Schematic-Level Transmission Line Models for the Pyramid Probe

Transcription

1 Schematic-Level Transmission Line Models for the Pyramid Probe Abstract Cascade Microtech s Pyramid Probe enables customers to perform production-grade, on-die, full-speed test of RF circuits for Known-Good Die (KGD). For some applications, it may be necessary to model the transmission lines within the thin film portion of the probe card. Modeling information is useful for impedance matching the device under test (DUT) to a particular load, or to predict the insertion loss of the overall assembly. This application note presents an electrical model for a microstrip Pyramid Probe transmission line. Two schematic models are presented, 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 loss and 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 the required outcome. For example, two-dimensional, schematic-level models are appropriate for determining phase delay through a line. This is also ideal for approximating the power loss as a function of frequency and length. For this application note, Agilent s ADS 1 is used. Alternate tools, 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 class of simulation tool, the entire 3-D structure is constructed, including the physical dimensions of the structure and all material properties. The structure is then meshed, and Maxwell s equations are solved. Once a converged model has been established, RF energy may be applied to the structure 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 models are 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 real measurement 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 Probe transmission lines. First, a generic lossy transmission line is presented. This model may be used with a variety of circuit simulators. It is suitable for designing impedance matching networks involving the thin film transmission line. Second, a 2-D microstrip model of the transmission line is presented. Although the generic transmission line is sufficient, some users may wish to replicate the transmission properties with a microstrip model. The model presented reveals how the generic microstrip model is adapted to match the embedded microstrip utilized within the Pyramid Probe.

2 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 impedance matching network is provided. The models presented are designed to match actual measurement data, to replicate impedance, phase velocity and loss as a function of length and frequency. 3-D effects, such as crosstalk and isolation, are not accounted for with the techniques presented here. Transmission Line Model The ADS model TLINP may be used to represent the thin film transmission line. Parameters for this model were obtained through measurements and are shown in Table 1. Variable Value Units Notes ADS Model TLINP Two-terminal physical transmission line Z 50 Ω Characteristic impedance L User-Defined m Line length K 3.23 Relative dielectric constant A 86 db/m Attenuation F 10 GHz Frequency for scaling attenuation TanD 0 Dielectric loss tangent Table 1 Transmission Line Model Parameters Phase Velocity Measurements were performed on a Pyramid Probe microstrip transmission line. The phase velocity 5 was measured to be 167µm/ps. From this, the relative dielectric constant may be determined: FIG. 1 Example ADS schematic, using the Transmission Line Model. For 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

3 Path Loss Transmission line path loss measurements were obtained: FIG. 2 Measured transmission line path loss vs. frequency. Sample material was 5mm of Pyramid Probe embedded microstrip. Variable Value Units Notes Length 5000 µm Measured distance of the thru-path Ref-Loss 0.43 db Measured thru-path loss Ref-Frequency 10 GHz Frequency of ref-loss Table 2 Transmission Line Path Loss Measurements The 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 transmission line (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 modeled through 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. It will yield adequate results through 12 GHz. APP NOTE :: Schematic-Level Transmission Line Models for the Cascade Microtech Pyramid Probe :: Cascade Microtech, Inc. 3

4 Microstrip Model A 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: Variable Value Units Notes Name Pyramid_Embedded_Microstrip Substrate name H 20 µm Substrate thickness Er 4.4 Relative dielectric constant,. Adjusted to match measured phase velocity. See text. Cond 5.8 e+07 S/m Conductor conductivity. (Copper) T 5 µm Conductor thickness TanD Dielectric loss tangent. Adjusted to match transmission loss. See text. Table 3 Defining the material substrate The transmission line references the substrate: Variable Value Units Notes ADS Model MLIN Microstrip line Subst Pyramid_Embedded_Microstrip (See Below) W 34 µm Line width. Adjusted to match impedance. See text. L User-Defined mil (default) Line length Table 4 The transmission line references the substrate Effective Dielectric Constant The microstrip model within ADS assumes the signal trace is on the surface of the substrate. A great portion of the RF field is actually in air. For Pyramid Probe, the microstrip signal trace is embedded within the dielectric. Most of the field is contained within the dielectric in this case. In order to use the microstrip model properly, the effective dielectric constant for the model must be determined. A model was constructed where two transmission lines of differing length were created. For a time-domain simulation, the delay through each transmission line is compared to determine the phase velocity. As a result of this experiment, an effective dielectric constant of 4.4 was determined. This value, used in conjunction with the microstrip model MLIN, produces a phase velocity of 167µm/ps, which matches the measured data. It is vital to remember that this value does not imply the dielectric constant of the material. It is only used to enable use of the simplified microstrip model. FIG. 3 Example ADS Model, using MLIN to emulate the thin film microstrip transmission line. Physical dimensions listed have been adjusted to match the electrical characteristics to the model. APP NOTE :: Schematic-Level Transmission Line Models for the Cascade Microtech Pyramid Probe :: Cascade Microtech, Inc. 4

