Application Note 905 Transmission Line RAPIDESIGNER Operation and Applications Guide Literature Number: SNLA035 National Semiconductor Application Note 905 James A. Mears May 1996 INTRODUCTION The National Semiconductor Transmission Line RAPIDESIGNER makes quick work of calculations frequently used in the design of data transmission line systems on printed circuit boards. Based on principles contained in our Interface Databook, the Transmission Line RAPIDESIGNER benefits from our many years experience in designing and manufacturing data transmission and interface products and from helping our valued customers obtain the most from National’s Interface products. Two versions of the Transmission Line RAPIDESIGNER are available while supplies last. RAPIDESIGNER (Lit. #633200) features ISO metric units. RAPIDESIGNER (Lit. #633201) features English units. If information about other National Semiconductor products is desired, please contact one of our Customer Response Centers: 1-800-272-9959 (USA), 49-0-180-532-78-32 (Europe, English language), or 81-043-299-2308 (Japan). Our Worldwide Web site is: http://www.national.com. For applications assistance on Interface products, call our Interface Applications Hotline, 1-408-721-8500 in Santa Clara, CA, USA. Transmission Line RAPIDESIGNER uses only h to represent dielectric (substrate) thickness. Differential lines are edge-coupled only. Striplines are centered between adjacent image ground planes. CAUTIONARY STATEMENT National Semiconductor assumes no responsibility and accepts no liability for results obtained or application of these results from the use of the Transmission Line RAPIDESIGNER. In order to obtain meaningful and useable results from this calculator, the user must be familiar with general transmission line theory and the application and analysis of transmission lines with pulse excitation. The resolution of results obtainable from the Transmission Line RAPIDESIGNER is similar to that of most common Napierian sliderules, that being two to three significant digits. The accuracy of results from the sliderule depends on the relationships of the numerical factors as inputs and the approximations used for the calculations. Accuracy limits and restrictions for approximations and calculations is given in Appendix A, if known. TRANSMISSION LINE GEOMETRY Microstrip and Stripline geometries as used in the Transmission line RAPIDESIGNER are defined as shown below. In common practice, h represents dielectric thickness for microstrip structures and b that for stripline. For simplicity, the © 2000 National Semiconductor Corporation AN011899 EXAMPLES 1. Find the capacitance value that will give 0.2Ω reactance at 50 MHz. A. Set 50 MHz on the Frequency scale opposite the arrow. B. Opposite 0.2Ω on the Capacitive Reactance scale, read 17 nF on the Capacitance scale. 2. Find the frequency at which 25 nH will have 10Ω reactance. A. Set 0.025 µH (25 nH) on the Inductance scale opposite 10Ω on the Inductive Reactance scale. B. Read 63 MHz on the Frequency scale at the arrow. 3. Find the capacitance value that will be resonant with 20 mH at 100 kHz. A. Set 100 kHz on the Frequency scale at the arrow. B. Opposite 20 mH on the Inductance scale, read 13 kΩ on the Inductive Reactance scale. C. Opposite 13 kΩ on the Capacitive Reactance scale, read 130 pF on the Capacitance scale. (The hand-calculated value is 127 pF.) DIFFERENTIAL Z0 (SIDE ONE) The differential Z0 scales find the approximate characteristic impedance of edge-coupled, differential-pair microstrips or striplines. Before using these scales, the characteristic impedance Z0, of the individual conductor must first be found using the Microstrip and Stripline Z0 scales on Side Two. Next, the differential impedance, Zdiff, is found based on the line spacing, s, and dielectric thickness, h. Both conductors of the pair must have the same physical cross sectional dimensions. Spacing between pairs of differential conductors should be greater than 2s to avoid excessive crosstalk between and avoid affecting the impedance of adjacent line structures. The formulations and computational method used are unique to the Transmission Line RAPIDESIGNER. The computation is based on an approximation of the reverse-crosstalk parameter of a coupled line pair. It has been