to set numbers into their proper context. For example, a 0.05dB error ininsertion loss will probably not cause a significant error in your final measurement. For impedance matching exercises, draw a 10dBreturn loss circle around the center of the Smith chart. When you have achieved an impedance transform that moves you into this circle,stop designing and start measuring.1More information on Agilent ADS may be found online at http://eesof.tm.agilent.com.2More information on Ansoft Designer may be found online at http://www.ansoft.com/products/hf/ansoft designer.3More information on AWR Microwave Office may be found online at http://web.appwave.com/Products/Microwave Office/Overview.php .4More information on Ansoft HFSS may be found online at http://www.ansoft.com/products/hf/hfss .5D. Pozar, Microwave Engineering, 3rd Edition. 2005 Wiley.6Linecalc, from Agilent’s eeSof division, shares the same transmission line models as ADS.7More information on AWR TXline may be found online at: http://web.appwave.com/Products/Microwave Office/Feature Guide.php?bullet id 98W. Hayward, Introduction to Radio Frequency Design. 1994, American Radio Relay League. Copyright 2009 Cascade Microtech, Inc.All rights reserved. No part of this document may bereproduced or transmitted in any form or by any means,electronic or mechanical, including photocopy, recording,or any information storage and retrieval system, withoutpermission in writing from Cascade Microtech, Inc.Data subject to change without noticeCascade Microtech, Inc.toll free: 1-800-550-3279phone: 1-503-601-1000email: cmi sales@cmicro.comCascade Microtech GmbHphone: 49-811-60005-0email: cmg h.comCascade Microtech Japanphone: 81-3-5615-5150email: cmj sales@cmicro.comCascade Microtech Singaporephone: 65-6873-7482email: cms sales@cmicro.comCascade Microtech Shanghaiphone: 86-21-3330-3188email: cmc sales@cmicro.comCascade Microtech Taiwanphone: 886-3-5722810email: cmt sales@cmicro.com
The classic circuit simulator SPICE includes two transmission line models. The lossless model may be used to calculate phase delay of the line. Three-dimensional field solvers, including Ansoft’s HFSS 4 , provide an alternate appro
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