5 FIG. 4 Comparison 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. Impedance ADS provides a transmission line calculator, LineCalc 6, as a part of the ADS product package. Physical parameters of the model were entered into LineCalc. The width of the signal trace W was adjusted in order to obtain a 50Ω impedance in the model. Because of the differences with the 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 TXline 7. It is important to remember that each tool will generate slightly different results for the parameters entered. This is due to the unique implementation of each model, and is not an error on the part of either product. For this model, AWR TXline will reveal a trace width approximately 2µm wider than the ADS model. FIG. 5 Agilent s LineCalc tool. Parameters listed were used to obtain 50Ω impedance. APP NOTE :: Schematic-Level Transmission Line Models for the Cascade Microtech Pyramid Probe :: Cascade Microtech, Inc. 5

6 Path Loss Actual path loss depends upon numerous factors, including the topology of the probe tips on the DUT, and the complexity of the membrane-to-pcb interface. The highest precision loss measurement should include the combination of the membrane and matching PCB. With the TLINP model revealed earlier, the measured transmission loss could be entered directly. For the MLIN model, the loss needs to be matched against the measured data. To match the loss of the transmission line, the conductivity of the material and the loss tangent were adjusted from ideal values until the loss matched the measured data. For the conductivity, copper was used, as the ground plane of the microstrip in the thin film is copper. The loss tangent was adjusted to align the remaining loss through the measured data. This is shown in Figure 6. FIG. 6 Transmission Loss, Measured vs. Model. Example 5mm Pyramid Embedded Microstrip. Example: Path Loss Estimate As an example, determine the scalar path loss of a microstrip transmission line for a GPS application. The operating frequency is GHz. For this example, the transmission line is 16,000µm. From the transmission line model, the loss of the transmission line is 10 GHz. A simulation is not necessary to determine the scalar 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 Network When designing a lumped-element impedance matching network, the location of the network on the transmission line must be known. Before designing the matching network, the impedance of the device including the transmission line needs to be calculated. Consider the example of a 2.4 GHz Bluetooth receiver, with an input impedance of 10+j15Ω. Determine the type of network required to match to 50Ω. The placement of lumped elements will be 6000µm from the complex load. FIG.7 Building the Impedance Matching Network The impedance of the load is: APP NOTE :: Schematic-Level Transmission Line Models for the Cascade Microtech Pyramid Probe :: Cascade Microtech, Inc. 6

7 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 coefficient rotates as a function of the length x of the transmission line 8 : So On the Smith chart, the phase rotation of the transmission line is approximately 62. Through simulation, we observe the reflection coefficient of , which corresponds to an impedance of j51.2ω. This is noted as point B on the Smith chart. The difference in magnitude accounts for the slight path loss of the transmission line. sweep_ab (S 11 ) sweep_bc (S 11 ) sweep_cd (S 11 ) FIG. 8 Tracking the Impedance through the Matching Network At this location on the transmission line, lumped elements are used to complete the impedance match. First, a capacitor of 1.7pF provides a shunt reactance of -39Ω. The impedance (at point C ) is now at 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 the circuit. The final impedance is 52.3+j0.85Ω. The reflection coefficient of 0.02 corresponds to > 32dB return loss. In other words, instruments looking into the network will see a real 50Ω load. This exercise may be replicated in tools such as Agilent ADS Set the frequency sweep to a single point at 2.4 GHz. Disable all lumped elements as well as the transmission line by using the deactivate feature. Verify your S 11 measurement reveals the device impedance on the Smith chart. From there, enable each element of the circuit from right to left. Use the parameter sweep or tuning functions to sweep the length of the transmission line, or the value of the components, to see how the impedance changes. FIG. 9 The complete matching network. 6000µm of the transmission line material becomes an integral part of the match. APP NOTE :: Schematic-Level Transmission Line Models for the Cascade Microtech Pyramid Probe :: Cascade Microtech, Inc. 7

8 Simulation Challenges This paper presented two transmission line models that match the characteristics of Cascade Microtech s Pyramid Probe microstrip transmission 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 as exact 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 possibility that one or more transmission line types may be utilized in the transmission path. Although these considerations are small, it may skew your delay computations slightly. Impedance scaling from this model is not possible. When the impedance of the transmission line increases, the phase velocity will increase (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 that may 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 in insertion loss will probably not cause a significant error in your final measurement. For impedance matching exercises, draw a 10dB return 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. 1 More information on Agilent ADS may be found online at 2 More information on Ansoft Designer may be found online at 3 More information on AWR Microwave Office may be found online at 4 More information on Ansoft HFSS may be found online at 5 D. Pozar, Microwave Engineering, 3rd Edition Wiley. 6 Linecalc, from Agilent s eesof division, shares the same transmission line models as ADS. 7 More information on AWR TXline may be found online at: 8 W. 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 be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from Cascade Microtech, Inc. Data subject to change without notice Cascade Microtech, Inc. toll free: phone: cmi_sales@cmicro.com Cascade Microtech GmbH phone: cmg_sales@cmicro.com Cascade Microtech Japan phone: cmj_sales@cmicro.com Cascade Microtech Shanghai phone: cmc_sales@cmicro.com Cascade Microtech Singapore phone: cms_sales@cmicro.com Cascade Microtech Taiwan phone: cmt_sales@cmicro.com TLMODEL-AN