shown(1–6) that this parameter can be used to express the mutual inductance and capacitance of the line pair. Therefore, the approximate characteristic impedance of the differential pair may be computed. www.national.com AN-905 AN011899-1 REACTANCE FREQUENCY (SIDE ONE) The reactance frequency scales are used to find capacitive reactance XC, capacitance C, or frequency ƒ, given any two of these parameters. Similarly, inductive reactance XL, inductance L, or frequency ƒ, may be found on the appropriate scales. In addition, the value of capacitance and inductance that are resonant at a given frequency may be found. Transmission Line RAPIDESIGNER Operation and Applications Guide Transmission Line RAPIDESIGNER r Operation and Applications Guide AN-905 Note: For the RAPIDESIGNER the range of s/h for microstrip is limited to 0.20 ≤ s/h ≤ 3.0. The range of s/h for stripline is 0.20 ≤ s/h ≤ 1.5. 1. 2. A. Move slide to set 93Ω on the Microstrip Z0 scale opposite 3.8 on the er scale. H.R. Kaupp, “Pulse Crosstalk Between Microstrip Transmission Lines”, 7th International Electronic Circuit Symposium Record. Aug. 1966, Wescon. B. Read +25 on the Microstrip Factor scale at the arrow. C. Move slide to set 0.0813 cm on the h-scale at the upper arrow. John A. DeFalco, “Predicting Crosstalk in Digital Systems”. Computer Design, June 1973, p.p. 69–75. D. In the section for t =1.78 x 10−3 cm (1⁄2 oz), read 0.051 cm on the w-scale opposite +25 on the Factor scale. 2. Find the impedance of a 0.127 cm wide microstrip conductor on a substrate with er = 4.3, t = 3.556 x 10 −3 cm (1 oz cu.) and h = 0.102 cm. A. Move slide to set 0.102 cm on the h-scale at the upper arrow. B. In the section for t = 3.556 x 10−3 cm (1 oz), read −15 on the Factor scale opposite 0.127 cm on the w-scale. C. Then move slide to set −15 on the Microstrip Factor scale at the arrow in middle window. D. Read 64Ω on the Microstrip Z0 scale opposite 4.3 on the er scale. 3. H.R. Kaupp, “Effects of Embedding Microstrip Interconnections”, Proceedings International Electronic Packaging and Production Conference (Inter/Nepcon 69), Oct. 1969, p.p. 189–201. 4. N.C. Arvanitakis, J.T. Kolias, and W. Radzelovage, “Coupled Noise Prediction in Printed Circuit Boards for a High-Speed Computer System”, 7th International Electronic Circuit Symposium Record, Aug. 1966, Wescon. 5. A. Feller, H.R. Kaupp and J.J. Digiacomo, “Crosstalk and Reflections in High-Speed Digital Systems”, Proceedings — Fall Joint Computer Conference, 1965, p.p. 511–525. 6. Ivor Catt, “Crosstalk (Noise) in Digital Systems”, IEEE Transactions on Electronic Computers, Vol. EC-16, No. 6, Dec. 1967, p.p. 743–763. INTRINSIC DELAY (SIDE TWO) This scale calculates the per unit-length propagation delay of a wave traveling on an unloaded microstrip or stripline transmission line. EXAMPLE 1. Find the differential impedance for an edge-coupled pair of 75Ω microstrips spaced 0.10 cm apart on a 0.076 cm thick substrate. A. Move slide to set 0.10 cm on the s-scale at 0.076 cm on the h-scale (upper window). B. Read 0.86 on the Microstrip Factor scale at the arrow (middle window). C. Move slide to set 75Ω on the Z0 scale opposite 0.86 on the Factor scale (lower window). D. Read 128Ω on the ZDIFF scale at arrow. EXAMPLE 1. Find the delay of a stripline with e r = 2.8. A. Move slide to set 2.8 on the Stripline e r scale at the upper arrow. B. Read 56 ps/cm on the Td scale at the lower arrow. MICROSTRIP AND STRIPLINE, C0 AND L0 (SIDE THREE) This scale computes the intrinsic per-unit-length values of capacitance, C0, and inductance, L0, for an unloaded microstrip or stripline. Normally, the known parameters are unloaded Z0 and er. The scales have been paired so that a simultaneous comparison of the same intrinsic property for both line types may be made with only one setting of the slide. MICROSTRIP AND STRIPLINE Z0 (SIDE TWO) The Microstrip and Stripline Z0 scales calculate the characteristic impedance of microstrip or stripline transmission lines. The formulations used are based on material published in the National Semiconductor Interface Databook, Section 12. Additional material may be found in our F100K ECL Data Book and Design Guide, Application Notes Section. In solving microstrip and stripline problems, the Transmission Line RAPIDESIGNER uses separate