ENGINEERING REFERENCE GUIDE 8851 SW Old Kansas Ave. Stuart, FL 34997, USA +1 772-286-9300 +1 800-544-5594 sales@emc-rflabs.com www.emc-rflabs.com EMC CAGE Code: 24602 FRFL CAGE Code: 2Y194 AS 9100, Nadcap, ISO 9001 & 14001 and OSHAS 18001 Certified EMC Technology & Florida RF Labs, a Smiths Microwave business, is an internationally recognized leader in the development and manufacturing of thin and thick film RF and Microwave resistive components, signal distribution products, and cable assemblies. Smiths Microwave is a leading provider of components, sub-assemblies, antennas and systems solutions, primarily for defense and aerospace applications, and solutions that test, filter and process high-frequency signals for wireless telecommunication networks. As a family of brands, Kaelus, Radio Waves, TECOM, TRAK, LORCH, TRAK Limited, Millitech, EMC Technology and Florida RF Labs provide exacting solutions for antenna systems for the military and commercial aerospace, transceivers, frequency sources, timing systems, component applications, and a wide range of innovative RF and Microwave solutions for the wireless telecommunications sector. © Smiths Interconnect Microwave Components, Inc. 2014 Brochure-Eng Rev 4/2014 ENGINEERING REFERENCE GUIDE EMC Technology & Florida RF Labs 8851 SW Old Kansas Ave. Stuart, Florida 34997 T: +1 772-286-9300 TF: +1 800-544-5594 F: +1 772-283-5286 www.emc-rflabs.com sales@emc-rflabs.com Table of Contents i 1 Product Frequency Bands 2 Useful Equations 8 Microstrip Transmission Line Reference Table 9 Effect of VSWR on Transmitted Power 12 Dielectric Constant & Loss Tangent 13 Material Properties 14 90˚ Hybrid Couplers Performance Parameters 15 Directional Couplers Performance Parameters 16 Normalized Dissipated Power 17 Normalized Dissipated Power in Attenuator Elements 20 Power Conversion Table 22 Thermal Discussion 25 Thermal Conductivity 27 Thermal Conductivity Conversion Factors 29 Temperature Conversion Table 30 Voltage vs. Power Plot 31 Decimal Equivalents Table 32 Alphabetized Conversion Tables 36 Derating Curves 37 Mounting High Power Devices 39 Mounting Surface Mount Terminations & Attenuators 41 Solders Per QQ-S-571 42 Microwave Test & Measurements 44 RF Matching 45 Temperature Co-efficient of Attenuation (TCA) Calculation 46 Coaxial Transmission Lines 49 Equations for Coaxial Transmission Lines 50 Symbols for Coaxial Transmission Lines 52 International System of Units 53 Standard & Current Frequency Designations 54 Electromagnetic Spectrum 55 Capacitance vs Reactance Smith Chart Product Category DC - 26.5 GHz DC - 50 GHz DC - 65 GHz DC - 50 GHz 35 Flexible Cable Assemblies Semi-Rigid Cable Assemblies Thermopad®s Terminations and Resistors DC - 6 GHz DC - 26.5 GHz Diamond Rf ™ Attenuators Smart Detectors DC - 28 GHz Diamond Rf Terminations ™ DC - 18 GHz 0 DC - 18 GHz 5 Diamond Rf ™ Resistors 10 HybriX® Couplers 15 DC - 18 GHz DC - 50 GHz 25 Attenuators 30 Complementary Signal Distribution Frequency (GHz) Product Frequency Bands 65 60 55 50 45 40 20 1 Useful Equations Reduction of SWR by a Matched Attenuator [ 1 dB 1 = tanh + tanh -1 SWR input 8.686 SWR load ] Input Reflection Coefficient in = S11 + S21 S12 1 - S22 l Reflection Coefficient () to SWR SWR = 1- 1+ Equivalent Parallel Capacitance CP = jB SWR to Reflection Coefficient () = SWR - 1 SWR + 1 Reflection Coefficient () to Return Loss R.L.(dB) = -20 log Return Loss to Reflection Coefficient () ( ) = log -1 R.L. -20 2 Useful Equations Reflected and Transmitted Power Due to SWR Prefl = Pin Ptrans = Pin 2 ( ) SWR - 1 = Pin 2 SWR + 1 4SWR = Pin (1- 2) 2 (SWR + 1) Normalized Impedance to Reflection Coefficient _ -1 = _ +1 Electrical Length (degrees) = -360 r Lf r L c = TD = Time Delay (seconds) = - 360 Td f = f f Total Power Dissipated in Attenuator Pd = Pin (1 - log -1 -10 ) dB Parallel Plate Capacitance Cpp = A r o h 3 Useful Equations (continued) “T” Attenuator Network Design R1 in = 50 R2 L = 50 R3 N = log -1(10db) R1 = ( N - 1) ( N + 1) R3 = 2 N N-1 R1 = R 2 앟 Attenuator Network Design R3 in = 50 R1 N = log -1(10db) R2 L = 50 R1 = ( N + 1) ( N - 1) R3 = (N - 1) 2 N R1 = R 2 N: the ratio of power corresponding to a given value of attenuation in decibels. 4 Useful Equations 159 X L = 6.28fGHzL nH and X C = fGHzCpF Reactance Conductance G = 1 and g = 1 R r Susceptance B = 1 and b = 1 X x Impedance (Z 0 is the Characteristic Impedance) Z Z = R ± jX = 1 = Z0 1 - and z = Y 1+ C ( ) Admittance (Y0 is the Characteristic Admittance) Y Y = G ± jB = 1 = Y0 1 - and Y = Z 1+ Y0 ( ) Reflection Coefficient = Voltage Standing Wave Ratio Return Loss Z - Z 0 Y0 - Y VSWR - 1 z - 1 = = = Z + Z 0 Y0 + Y VSWR +1 z + 1 VSWR = 1+ R = LARGER 1- RSMALLER RL = 20log = -20log Z - Z0 Z + Z0 5 Useful Equations (continued) Mismatch Loss (S = 0, L =⁄ 0) 2 ( ML = -10log (1- L ) = -10log 1- Z L - Z0 Z L + Z0 Mismatch Loss (S =⁄ 0, L =⁄ 0) Wavelength Conversion to dB 6 2 ) [( = -10log 1 - ML = -10log = c fr dB = 20log = r V2 V1 [ )] VSWR-1 2 VSWR+1 2 2 ] (1- S )(1- L ) 1- LS 8 3 . 