scale sets based on the conductor thickness t. The values for t are the standard thicknesses for copper cladding used in printed circuit board material manufacture. As a convenience to those who are not familiar with metric representations, thickness is also given in the common oz/ft2 values. The two most common uses of these scales are to find: 1. impedance Z0, given line width w , dielectric thickness h , conductor thickness t , and dielectric constant er; or 2. line width w given the other factors. EXAMPLES 1. Find C0 and L0 for a 75Ω microstrip on a substrate having er = 3.8. A. Move slide to set 75Ω on the Unloaded Z0 scale at the arrow. B. Read 0.70 pF/cm on the Microstrip C0 scale at 3.8 on the upper er scale of the middle window. C. Read 3.95 nH/cm on the Microstrip L0 scale at 3.8 on the upper er scale of the lower window. 2. Find C0 and L0 for a 35Ω stripline on a substrate having er = 2.4. A. Move slide to set 35Ω on the Unloaded Z0 scale at the arrow. B. Read 1.47 pF/cm on the Stripline C0 scale at 2.4 on the lower er scale of the middle window. C. Read 1.8 nH/cm on the Stripline L0 scale at 2.4 on the lower er scale of the lower window. The procedures given in the following examples are the same for either microstrip or stripline. Of course, the Factor and Z0 scales appropriate to the particular line type must be used. EXAMPLES 1. Find the conductor line width to yield a 93Ω microstrip on a 0.0813 cm substrate with 1.78 x 10 −3 cm (1⁄2 oz) copper cladding and dielectric constant of 3.8. www.national.com 2 be the loaded (reduced) value. This loaded impedance is useful for determining either termination network resistances or additional propagation delay. Bear in mind that this so-called loaded line impedance is only a useful mathematical fiction. The effect of the finite risetime of the signal versus the distance (meaning delay) between the loads only makes the impedance appear to have been uniformly reduced. The actual impedance of the line segments is still their unloaded characteristic impedance. This effect can be seen clearly when the Z0 of a transmission line with added lumped loads is measured using a device with an extremely fast risetime like a time-domain reflectometer. The Z0 is seen to be reduced only at the point of the attached load. These scales find the allowable maximum length of a transmission line or line stub which is terminated by a single capacitance load. This capacitance is normally the input capacitance of an active device. The known parameters are unloaded line impedance Z0 and termination capacitance C t. The scales were formulated using a nominal risetime of 3.5 ns. LMAX will change in proportion as tr changes. If t r is halved, LMAX is halved. EXAMPLES 1. Find the maximum length of a 50Ω microstrip stub on a substrate with er = 4.3 which is terminated by 10 pF. A. Move slide to set 10 pF on the C t scale opposite 50Ω on the Z0 scale. EXAMPLES 1. Find the loaded line impedance and per-unit-length propagation delay resulting from adding 4 pF/cm to a micro-strip line having an unloaded Z0 of 50Ω and er of 4.3. A. Move the slide to set 4 pF/cm on the CD scale opposite 50Ω on the Unloaded Z0 scale. B. Read 3100 on the Microstrip δ' Factor scale at 4.3 on the upper er scale of the left-hand, middle window. Also, read 2.13 on the Microstrip Z0' Factor scale at 4.3 on the upper er scale of the left-hand, bottom window. C. Then move slide to set 3100 on the Factor scale (upper right-hand window) at the arrow. D. Read 120 ps/cm on the Loaded δ' scale opposite er = 4.3 in the right-hand, middle window. E. Reset slide to set 2.13 on the Factor scale (upper right-hand window) at the arrow. F. Read 24Ω on the Microstrip Loaded Z0' scale opposite 50Ω on the upper Z0 scale of the lower right-hand window. 