10 m 30cm = fHzr r fGHzr = 20log i2 i1 = 10log r P2 P1 Notes 7 Microstrip Transmission Line Reference Table o w h r Trace width for a 50 ± 1 microstrip, transmission line (in mils) 1 oz copper @ 1 GHz 2.1 2.2 2.33 2.5 3 8.6 8.3 8 3 4.5 5.7 7.6 6.7 4.9 4 Data from MWO 6 6.5 8 8.6 9.4 10 3.8 3.5 2.8 4 11.7 11.3 10.9 10.4 9.1 6.7 5.5 5.2 4.8 3.9 3.7 3.3 3.1 Dielectric Thickness (h mils) 5 14.8 14.3 13.8 13.1 11.6 8.5 7 6.7 6.2 5.1 4.7 4.3 10 30.4 29.5 28.4 27.1 23.9 17.7 14.6 14 13.1 10.8 10 4 9.2 8.6 15 46.2 44.8 43.1 41.2 36.4 27 22.4 21.4 20 16.5 15.4 14.1 13.3 20 61.9 60.1 57.9 55.3 48.9 36.4 30.1 28.8 26.9 22.3 20.9 19.1 18 25 77.7 75.4 72.7 69.4 61.4 45.7 37.9 36.3 33.9 28.2 26.3 24.1 22.7 31 96.7 93.9 90.4 86.4 76.4 56.9 47.2 45.2 42.3 35.1 32.8 30.1 28.3 40 125 122 117 112 98.9 73.8 61.2 58.7 54.8 45.6 42.6 39.1 36.8 50 157 152 147 140 124 92.5 76.8 73.6 68.8 57.3 53.6 49.2 46.3 62 195 189 182 174 154 115 95.5 91.6 85.6 71.3 66.7 61.2 57.6 The above values are from the Txline 2003 calculator 8 The Effect of VSWR on Transmitted Power VSWR Return Loss (dB) Trans. Loss (dB) Volt. Refl. Coeff. Power Trans. (%) Power Refl. (%) 1.00 1.01 1.02 1.03 1.04 46.1 40.1 36.6 34.2 .000 .000 .000 .001 .002 .00 .00 .01 .01 .02 100.0 100.0 100.0 100.0 100.0 .0 .0 .0 .0 .0 1.05 1.06 1.07 1.08 1.09 32.3 30.4 29.4 28.3 27.3 .003 .004 .005 .006 .008 .02 .03 .03 .04 .04 99.9 99.9 99.9 99.9 99.8 .1 .1 .1 .1 .2 1.10 1.11 1.12 1.13 1.14 26.4 25.7 24.9 24.3 23.7 .010 .012 .014 .016 .019 .05 .05 .06 .06 .07 99.8 99.7 99.7 99.6 99.6 .2 .3 .3 .4 .4 1.15 1.16 1.17 1.18 1.19 23.1 22.6 22.1 21.7 21.2 .021 .024 .027 .030 .033 .07 .07 .08 .08 .09 99.5 99.5 99.4 99.3 99.2 .5 .5 .6 .7 .8 1.20 1.21 1.22 1.23 1.24 20.8 20.4 20.1 19.7 19.4 .036 .039 .043 .046 .050 .09 .10 .10 .10 .11 99.2 99.1 99.0 98.9 98.9 .8 .9 1.0 1.1 1.1 1.25 1.26 1.27 1.28 1.29 19.1 18.8 18.5 18.2 17.9 .054 .058 .062 .065 .070 .11 .12 .12 .12 .13 98.8 98.7 98.6 98.5 98.4 1.2 1.3 1.4 1.5 1.6 1.30 17.7 .075 .13 98.3 1.7 9 The Effect of VSWR on Transmitted Power (continued) VSWR Return Loss (dB) Trans. Loss (dB) Volt. Refl. Coeff. Power Trans. (%) Power Refl. (%) 1.32 1.34 1.36 1.38 17.2 16.8 16.3 15.9 .083 .093 .102 .112 .14 .15 .15 .16 98.1 97.9 97.7 97.5 1.9 2.1 2.3 2.5 1.40 1.42 1.44 1.46 1.48 15.6 15.2 14.9 14.6 14.3 .122 .133 .144 .155 .166 .17 .17 .18 .19 .19 97.2 97.0 96.7 96.5 96.3 2.8 3.0 3.3 3.5 3.7 1.50 1.52 1.54 1.56 1.58 14.0 13.7 13.4 13.2 13.0 .177 .189 .201 .213 .225 .20 .21 .21 .22 .22 96.0 95.7 95.5 95.2 94.9 4.0 4.3 4.5 4.8 5.1 1.60 1.62 1.64 1.66 1.68 12.7 12.5 12.3 12.1 11.9 .238 .250 .263 .276 .289 .23 .24 .24 .25 .25 94.7 94.4 94.1 93.8 93.6 5.3 5.6 5.9 6.2 6.4 1.70 1.72 1.74 1.76 1.78 11.7 11.5 11.4 11.2 11.0 .302 .315 .329 .342 .356 .26 .26 .27 .28 .28 93.3 93.0 92.7 92.4 92.1 6.7 7.0 7.3 7.6 7.9 1.80 1.82 1.84 1.86 1.88 10.9 10.7 10.6 10.4 10.3 .370 .384 .398 .412 .426 .29 .29 .30 .30 .31 91.8 91.5 91.3 91.0 90.7 8.2 8.5 8.7 9.0 9.3 1.90 1.92 10.2 10.0 .440 .454 .31 .32 90.4 90.1 9.6 9.9 10 The Effect of VSWR on Transmitted Power VSWR Return Loss (dB) Trans. Loss (dB) Volt. Refl. Coeff. Power Trans. (%) Power Refl. (%) 1.94 1.96 1.98 9.9 9.8 9.7 .468 .483 .497 .32 .32 .33 89.8 89.5 89.2 10.2 10.5 10.8 2.00 2.50 3.00 3.50 4.00 9.5 7.4 6.0 5.1 4.4 .512 .881 1.249 1.603 1.938 .33 .43 .50 .56 .60 88.9 81.6 75.0 69.1 64.0 11.1 18.4 25.0 30.9 36.0 4.50 5.00 5.50 6.00 6.50 3.9 3.5 3.2 2.9 2.7 2.255 2.553 2.834 3.100 3.351 .64 .67 .69 .71 .73 59.5 55.6 52.1 49.0 46.2 40.5 44.4 47.9 51.0 53.8 7.00 7.50 8.00 8.50 9.00 2.5 2.3 2.2 2.1 1.9 3.590 3.817 4.033 4.240 4.437 .75 .76 .78 .79 .80 43.7 41.5 39.5 37.7 36.0 56.2 58.5 60.5 62.3 64.0 9.50 10.00 11.00 12.00 13.00 1.8 1.7 1.6 1.5 1.3 4.626 4.807 5.149 5.466 5.762 .81 .82 .83 .85 .86 34.5 33.1 30.6 28.4 26.5 65.5 66.9 69.4 71.6 73.5 14.00 15.00 16.00 17.00 18.00 1.2 1.2 1.1 1.0 1.0 6.042 6.301 6.547 6.780 7.002 .87 .88 .88 .89 .89 24.9 23.4 22.1 21.0 19.9 75.1 76.6 77.9 79.0 80.1 19.00 20.00 25.00 30.00 .9 .9 .7 .6 7.212 7.413 8.299 9.035 .90 .90 .92 .94 19.0 18.1 14.8 12.5 81.0 81.9 85.2 87.5 11 Dielectric Constant ( r ) & Loss Tangent (tan ) @ 3.0 GHz Material r Air tan 1.000649 Polystyrene Foam 1.03 .0001 PTFE 2.1 .0002 2.16 .00066 2.2 .0004 Polyethylene 2.3 .0003 Polystyrene 2.55 .00033 RO/Duroid 3003 3.0 .0013 Quartz 3.78 .00006 Glass, Soda 4.82 .0054 Mica, Ruby 5.4 .0003 Diamond (CVD) 5.6 .0005 6.15 .0027 Beryllium Oxide (BeO) 6.5 .004 Aluminum Nitride (AIN) 8.9 .0005 Alumina (AI2O3) 99.6% 9.9 .0001 10.2 .0028 Vaseline ® RT/Duroid 5880 ® ® RT/Duroid 6006 ® RT/Duroid 6010 RT/Duroid is a registered trademark of Rogers Corporation 12 Material Properties Material Conductivity, (Mho/meter) x 10 8 Tantalum Nitride . . . . . . . . . . . . . . . . . . . . .000074 Carbon . . . . . . . . . . . . . . . . . . . . . . . . . . . .0006 - .0007 Nichrome (80%Ni, 20%Cr) . . . . . . . . . . . .0093 Lead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .047 Sn63 Solder . . . . . . . . . . . . . . . . . . . . . . . .0667 Tin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .087 Palladium . . . . . . . . . . . . . . . . . . . . . . . . . .0926 Indium . . . . . . . . . . . . . . . . . . . . . . . . . . . .1111 Nickel . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1449 Tungsten . . . . . . . . . . . . . . . . . . . . . . . . . .184 Rhodium . . . . . . . . . . . . . . . . . . . . . . . . . . .1961 Beryllium . . . . . . . . . . . . . . . . . . . . . . . . . .2188 Brass (66% Cu, 34% Zn) . . . . . . . . . . . . . .2564 Aluminum . . . . . . . . . . . . . . . . . . . . . . . . . .3817 Gold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4098 Copper . . . . . . . . . . . . . . . . . . . . . . . . . . . .5800 Silver . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6173 13 90˚ Hybrid Couplers Performance Parameters 90˚ Hybrid Couplers INPUT PORT 1 ISOLATED PORT 2 COUPLED PORT 4 PORT 1 2 3 4 1 IN ISO -90˚ 0˚ 2 ISO IN 0˚ -90˚ 3 -90˚ 0˚ IN ISO 4 0˚ -90˚ ISO IN DIRECT PORT 3 90˚ Crossover Hybrid Performance Parameters Vmax VSWR VSWR = Return Loss Return Loss (dB) = 20 • Log Insertion Loss Insertion Loss (dB) = 10 • Log Isolation Isolation (dB) = 10 • Log Phase Balance Amplitude Balance Vmin Phase Balance (0) = ± VSWR+1 VSWR-1 Pin ( Pcoupled + Pdirect ) Pin ( ) Pisolated Phasecoupled - Phasedirect Amplitude Balance (dB) = 10 • Log Amplitude Balance (dB) = 10 • Log 14 ) ( 2 Pcoupled ( Pcoupled + Pdirect ( 2 Pdirect Pdirect + Pcoupled 2 ) ) Directional Couplers Performance Parameters Directional Couplers INPUT PORT 1 DIRECT PORT 2 COUPLED PORT 4 ISOLATED PORT 3 Directional Coupler Performance Parameters Pcoupled ( ) Coupling Ratio Coupling Ratio (dB) = 10 • Log VSWR VSWR = Return Loss Return Loss (dB) = 20 • Log Insertion Loss Insertion Loss (dB) = 10 • Log Transmission Loss Pin Transmission Loss (dB) = 10 • Log P direct Directivity Pcoupled Directivity (dB) = 10 • Log P isolated Frequency Sensitivity [C [C Pin Vmax Vmin ) ( VSWR+1 VSWR-1 ( Pin Pcoupled + Pdirect ) ( ) ( ) max min (dB) - Cmean (dB)] (dB) - Cmean (dB)] 15 Normalized Dissipated Power “T” Attenuator Network Design R1 in = 50 R2 L = 50 R3 앟 Attenuator Network Design R3 in = 50 R1 R2 L = 50 EXAMPLE: • Input Power = 75 Watts • Attenuation = 3.75 dB • Power Dissipated in R1 = .213 (75) = 15.975 Watts 16 Normalized Dissipated Power in “T” & Attenuator Elements Attenuation Power Dissipation (watts) (dB) R1 R2 R3 0.25 .014 .014 .028 0.50 .029 .026 .054 0.75 .043 .037 .079 1.00 .058 .046 .103 1.25 .072 .054 .124 1.50 .086 .061 .145 1.75 .100 .068 .164 2.00 .115 .073 .182 2.25 .129 .076 .199 2.50 .143 .081 .214 2.75 .157 .083 .229 3.00 .171 .086 .242 3.25 .185 .088 .254 3.50 .199 .088 .266 3.75 .213 .089 .276 4.00 .226 .091 .285 4.25 .240 .090 .294 17 Normalized Dissipated Power in “T” & Attenuator Elements (continued) Attenuation R1 R2 R3 4.50 .253 .090 .302 4.75 .267 .089 .309 5.00 .280 .089 .315 5.25 .293 .087 .321 5.50 .306 .087 .325 5.75 .319 .085 .330 6.00 .332 .084 .333 7.00 .382 .076 .342 8.00 .431 .068 .342 9.00 .476 .060 .338 10.00 .519 .052 .329 12.00 .598 .038 .301 14.00 .667 .027 .266 16.00 .726 .018 .230 18.00 .776 .013 .195 20.00 .818 .008 .164 30.00 .939 .001 .059 (dB) 18 Power Dissipation (watts) Notes 19 Power Conversion Table 20 dBm Watts dBm Watts dBm Watts 30.0 30.2 30.4 30.6 30.8 31.0 31.2 31.4 31.6 31.8 32.0 32.2 32.4 32.6 32.8 33.0 33.2 33.4 33.6 33.8 34.0 34.2 34.4 34.6 34.8 35.0 35.2 35.4 35.6 35.8 36.0 36.2 36.4 36.6 1.00 1.05 1.10 1.15 1.20 1.26 1.32 1.38 1.45 1.51 1.58 1.66 1.74 1.82 1.91 2.00 2.09 2.19 2.29 2.40 2.51 2.63 2.75 2.88 3.02 3.16 3.31 3.47 3.63 3.80 3.98 4.17 4.37 4.57 36.8 37.0 37.2 37.4 37.6 37.8 38.0 38.2 38.4 38.6 38.8 39.0 39.2 39.4 39.6 39.8 40.0 40.2 40.4 40.6 40.8 41.0 41.2 41.4 41.6 41.8 42.0 42.2 42.4 42.6 42.8 43.0 43.2 43.4 4.79 5.01 5.25 5.50 5.75 6.03 6.31 6.61 6.92 7.24 7.59 7.94 8.32 8.71 9.12 9.55 10.00 10.47 10.96 11.48 12.02 12.59 13.18 13.80 14.45 15.14 15.85 16.60 17.38 18.20 19.05 19.95 20.89 21.88 43.6 43.8 44.0 44.2 44.4 44.6 44.8 45.0 45.2 45.4 45.6 45.8 46.0 46.2 46.4 46.6 46.8 47.0 47.2 47.4 47.6 47.8 48.0 48.2 48.4 48.6 48.8 49.0 49.2 49.4 49.6 49.8 50.0 50.2 22.91 23.99 25.12 26.30 27.54 28.84 30.20 31.62 33.11 34.67 36.31 38.02 39.81 41.69 43.65 45.71 47.86 50.12 52.48 54.95 57.54 60.26 63.10 66.07 69.18 72.44 75.86 79.43 83.18 87.10 91.20 95.50 100.00 105.00 Power Conversion Table dBm Watts dBm Watts dBm Watts 50.4 50.6 50.8 51.0 51.2 51.4 51.6 51.8 52.0 52.2 52.4 52.6 52.8 53.0 53.2 53.4 53.6 53.8 54.0 54.2 54.4 54.6 54.8 55.0 55.2 55.4 55.6 55.8 56.0 56.2 56.4 56.6 56.8 110 115 120 126 132 138 145 151 158 166 174 182 191 200 209 219 229 240 251 263 275 288 302 316 331 347 363 380 398 417 437 457 479 57.0 57.2 57.4 57.6 57.8 58.0 58.2 58.4 58.6 58.8 59.0 59.2 59.4 59.6 59.8 60.0 60.2 60.4 60.6 60.8 61.0 61.2 61.4 61.6 61.8 62.0 62.2 62.4 62.6 62.8 63.0 63.2 63.4 501 525 550 575 603 631 661 692 724 759 794 832 871 912 955 1000 1047 1096 1148 1202 1259 1318 1380 1445 1514 1585 1660 1738 1820 1905 1995 2089 2188 63.6 63.8 64.0 64.2 64.4 64.6 64.8 65.0 65.2 65.4 65.6 65.8 66.0 66.2 66.4 66.6 66.8 67.0 67.2 67.4 67.6 67.8 68.0 68.2 68.4 68.6 68.8 69.0 69.2 69.4 69.6 69.8 70.0 2291 2399 2512 2630 2754 2884 3020 3162 3311 3467 3631 3802 3981 4169 4365 4571 4786 5012 5248 5495 5754 6026 6310 6607 6918 7244 7586 7943 8318 8710 9120 9550 10000 21 Thermal Discussion Heat Flow Flange power devices are all conduction cooled. Conduction cooling is the transfer of heat by molecular motion within one body or between other bodies in contact. This means that the heat dissipated in the resistive element flows through the substrate, to the mounting flange, then to the heat sink and ground plane. Heat flow is a quantity of heat per unit time, such as calories per second or watts. To maintain the heat flow, there must be a temperature difference ( T) between the resistive element and the ground plane. The temperature difference is analogous to voltage. The rate at which the heat will flow is directly proportional to the area perpendicular to the heat flow, the temperature, and the thermal conductivity of the material and is inversely proportional to the distance the heat has to travel. In equation form we have: P= 22 KA • x T Thermal Discussion where: P = dissipated power, (W) K = thermal conductivity of material, W cm˚C T = T2 - T1 T2 = temperature of source, (˚C) T1 = reference temperature (heat sink), (˚C) x = length of heat flow path, (cm) A = area of heat source, (cm2) = thermal resistance (˚C/W) Thermal Resistance Rearranging equation 1 will yield an equation that will relate power dissipation and temperature differences. T x = P KA The term, x , is called the thermal resistance (), KA therefore: P = T which will give the temperature rise when the element is dissipating power. 