2. Find the individual capacitance value for 10 loads uniformly spaced along a 30 cm length of 75Ω microstrip transmission line if a 50Ω termination resistance results in no reflections. The substrate is known to have an er of 3.8. This type of measurement and computation is particularly useful for determining the actual value of loads distributed along a transmission line. A. Move slide to set 50Ω on the Microstrip Loaded Z0' scale (lower, right-hand window) opposite 75Ω on the upper Z0 scale. B. Read 1.55 on the Factor scale in the upper, right-hand window. C. Then move slide to set 1.55 on the Microstrip Z0' Factor scale (lower, left-hand window) opposite 3.8 on the upper er scale. D. Read 1.0 pF/cm on the CD scale (upper, left-hand window) opposite 75Ω on the Unloaded Z0 scale. E. A total of 30 pF is distributed among 10 loads; therefore, the capacitance of each load is 3 pF. B. Read 3040 on the Factor scale in the same window at the arrow. C. Move slide to set 3040 on the Factor scale (middle window) at the arrow. D. Read 27.7 cm on the Microstrip L max scale (bottom window) opposite 4.3 on the upper er scale. 2. A 35 cm stripline stub is terminated by 5 pF. If the substrate has an er = 2.4 and the line impedance is 75Ω, is the stub length too long? A. Move slide to set 5 pF on the C t scale opposite 75Ω on the Z0 scale. B. Read 3150 on the Factor scale in the same window at the arrow. C. Move slide to set 3150 on the Factor scale (middle window) at the arrow. D. Read 30.5 cm on the Stripline L max scale (bottom window) opposite 2.4 on the lower er scale. The 35 cm stub is more than 10% longer than calculated. Therefore, reflections may result unless the stub is terminated in a value near its characteristic impedance. PROPAGATION DELAY AND LOADED Z0 (SIDE FOUR) These scales find the loaded line impedance and per-unit-length value of propagation delay which result from adding distributed capacitance to a line. The capacitance may be associated with any type of line discontinuity including vias, line junctions or semiconductor device inputs or outputs. Normally, this capacitance occurs in discrete lumps. To simplify calculating its effect on the line, the total capacitance can be treated as though it is uniformly distributed along the line. This is permissible in most cases because the distance between loads is small compared to the distance traversed by the propagating wavefront during its risetime. Therefore, in preparation for this calculation, sum the value of all capacitances connected along the line and divide this total by the line’s length to obtain CD. Loaded line impedance is the apparent instantaneous value of impedance seen by the propagating wavefront as it encounters a discontinuity. Since the wavefront has a large and finite risetime, the line’s impedance may be considered as appearing altered over a distance approximately equal to that traversed by the propagating wavefront during its risetime. In actual fact, the presence of discontinuities along a line causes the apparent impedance of the line to be tapered to a lower value. If the line were to be severed an infinitesimal distance down-stream from a discontinuity, the impedance seen looking up-stream into the line at that point would REFLECTION COEFFICIENT (SIDE FOUR) These scales calculate the reflection coefficient when line impedance Z0, and the source or load impedance are known. The reflection coefficient, a dimensionless quantity, is the fraction of voltage reflected back toward the driving 3 www.national.com AN-905 UNTERMINATED STUB LENGTH (SIDE THREE) AN-905 source (or load) by a discontinuity in a transmission line. A discontinuity results from any physical change to the line that alters its characteristic impedance. The discontinuity may be an attached load, transmission line intersection, via in the line, termination device or even a change in the line’s geometry. MICROSTRIP AND STRIPLINE, Co AND Lo (SIDE THREE) 1. A. Move slide to set 75Ω on the Unloaded Z0 scale at the arrow. B. Read 1.78 pF/in on the Microstrip Co scale opposite 3.8 on the upper er scale. EXAMPLES 1. Find the reflection coefficient when a 50Ω line is terminated in 75Ω. A. Move slide to set 50Ω at arrow. B. Read ρL = +0.2 at 75Ω. 2. C. Next read 10 nH/in on the Microstrip Lo scale opposite 3.8 on the upper er scale. UNTERMINATED STUB LENGTH (SIDE THREE) 1. Find the maximum length of an unterminated 50Ω microstrip on a substrate with er = 4.3 and loaded by 10 pF. Find the line impedance if a 5V transmitted pulse measures 3.3V across a 20Ω termination resistor. A. Since only 67% of the 5V pulse was measured at the load, the ρL = −0.33. Move slide to set 20Ω at −0.33. B. Read Z0 = 40Ω at arrow. A. Move slide to set 10 pF on the C t scale opposite 50Ω on the Z0 scale. B. Read 3040 on the Factor