23 Thermal Discussion (continued) Calculating Thermal Resistance Examining = x KA , it can be seen that thermal resistance decreases when x is made as small as possible. The same is true when thermal conductivity (K) and area (A) are increased. The area is difficult to define because of thermal spreading. The flow of heat will travel laterally, effectively increasing the area and further reducing the thermal resistance. For calculation purposes, assume a 45˚ spreading angle. When the heat source is a rectangle. = L 2x + W 1 • In 2K(L - W) W 2x + L ( ) And when the source is square, L = W 24 = x KL(L + 2x) Thermal Conductivity (cmWatts˚C) • METALS Silver Copper Gold Aluminum Beryllium Tungsten Rhodium Molybdenum Brass Chromium Nickel Platinum Tin Tantalum Lead Titanium Manganese (Ag) (Cu) (Au) (Al) (Be) (W) (Rh) (Mo) (66% Cu, 34% Zn) (Cr) (Ni) (Pt) (Sn) (Ta) (Pb) (Ti) (Mn) 4.08 3.94 2.96 2.18 2.00 1.74 1.50 1.46 1.110 0.937 0.920 0.716 0.666 0.575 0.353 0.219 0.078 PC BOARD MATERIAL ® RT/ Duroid 5880 G10 / FR4 ® RT/ Duroid 60 (XX) ® TMM (X) .0026 .0027 .0041 - .0048 .0068 - .0075 RT/Duroid and TMM are registered trademarks of Rogers Corporation 25 Thermal Conductivity (cmWatts˚C) • (continued) INSULATORS Diamond Beryllium Oxide 99.5% Aluminum Nitride Boron Nitride Sapphire Alumina Oxide 99.6% Alumina Oxide 96% Alumina Oxide 91% Glass Mica Air (CVD) 10.0 - 16.0 (BeO) 2.61 (AlN) 1.70 (HBN 500º) 0.59 0.46 (Al2O3) 0.36 (Al2O3) 0.26 (Al2O3) 0.13 0.015 0.0043 - 0.0062 0.00026 BONDING Gold Germanium 88/12 Gold Tin 80/20 Tin Lead Solder Indium 100% Silver Filled Epoxy Epoxy (Sn62) .8834 .6824 .4921 .2386 .0156 .0099 MISC. Thermal Grease 26 .0042 - .0049 Thermal Conductivity Conversion Factors Thermal Conductivity To Convert To Multiply By Watt m • ˚K Watt cm • ˚C 0.01 cal • cm sec • cm 2 • ˚C Watt cm • ˚C 4.1868 BTU • ft hr • ft 2 • ˚F Watt cm • ˚C .01731 BTU • ft hr • ft 2 • ˚F cal • cm sec • cm 2 • ˚C .004134 Watt m • ˚K cal • cm sec • cm 2 • ˚C .002397 Watt cm • ˚C Watt inch • ˚C 2.54 BTU • in ft 2 • h • ˚F Watt cm • ˚C 1.422 - 3 (AT 20°C) 27 Thermal Conductivity Conversion Factors (continued) Power To Convert To Multiply By Calories sec Watts 4.186 BTU hr Watts .293 (AT 20°C) 28 Temperature Conversion Table TEMPERATURE CONVERSION TABLE ˚C - 100 - 95 - 90 - 85 - 80 - 75 - 70 - 65 - 60 - 55 - 50 - 45 - 40 - 35 - 30 - 25 - 20 - 15 - 10 - 5 0 + 5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50 + 55 ˚F - 148 - 139 - 130 - 121 - 112 - 103 - 94 - 85 - 76 - 67 - 58 - 49 - 40 - 31 - 22 - 13 - 4 + 5 + 14 + 23 + 32 + 41 + 50 + 59 + 68 + 77 + 86 + 95 +104 +113 +122 +131 ˚C + 60 + 65 + 70 + 75 + 80 + 85 + 90 + 95 +100 +105 +110 +115 +120 +125 +130 +135 +140 +145 +150 +155 +160 +165 +170 +175 +180 +185 +190 +195 +200 +205 +210 +215 ˚F + 140 + 149 + 158 + 167 + 176 + 185 + 194 + 203 + 212 + 221 + 230 + 239 + 248 + 257 + 266 + 275 + 284 + 293 + 302 + 311 + 320 + 329 + 338 + 347 + 356 + 365 + 374 + 383 + 392 + 401 + 410 + 419 ˚C + 220 + 225 + 230 + 235 + 240 + 245 + 250 + 255 + 260 + 265 + 270 + 275 + 280 + 285 + 290 + 295 + 300 + 305 + 310 + 315 + 320 + 325 + 330 + 335 + 340 + 345 + 350 + 355 + 360 + 365 + 370 + 375 ˚F + 428 + 437 + 446 + 455 + 464 + 473 + 482 + 491 + 500 + 509 + 518 + 527 + 536 + 545 + 554 + 563 + 572 + 581 + 590 + 599 + 608 + 617 + 626 + 635 + 644 + 653 + 662 + 671 + 680 + 689 + 698 + 707 ˚C + 380 + 385 + 390 + 395 + 400 + 405 + 410 + 415 + 420 + 425 + 430 + 435 + 440 + 445 + 450 + 455 + 460 + 465 + 470 + 475 + 480 + 485 + 490 + 495 + 500 + 505 + 510 + 515 + 520 + 525 +530 + 535 ˚F +716 +725 +734 +743 +752 +761 +770 +779 +788 +797 +806 +815 +824 +833 +842 +851 +860 +869 +878 +887 +896 +905 +914 +923 +932 +941 +950 +959 +968 +977 +986 +995 Conversion of Temperatures: Celsius to Fahrenheit TF = 1.8 TC + 32 Celsius to Kelvin TK = TC + 273.15 Fahrenheit to Celsius TC = Kelvin to Celsius TF - 32 = .5556 (TF - 32) 1.8 TC = TK - 273.15 29 Voltage vs. Power (50 ohm system) POWER (milliwatts) 1E-10 1E-8 1E-6 1E-4 .01 1 100 1000 10.0 1.0 0.1 VOLTAGE (rms) 0.01 .001 1E-4 1E-5 1E-6 1E-7 -110 -100 -90 -80 -70 -60 -50 -40 - 30 LEVEL (dBm) 30 -20 -10 0 10 20 30 Decimal Equivalents Table STANDARD DECIMAL PREFIXES MULTIPLIER 1018 1015 1012 109 106 103 10-1 PREFIX exa peta tera giga mega kilo deci 1 ⁄ 64 1 ⁄ 32 3 ⁄ 64 1⁄ 16 5 ⁄ 64 3 ⁄ 32 7⁄ 64 1⁄ 8 9 ⁄ 64 5 ⁄ 32 11⁄ 64 3 ⁄ 16 13 ⁄ 64 7⁄ 32 15 ⁄ 64 1⁄4 17⁄ 64 9 ⁄ 32 19 ⁄ 64 5 ⁄ 16 21⁄ 64 11⁄ 32 23 ⁄ 64 3⁄8 25 ⁄ 64 13 ⁄ 32 27⁄ 64 7⁄ 16 29 ⁄ 64 15 ⁄ 32 31⁄ 64 1⁄ 2 ABBREVIATION E P T G M k d .015625 .03125 .046875 .0625 .078125 .09375 .109375 .125 .140625 .15625 .171875 .1875 .203125 .21875 .234375 .25 .265625 .28125 .296875 .3125 .328125 .34375 .359375 .375 .390625 .40625 .421875 .4375 .453125 .46875 .484375 .50 MULTIPLIER 10-2 10-3 10-6 10-9 10-12 10-15 10-18 PREFIX centi milli micro nano pico femto atto ABBREVIATION c m 33 ⁄ 64 17⁄ 32 35 ⁄ 64 9 ⁄ 16 37⁄ 64 19 ⁄ 32 39 ⁄ 64 5⁄8 41⁄ 64 21 ⁄ 32 43 ⁄ 64 11⁄ 16 45 ⁄ 64 23 ⁄ 32 47⁄ 64 3 ⁄4 49 ⁄ 64 25 ⁄ 32 51 ⁄ 64 13 ⁄ 16 53 ⁄ 64 27⁄ 32 55 ⁄ 64 7⁄ 8 57⁄ 64 29 ⁄ 32 59 ⁄ 64 15 ⁄ 16 61⁄ 64 31⁄ 32 63 ⁄ 64 1 n p f a .515625 .53125 .546875 .5625 .578125 .59375 .609375 .625 .640625 .65625 .671875 .6875 .703125 .71875 .734375 .75 .765625 .78125 .796875 .8125 .828125 .84375 .859375 .875 .890625 .90625 .921875 .9375 .953125 .96875 .984375 1.00 31 Alphabetized Conversion Table TO CONVERT MULTIPLY BY TO OBTAIN amperes/sq. cm. amperes/sq. in. angstrom unit angstrom unit A 6.452 1.550 x 10 -1 3.937 x 10 -9 1.0 x 10 -4 amps/sq. in. amps/sq. cm. inches microns or (mu) btu btu/hr. btu/min. B 2.928 x 10 -4 2.931 x 10 -1 1.757 x 101 kilowatt - hours watts watts centigrade (degrees) centigrade (degrees) centipoise circumference cubic centimeters cubic centimeters cubic inches cubic inches C (C x 9⁄5) + 32 C + 273.18 1.0 x 10 -2 6.283 6.102 x 10 -2 2.642 x 10 -4 1.639 x 101 1.639 x 10 -2 fahrenheit (degrees) kelvin (degrees) gr./cm. - sec. radians cubic in. gallons (u.s. liquid) cu cms. liters days days days degrees (angle) degrees (angle) D 8.64 x 10 4 1.44 x 10 3 2.4 x 101 1.745 x 10 -2 3.6 x 10 3 seconds minutes hours radians seconds 32 Alphabetized Conversion Table TO CONVERT MULTIPLY BY TO OBTAIN ergs ergs ergs ergs/sec. ergs/sec. E 9.486 x 10 -11 1.0 x 10 -7 2.773 x 10 -14 5.668 x 10 -9 1.0 x 10 -10 btu joules kilowatt - hrs. btu/min kilowatts fathoms foot - candle F 6.0 1.0764 x 101 feet lux gallons gausses gausses gausses grams grams grams G 3.785 x 10 3 1.0 x 10 -8 6.452 x 10 -8 7.958 x 10 -1 3.527 x 10 -2 3.215 x 10 -2 2.205 x 10 -3 cu. cms. webers/sq. cm. webers/sq. in. amp. - turn/cm. ounces (avdp) ounces (troy) pounds horsepower horsepower H 4.244 x 101 7.457 x 10 -1 btu/min. kilowatts 33 Alphabetized Conversion Table (continued) TO CONVERT MULTIPLY BY TO OBTAIN inches inches inches I 2.540 2.54 x 101 2.54 x 10 8 centimeters millimeters angstrom units joules joules joules J 9.486 x 10 -4 1.0 x 10 7 2.778 x 10 -4 btu ergs watt-hrs. kilograms kilowatts knots K 2.2046 1.434 x 101 1.151 pounds kg. - calories/hr. statute miles/hr. miles (statute) miles (statute) miles/hr. millimeters millimeters mils M 1.609 8.684 x 10 -1 1.6093 3.937 x 10 -2 3.937 x 101 2.54 x 10 -3 kilometers miles (nautical) kms./hr. inches mils centimeters ounces O 2.8349 x 101 grams 34 Alphabetized Conversion Table TO CONVERT MULTIPLY BY TO OBTAIN pounds pounds/sq. in. P 4.5359 x 10 2 7.03 x 10 -2 grams kgs./sq. cm. radians reams R 5.7296 x 101 5.0 x 10 2 degrees sheets square centimeters square inches S 1.550 x 10 -1 6.452 sq. inches sq. cms. volt/inch V 3.937 x 10 -1 volt/cm. watts watts watts watt-hours weeks weeks W 3.4129 1.0 x 10 7 9.48027 x 10 -4 3.6 x 1010 1.68 x 10 2 1.008 x 10 4 btu/hr. ergs/sec. btu/sec. ergs hours minutes yards yards yards Y 9.144 x 101 9.144 x 10 -1 9.144 x 10 2 centimeters meters millimeters 35 Standard Derating Curves Standard Derating Curve for Attenuators 100% PERCENT OF RATED POWER 50% SAFE OPERATING AREA 0% 25 50 85 75 100 125 HEAT SINK TEMPERATURE IN °C Standard Derating Curve for Resistors and Terminations 100% PERCENT OF RATED POWER 50% SAFE OPERATING AREA 0% 25 50 75 100 HEAT SINK TEMPERATURE IN °C 36 125 150 Mounting High Power Devices The area under the device should be flat to less than .001” and be free of burrs and scratches. The main criteria when mounting flange power devices is to make intimate contact with the heat sink. Air gaps at this interface will cause a very high thermal resistance barrier and must be avoided. Prior to drilling and tapping threads for the mounting screws, countersink the locations. This operation will prevent raising the threads above the mounting surface while tapping. The heat sink can now be given a coat of thermal grease, keeping the thickness to about .001 to .002 inches. The thermal grease will fill any small air gaps helping maintain good thermal contact. Before mounting the device, a small strain relief should be formed within the tab. While forming a small half loop, the tab should be supported to prevent excessive force toward the cover substrate. Pretinning the tab prior to installation and wicking off the excess will remove most of the gold plating. This is highly recommended as it will prevent gold embrittlement in the final solder connection. Seat the device into the thermal grease, install screws with a lock washer and a flat washer, and torque as specified in the following table: Thread No. Mounting Torque 4 - 40 6 inch - lbs 6 - 32 8 inch - lbs 8 - 32 12 inch - lbs 10 - 24 18 inch - lbs 37 Mounting High Power Devices (continued) Position the tab over the circuit and solder in place. Sn63 is recommended for all solder operations. When mounting an unflanged device, pretinning the device ground plane and the heat sink are necessary. In this operation, the device and the heat sink will become an integral part. Sn62 solder is used here because it reduces the amount of leaching between the silver in the ground plane and the solder. The tab contacts are treated the same way as a flanged device. Reflow the solder and position the device on the heat sink. Apply a downward force overcoming the surface tension of the solder, and settle the device down to the heat sink surface. The goal is to eliminate air voids and make the solder junction thin. While maintaining the downward force, allow the solder to cool. It is recommended that a small amount of RMA flux (per MIL-F-14256) be used in any of the soldering operations. Remove flux when complete with isopropyl alcohol. 