scale in the same window at the arrow. C. Move slide to set 3040 on the Factor scale, middle window at the arrow. D. Read 10.9 in. on the Microstrip L max scale opposite 4.3 on the upper er scale. EXAMPLE CALCULATIONS — ENGLISH UNITS DIFFERENTIAL Zo (SIDE ONE) 1. Find the differential impedance for a coupled pair of 75Ω microstrips spaced 10 mils apart on a 20 mils thick substrate. A. Move slide to set 10 mils on the s scale at 20 mils on the h scale. B. Read 0.702 on the Microstrip Factor scale at the arrow. C. Move slide to set 75Ω on the Z0 scale opposite 0.702 on the Factor scale in lower window. D. Read 105Ω on the Zdiff scale at the arrow. PROPAGATION DELAY AND LOADED Z0 (SIDE FOUR) 1. Find the propagation delay and loaded line impedance when 4 pF/in of load capacitance is added to a microstrip line with unloaded Z0 = 50Ω and er of 2.4. A. Move slide to set 4 pF/in on the Distributed CD scale opposite 50Ω on the Unloaded Z0 scale. B. Read 2000 on the Microstrip δ' Factor scale opposite 2.4 on the er scale directly above. Read 1.53 on the Microstrip Z0’ Factor scale opposite 2.4 on the e r scale directly above. C. Next, move slide to set 2000 at the arrow for the Factor scale, upper right-hand window. D. Read 190 ps/in on the Microstrip Loaded δ' scale opposite 2.4 on the er scale directly above. E. Next, move slide to set 1.53 at the arrow for the Factor scale at the upper right-hand window. F. Read 33Ω on the Microstrip Loaded Z0’ scale opposite 50Ω on the Z0 scale directly above. MICROSTRIP AND STRIPLINE Z0 (SIDE TWO) 1. Find the conductor width to yield a 93Ω microstrip on a 30 mil substrate with 0.7 mil (1⁄2 oz) copper cladding and dielectric constant of 3.8. A. Move slide to set 93Ω on the Microstrip Z0 scale opposite 3.8 on the er scale directly below. B. Read 25 on Microstrip Factor scale at the arrow. C. Move slide to set 30 mils on the h scale at the arrow, top window. D. In the window for t = 0.7 mils (1⁄2 oz), read 18 mils on the w scale opposite 25 on the Factor scale directly above. 2. Find the impedance of a 25 mils wide microstrip line on a substrate with er = 4.3, t = 1.4 mils ( 1 oz cu.) and h = 20 mils. A. Move slide to set 20 mils on the h scale at the upper arrow, top window. B. In the section for t = 1.4 mils (1 oz) opposite 25 mils on the t scale, read −17 on the Factor scale directly below. C. Move slide to set −17 on the Microstrip Factor scale at the arrow. D. Read 63Ω on the Microstrip Z 0 scale opposite 4.3 on the er scale directly below. INTRINSIC DELAY (SIDE TWO) 1. Find the per unit length delay of a stripline with er = 2.8. A. Move slide to set 2.8 on the Stripline e r scale at the arrow. B. Read 142 ps/in on the Td scale at the lower arrow. www.national.com Find Co and Lo for a 75Ω microstrip on a substrate having er = 3.8. 4 AN-905 APPENDIX A — SCALE FORMULATIONS — ISO METRIC UNITS and the intrinsic inductance is: MICROSTRIP AND STRIPLINE Z0 Microstrip characteristic impedance is: PROPAGATION VELOCITY AND INTRINSIC DELAY The velocity of propagation for microstrip is: If w ≤ 2h (maximum error ≅ 3%). Microstrip line width is: The intrinsic propagation delay for microstrip is: The velocity of propagation for stripline is: Where: w = trace width in cm., t = trace thickness in cm., h = dielectric thickness in cm., er = relative dielectric constant (dimension less). Note: All geometric variables must be in the same dimensional units. Stripline characteristic impedance is: The intrinsic propagation delay for stripline is: Where, er = relative dielectric constant (dimensionless) and ereff = effective relative dielectric constant. PROPAGATION DELAY AND LOADED Z0 Best accuracy results if parameters are kept within these guiding ratios: b − t > 2w and b > 4t. The general formula for loaded propagation delay is: Stripline line width is: Loaded line impedance is: Where: b = dielectric thickness (between ground planes) in cm. All other variables are as previously defined. Note: As for Z0, guiding ratios apply. Where: for microstrip DIFFERENTIAL Z0 For microstrip line the differential impedance, Zdiff , is: and for stripline. CD is in pF and Z0 is in Ohms. For stripline the differential impedance, Zdiff, is: Note: For er > 1, e reff < er 1. For Microstrip, the complete forms are: 1. For Stripline, the complete