38 Mounting Surface Mount Terminations & Attenuators The low cost and convenience of surface mount components and automated installation is inspiring new surface mount high power components that have previously required chassis mounting. The design of systems using high power surface mount components requires careful attention to the electrical grounding and heat sinking of the component to achieve specified performance and power handling. Because the component will be attached to a printed circuit board instead of a metal chassis, finite inductance to ground will be introduced. For terminations, VSWR may rise with increasing frequency and for attenuators, attenuation flatness may degrade. The relatively high thermal resistance of the printed circuit board compared to a metal mounting surface will result in lower power handling limits to maintain reliable operating temperatures. Properly designed surface mount printed circuit will minimize these effects and allow high performance. The best way to decrease printed circuit board inductance to ground and thermal resistance is to maximize the amount of plated through via holes under and around the surface mount component and specify heavy copper cladding (2 oz.) to spread the dissipated heat. 39 Mounting Surface Mount Terminations & Attenuators (continued) Typical Printed Circuit Board Layout for a High Power Surface Mount Component Filled or plugged via holes should be used to avoid component attachment solder from wicking down to the bottom surface of the printed circuit board. High Temperature solder such as Sn96 is preferable to Sn62. Because of relatively high thermal resistance mounting, most devices will be capable of reflowing their attachment solder before device damage occurs if extremely high RF power is applied. Application of thermally conductive elastomers or epoxies around the perimeter of the part will aid in heat spreading also, however the top surface should be avoided to eliminate detuning of the internal matching structures. 40 Solders Per QQ-S-571 Composition Sn96 Sn70 Sn63 Sn62 Sn60 Sn50 Sn40 Sn35 Sn30 Sn20 Sn10 Sn5 Sb5 Pb80 Pb70 Pb65 Ag1.5 Ag2.5 Ag5.5 Melting Range Solidus Liquidus 221˚C 183˚C 183˚C 179˚C 183˚C 183˚C 183˚C 185˚C 185˚C 184˚C 268˚C 308˚C 235˚C 183˚C 183˚C 183˚C 309˚C 304˚C 304˚C 221˚C 193˚C 183˚C 179˚C 191˚C 216˚C 238˚C 243˚C 250˚C 270˚C 290˚C 312˚C 240˚C 277˚C 254˚C 246˚C 309˚C 304˚C 380˚C Other Commonly Used Solders Gold Germanium 88 ⁄12 Gold Tin 80 ⁄20 Indium 100% 356˚C 280˚C 157˚C 356˚C 280˚C 157˚C 41 Microwave Test & Measurements Most microwave testing can be accomplished with scalar analyzers. The classic parameters SWR, return loss, insertion loss and attenuation are magnitude only and are scalar measurements. There are uncertainties in making these measurements but broadband high directivity and well matched detectors minimize them. As such the measurements are adequate for characterizing coaxial cable assemblies, attenuators and terminations. The electrical lengths of coaxial cable assemblies are often required to be the same. For this kind of measurement, a vector network analyzer is required. A vector network analyzer gives the phase information required to measure electrical length. Measurements can be relative or an absolute electrical length and are units of degrees. It is advisable to create a phase standard when an electrical length requirement is imposed. The derivative of the above measurement, which is the phase slope vs. frequency, is an important parameter and is called group delay. It is a measure of transit time through an assembly and for distortion free output the delay should be linear. Here again a standard should be created and maintained. Characterizing flanged resistors, terminations, and attenuators begins with fixturing. Florida RF Labs uses soft micostrip transmission lines in its fixtures. Various 50Ω lines with dielectric constants of 2.20 and 6.15 and board thicknesses of .025, .050, and .062 inches allow broad frequency coverage and accommodates different tab contact widths without causing mismatches. Coaxial transitions are also selected to minimize mismatches on both one port and two port test fixtures. Measurements are made with a Wiltron 360 Vector Network Analyzer with 40 GHz capability. The procedure is to set a gate around the DUT (Device Under Test) in time domain and 42 Microwave Test & Measurements applying the gate in the frequency domain, removing unwanted reflections of the test fixtures. This will allow a clean SWR or Return Loss measurement of the DUT. When impedance information is required the measurement plane is electronically moved to the input of the DUT yielding useful impedance data. When attenuation measurements are required the fixture losses are normalized by the network analyzer. 43 RF Matching In most applications of flanged power devices, minimum reflection is the main criteria. Reflections cause standing waves which result in inefficient transmission of energy. The worst case is when the forward wave and the reflected wave are in phase, creating a voltage peak which can lead to total breakdown of the transmission line. When mounting a device, the line impedance should be considered. If the transmission line is narrow, select a tab width that is slightly narrower, thus eliminating an unwanted shunt capacitive susceptance which would be created by a wider tab. That same tab width can also be used as an inductive reactance by sliding the device away from the end of the transmission line. This kind of a manipulation of a tab usually results in a narrower band match. Broadband matching will require additional elements in the form of a quarter wave open and shorted stubs. There are two types of matching that can be accomplished. One is a conjugate match that results in the maximum transfer of power from the source to the load. In the second, the load is matched to the transmission line and yields a minimum of reflections on the line. Terminations such as 32-1034 (30 watts), 32-1036 (60 watts), 32-1026 (150 watts), and 32-1037 (250 watts) have been internally matched to reduce the reactive components to a minimum. The only requirement is careful mounting to obtain repeatable performance. Impedance plots are available from Florida RF Labs for these and other high power terminations. 44 Temperature Co-efficient of Attenuation (TCA) Calculation DEFINITIONS: dB - Total amount of compensation required T - Total amount of temperature change in the system. dBnom - Nominal Attenuation Temp. (C˚) -55 25 125 Atten. (dB) 4 3 1.8 T = 180 dB = 2.2 TCA = dB / dBnom. / T = 2.16 dB / 3 dB / 180˚C = -0.0041 Attenuation vs. Temperature 4.5 Attenuation (dB) 4 -55, 4 3.5 } 25, 3 3 2.5 2 dB 125, 1.8 1.5 1 T 0.5 0 -55 -35 -15 5 25 45 65 85 105 125 3N04 Temperature (degree C) TCA (dB/dB/˚C) TCA Slope (N = Negative) Nominal Attenuation 45 Coaxial Transmission Lines All communication and radar systems incorporate some form of transmission lines. Coaxial transmission lines integrate systems by way of black box interconnections. Configurations include connector cable assemblies ranging from less than one inch to more than a hundred feet. Construction consists of two concentric inner and outer conductors separated by an insulation material. The conductor’s diameter ratio and insulator’s dielectric constant will determine an important parameter, the Characteristic Impedance (Z o). This typically is 50 ohms for most microwave applications. There are two basic types of coaxial cable. One is flexible, which has an outer conductor made up of fine silver plated copper wires braided over the insulation material. Other outer conductors using silver plated, wide copper strips braided into a basket weave configuration to hundreds of silver plated, copper wires running parallel to one another in a long spiral have been designed to improve the shielding effectiveness and stability of flexible cables. Semi-rigid coaxial cable has a solid outer conductor and is manufactured by drawing seamless copper or aluminum tubing over the insulating material. It is electrically superior with 100% shielding effectiveness, lower loss, extended frequency range and uniform impedance. Other outer conductors may include stainless steel, used in cryogenic systems. Insulating materials are commonly known as dielectrics. The more prominent dielectrics are Polyethylene and Polytetrafluoroethylene (PTFE). PTFE is available in solid, splined and expanded or perforated tape wrap. Polyethylene is available in solid or foamed. 46 Coaxial Transmission Lines Various inner conductors are available to meet a variety of requirements. Semi-rigid inner conductors are typically solid silver plated copper and have the advantage of being non-magnetic with the lowest loss. Silver plated copper clad steel in .141 diameter size allows the center conductor to be used as the mating contact of the SMA interface. Stranded, flexible inner conductors are common in flexible cable. Larger flexible cables may use copper clad aluminum for weight requirements. Selection of coaxial cable should begin with the characteristic impedance and operating frequency required for the system. Equation 1 (in the table of Equations for Coaxial Transmission Lines) denotes impedance as a function of the inner and outer conductor’s dimensional ratio with the dielectric constant of the insulating material. Maintaining the proper ratio will give a wide variety of cable sizes. The operation frequency will dictate the size of cable to select. A large diameter cable will not operate as high in frequency as a smaller diameter cable. If the conductor materials and the cable dielectric are the same, the larger cable will have lower attenuation. Equation 6 and the cable’s specifications for attenuation vs. frequency will aid in making a decision as to which cable to choose. Expanded PTFE and foamed polyethylene are used for low loss applications. If the application is for a specific time delay, the low loss cables may not be an advantage because the propagation velocity is higher. This requires additional line length to obtain a given delay. In systems such as multichannel radar systems, the signals must arrive at the antenna elements with 47 Coaxial Transmission Lines (continued) equal magnitude and at precisely the same time. For this application, the dielectric constant must be uniform and constant with frequency. When selecting connectors, there are sometimes many variables to consider. Frequency range, VSWR, insertion loss, phase, repeatability, cost and size are among a few. When choosing cable to match a connector, you will always obtain better results by attempting to match cable and connector sizes. For example: A Type N connector is chosen for a particular system. Type N parameters are Body I.D. = .390 and Contact O.D. = .120. A small cable will require a large (or many) transitions, yielding high magnitude reflections. A good example of compatible sizing would be the case of an SMA connector matched with .141 semi-rigid or RG/U 142 flexible cables. This match will yield low magnitude reflections, resulting in low magnitude and phase deviations over frequency. 