forms are: Note: These functions were derived from empirical data. The actual accuracy has not been determined experimentally. Various sources cite possible errors of up to ± 10%. The practical ranges for Z0 and Zdiff are from 20Ω to about 150Ω. MICROSTRIP AND STRIPLINE, C0 AND L0 For microstrip, the intrinsic capacitance is: and the intrinsic inductance is: For stripline, the intrinsic capacitance is: 5 www.national.com AN-905 UNTERMINATED STUB LENGTH and the intrinsic inductance is: The general equation for unterminated stub length is: PROPAGATION VELOCITY AND INTRINSIC DELAY Where: Ct in pF, tr in ps and T d The velocity of propagation for microstrip is the same as shown in Appendix A. The intrinsic propagation delay for microstrip is: in ps/cm. As implemented for microstrip, The velocity of propagation for stripline is the same as shown in Appendix A. The intrinsic propagation delay for stripline is: and for stripline, Where: Z0 = line characteristics impedance (in Ohms), Ct = the total lumped value of capacitance terminating the line or stub (in pF), er = the relative dielectric constant. These equations were formulated assuming tr = 3.5 ns = 3.5 x 103 ps. Where, er = relative dielectric constant (dimensionless) and ereff = effective relative dielectric constant. PROPAGATION DELAY AND LOADED Z0 REFLECTION COEFFICIENT The general formula for loaded propagation delay is the same as shown in Appendix A. Loaded line impedance is the same as shown in Appendix A. Except: for microstrip and Where: ρL = load reflection coefficient, ρ S = source reflection coefficient, RL = load resistance in Ohms, RS = source driving-point resistance in Ohms, Z0 = transmission line impedance in Ohms for stripline. CD is in pF and Z0 is in Ohms. Note: For er REACTANCE FREQUENCY APPENDIX B — SCALE FORMULATIONS — ENGLISH UNITS MICROSTRIP AND STRIPLINE Z0 Same as shown in Appendix A. All units are mils. DIFFERENTIAL Z0 Same as shown in Appendix A. All units are mils. MICROSTRIP AND STRIPLINE, C0 AND L0 For microstrip, the intrinsic capacitance is: and the intrinsic inductance is: For stripline, the intrinsic capacitance is: www.national.com 6 > 1, e reff < er 1. For Microstrip, the complete forms are: 2. For Stripline, the complete forms are: Where: Z0 = line characteristic impedance (in Ohms), Ct = the total lumped value of capacitance terminating the line or stub (in pF), er = the relative dielectric constant. These equations were formulated assuming tr = 3.5 ns = 3.5 x 103 ps. The general equation for unterminated stub length is: REFLECTION COEFFICIENT See Appendix A Where: Ct in pF, tr in ps and Td in ps/in. As implemented for microstrip, REACTANCE FREQUENCY See Appendix A and for stripline, APPENDIX C — STANDARD 1% RESISTOR DECADES STANDARD 1% RESISTOR DECADES 10.0 12.1 14.7 17.8 21.5 26.1 31.6 38.3 46.4 56.2 68.1 82.5 10.2 12.4 15.0 18.2 22.1 26.7 32.4 39.2 47.5 57.6 69.8 84.5 10.5 12.7 15.4 18.7 22.6 27.4 33.2 40.2 48.7 59.0 71.5 86.6 10.7 13.0 15.8 19.1 23.2 28.0 34.0 41.2 49.9 60.4 73.2 88.7 11.0 13.3 16.2 19.6 23.7 28.7 34.8 42.2 51.1 61.9 75.0 90.9 11.3 13.7 16.5 20.0 24.3 29.4 35.7 43.2 52.3 63.4 76.8 93.1 11.5 14.0 16.9 20.5 24.9 30.1 36.5 44.2 53.6 64.9 78.7 95.3 11.8 14.3 17.4 21.0 25.5 30.9 37.4 45.3 54.9 66.5 80.6 97.6 Note 1: To obtain Standard Values, multiply values from Decade Table by powers of 10. APPENDIX D — VALUES OF er FOR COMMON MATERIALS Description Dielectric er Epoxy/Glass FR-4 Generic 4.3 Epoxy/Glass G-10 Generic 4.3 ± 0.05 Polyimide G-30 Polyimide PTFE/Glass PTFE 2.4 nom Polysulfone Polysulfone 3.5–3.9 4.2 Transmission Line RAPIDESIGNER Operation and Applications Guide UNTERMINATED STUB LENGTH LIFE SUPPORT POLICY NATIONAL’S PRODUCTS ARE NOT AUTHORIZED FOR USE AS CRITICAL COMPONENTS IN LIFE SUPPORT DEVICES OR SYSTEMS WITHOUT THE EXPRESS WRITTEN APPROVAL OF THE PRESIDENT AND GENERAL COUNSEL OF NATIONAL SEMICONDUCTOR CORPORATION. As used herein: 1. Life support devices or systems are devices or systems which, (a) are intended for surgical implant into the body, or (b) support or sustain life, and whose failure to perform when properly used in accordance with instructions for use provided in the labeling, can be reasonably expected to result in a significant injury to the user. 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