48 Equations for Coaxial Transmission Lines Characteristic Impedance (eq 1) Velocity of Propagation (eq 2) Free Space Wavelength (eq 3) Electrical Length (eq 4) Time Delay (eq 5) Cutoff Frequency (eq 6) Capacitance (eq 7) Inductance (eq 8) b Z O = 59.959 . In a r VP = c r c f = = -360 r . Lf c TD = fC = r . L c c (a + b) rr 2 C´ = L´ = o r In b a o r 2 S = . In b a 1 f o r Skin Depth (eq 9) Conductor Loss (eq 10) C = 13.6 Sr .1+ ba b . In ab Dielectric Loss (eq 11) = 27.3 r . tan () Coaxial Line Loss (eq 12) T = C + 49 Symbols for Coaxial Transmission Lines Symbol Description Units b Inside radius of outer conductor meter a Outside radius of center conductor meter Relative permittivity (dielectric constant) 1 Permittivity of free space (8.854 x 10 -12) Farad /meter r o c Velocity of light in free space meter/second (299.7925 x 10 6) Relative permeability 1 Permeability of free space (4 x 10 -7) Henry/meter f Frequency Hertz fC Cutoff frequency Hertz Phase length degree TD Time delay second VP Velocity of propagation meter/second r o 50 Symbols for Coaxial Transmission Lines Symbol Description Units Zo Characteristic impedance ohm C Capacitance per unit length Farad /meter L Inductance per unit length Henry/meter s Skin depth meter Conductivity Mho/meter c Attenuation constant, conductors dB/meter d Attenuation constant, dielectric dB/meter Attenuation constant, total dB/meter Wavelength in free space meter Loss tangent meter T tan 51 International System of Units INTERNATIONAL SYSTEM OF UNITS Quantity Unit Symbol Dimensions Capacitance farad F C/V Conductance siemens S A/V Current ampere A A Electric charge coulomb C A-s Energy joule J N-m Force newton N kg-m/s2 Frequency hertz Hz 1/s Inductance henry H Wb/A Length meter m m Magnetic flux weber Wb V-s Magnetic induction tesla T Wb/m2 Mass kilogram kg kg Potential volt V J/C Power watt W J/s Pressure pascal Pa N/m2 Resistance ohm 액 V/A Temperature kelvin K K Time second s s 52 Standard & Current Frequency Designations STANDARD FREQUENCY DESIGNATIONS HF VHF UHF L S C X Ku K Ka 3 MHz 30 MHz 300 MHz 1.0 GHz 2.0 GHz 4.0 GHz 8.0 GHz 12.0 GHz 18.0 GHz 27.0 GHz - 30 MHz 300 MHz 1.0 GHz 2.0 GHz 4.0 GHZ 8.0 GHZ 12.0 GHz 18.0 GHz 27.0 GHz 40.0 GHz CURRENT FREQUENCY DESIGNATIONS A B C E F G H I J K L M 250 MHz 500 MHz 1.0 GHz 2.0 GHz 3.0 GHz 4.0 GHz 6.0 GHz 8.0 GHz 10.0 GHz 20.0 GHz 40.0 GHz 60.0 GHz - 500 MHz 1.0 GHz 2.0 GHz 3.0 GHz 4.0 GHz 6.0 GHz 8.0 GHZ 10.0 GHz 20.0 GHz 40.0 GHz 60.0 GHz 100.0 GHz 53 Electromagnetic Spectrum FREQUENCY < 3 Hz 3-30 Hz 30-300 Hz 0.3-3 kHz 3-30 kHz 30-300 kHz 0.3-3 MHz 3-30 MHz 30-300 MHz 54-72 76-88 88-108 174-216 WAVELENGTH DESIGNATION APPLICATIONS (free space) > 100 Mm 10-100 Mm 1-10 Mm 0.1-1 Mm 10-100 km 1-10 km 0.1-1 km 10-100 m 1-10 m 10-100 cm 0.3-3 GHz 470-890 MHz 915 MHz 800-2500 MHz 1-2 2.45 2-4 3-30 GHz 4-8 8-12 12-18 18-27 30-300 GHz 27-40 40-60 60-80 80-100 0.3-1 THz 1012-1014 Hz 3.95 x 10147.7 x 1014 Hz 1015-1018 Hz 1016-1021 Hz 1018-1022 Hz > 1022 Hz 54 ELF SLF ULF VLF LF MF HF VHF UHF “money band” 1-10 cm SHF 0.1-1 cm EHF Geophysical prospecting Detection of buried metals Power transmission, submarine communications Telephone, audio Navigation, positioning, naval communications Navigation, radio beacons AM broadcasting Short wave, citizens’ band TV, FM, police TV channels 2-4 TV channels 5-6 FM radio TV channels 7-13 Radar, TV, GPS, cellular phone TV channels 14-83 Microwave ovens (Europe) PCS cellular phones, analog at 900 MHz, GSM/CDMA at 1900 L-band, GPS system Microwave ovens (U.S.) S-band Radar, satellite communications C-band X-band (Police radar at 11 GHz) Ku-band (dBS Primestar at 14 GHz) K-band (Police radar at 22 GHz) Radar, remote sensing Ka-band (Police radar at 35 GHz) U-band V-band W-band 0.3-1 mm Millimeter Astronomy, meteorology 3-300 m Infrared Heating, night vision, optical communications 390-760 nm Visible light Vision, astronomy, optical communications 625-760 Red 600-625 Orange 577-600 Yellow 492-577 Green 455-492 Blue 390-455 Violet 0.3-300 nm Ultraviolet X-rays -rays Cosmic rays Sterilization Medical diagnosis Cancer therapy, astrophysics Astrophysics Impedance Smith Chart ENGINEERING REFERENCE GUIDE 8851 SW Old Kansas Ave. Stuart, FL 34997, USA +1 772-286-9300 +1 800-544-5594 sales@emc-rflabs.com www.emc-rflabs.com EMC CAGE Code: 24602 FRFL CAGE Code: 2Y194 AS 9100, Nadcap, ISO 9001 & 14001 and OSHAS 18001 Certified EMC Technology & Florida RF Labs, a Smiths Microwave business, is an internationally recognized leader in the development and manufacturing of thin and thick film RF and Microwave resistive components, signal distribution products, and cable assemblies. Smiths Microwave is a leading provider of components, sub-assemblies, antennas and systems solutions, primarily for defense and aerospace applications, and solutions that test, filter and process high-frequency signals for wireless telecommunication networks. As a family of brands, Kaelus, Radio Waves, TECOM, TRAK, LORCH, TRAK Limited, Millitech, EMC Technology and Florida RF Labs provide exacting solutions for antenna systems for the military and commercial aerospace, transceivers, frequency sources, timing systems, component applications, and a wide range of innovative RF and Microwave solutions for the wireless telecommunications sector. © Smiths Interconnect Microwave Components, Inc. 2014 Brochure-Eng Rev 4/2014