ENGINEERING REFERENCE GUIDE
8851 SW Old Kansas Ave.
Stuart, FL 34997
(800) 544-5594
(772) 286-9300
Fax: (772) 283-5286
Website: www.rflabs.com
www.emct.com
email: info@rflabs.com
CERT.
NO. 19.2523
CERT. NO.
The name FLORIDA RF LABS and LOGO are Registered Trademarks of Florida RF Labs.
The name EMC Technology and LOGO are Registered Trademarks of EMC Technology.
ENGINEERING
REFERENCE
GUIDE
Engineering
Reference Guide
Revised 6/07
This Reference Guide is the property of:
Florida RF Labs
EMC Technology
8851 SW Old Kansas Ave., Stuart, Florida 34997
Telephone: (772) 286-9300 Toll-Free: (800) 544-5594
Fax: (772) 283-5286
Website: www.rflabs.com
www.emct.com
email: info@rflabs.com
© 2001-2007
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 - 36 GHz
20
Thermopad
DC - 26.5 GHz
DC - 6 GHz
DC - 2.4 GHz
2 - 18 GHz
DC - 12 GHz
DC - 18 GHz
DC - 3.6 GHz
15
Terminations
Smart Load
Power Dividers
Equalizers
Diamond
Terminations
Diamond
Resistors
Couplers
DC - 10 GHz
5
Complementary
Signal Processing
DC - 18 GHz
10
Attenuators
Frequency (GHz)
Product Frequency Bands
40
35
30
25
0
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
Gin = S11 +
S21 S12
1 - S22 Gl
Reflection Coefficient (r) to SWR
SWR =
1+
r
1-r
Equivalent Parallel Capacitance
CP =
jB
v
SWR to Reflection Coefficient (r)
r = SWR - 1
SWR + 1
Reflection Coefficient (r) to Return Loss
R.L.(dB) = -20 logr
Return Loss to Reflection Coefficient (r)
2
r = log -1 R.L.
( )
-20
Useful Equations
Reflected and Transmitted Power Due to SWR
Prefl = Pin
Ptrans = Pin
SWR - 1
= Pin r2
SWR + 1
2
(
)
4SWR
= Pin (1- r2)
2
(SWR + 1)
_
Z-1
G= _
Z+1
Normalized Impedance to Reflection Coefficient
Electrical Length f (degrees)
=­
«r L
c
« Lf
f = -360=­
c
r
= TD = Time Delay (seconds)
f = - 360 Td f
f=
Df
f
Df
Pd = Pin (1 - log -1 -10 )
Total Power Dissipated in Attenuator
dB
Parallel Plate
Capacitance
Cpp =
A «r «o
h
3
Useful Equations
(continued)
“T” Attenuator Network Design
Z in = 50V
R1
R2
R3
N = log -1(10db)
R1 =
R1 = R 2
R3 =
Z L = 50V
Z(=­
N - 1)
(=­
N + 1)
N
2 Z=­
N-1
f Attenuator Network Design
Z in = 50V
R3
R1
N = log -1(10db)
R1 = R 2
R2
R1 =
R3 =
Z L = 50V
Z(=­
N + 1)
(=­
N - 1)
Z(N - 1)
2=­
N
N: the ratio of power corresponding to a given value of attenuation in decibels.
4
Useful Equations
X L = 6.28fGHzL nH and X C = 159
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 - G and z =
Y
1+ G
C
( )
Admittance (Y0 is the Characteristic Admittance)
Y
Y = G ± jB = 1 = Y0 1 - G and Y =
Z
1+ G
Y0
Reflection Coefficient
G=
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+ G
R
= LARGER
1- G
RSMALLER
RL = 20log G = -20log
Z - Z0
Z + Z0
5
Useful Equations
(continued)
(
Mismatch Loss (GS = 0, GL =⁄ 0)
ML = -10log (1- GL ) = -10log 12
Z L - Z0
Z L + Z0
Mismatch Loss (GS =⁄ 0, GL =⁄ 0)
Wavelength
Conversion to dB
6
l=
2
)
[
[(
= -10log 1 -
ML = -10log
)]
VSWR-1
VSWR+1
2
]
(1- GS )(1- GL )
2
1- GLGS
2
8
c
3 . 10 m
30cm
=
=
«r mr
«r mr
«r mr
fHz=­
fGHz=­
f=­
dB = 20log
V2
V1
= 20log
i2
i1
= 10log
P2
P1
Notes
7
Microstrip Transmission Line
Reference Table
«o
w
h
«r
Trace width for a 50V ± 1V 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
1.00
1.01
1.02
1.03
1.04
Return
Loss
(dB)
Trans.
Loss
(dB)
Volt.
Refl.
Coeff.
Power
Trans.
(%)
Power
Refl.
(%)
.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
`
46.1
40.1
36.6
34.2
.000
.000
.000
.001
.002
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
1.20
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
1.30
17.7
.075
.13
98.3
1.7
1.05
1.06
1.07
1.08
1.09
32.3
30.4
29.4
28.3
27.3
1.15
1.16
1.17
1.18
1.19
23.1
22.6
22.1
21.7
21.2
1.10
1.11
1.12
1.13
1.14
1.25
1.26
1.27
1.28
1.29
19.1
18.8
18.5
18.2
17.9
.021
.024
.027
.030
.033
.054
.058
.062
.065
.070
.00
.00
.01
.01
.02
.07
.07
.08
.08
.09
.11
.12
.12
.12
.13
100.0
100.0
100.0
100.0
100.0
99.5
99.5
99.4
99.3
99.2
98.8
98.7
98.6
98.5
98.4
.0
.0
.0
.0
.0
.5
.5
.6
.7
.8
1.2
1.3
1.4
1.5
1.6
9
The Effect of VSWR
on Transmitted Power
VSWR
Return
Loss
(dB)
Trans.
Loss
(dB)
Volt.
Refl.
Coeff.
Power
Trans.
(%)
Power
Refl.
(%)
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
1.60
1.62
1.64
1.66
1.68
12.7
12.5
12.3
12.1
11.9
1.32
1.34
1.36
1.38
1.50
1.52
1.54
1.56
1.58
1.70
1.72
1.74
1.76
1.78
1.80
1.82
1.84
1.86
1.88
10
(continued)
1.90
1.92
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
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
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
.440
.454
.31
.32
90.4
90.1
9.6
9.9
10.9
10.7
10.6
10.4
10.3
10.2
10.0
.238
.250
.263
.276
.289
.370
.384
.398
.412
.426
.23
.24
.24
.25
.25
.29
.29
.30
.30
.31
94.7
94.4
94.1
93.8
93.6
91.8
91.5
91.3
91.0
90.7
5.3
5.6
5.9
6.2
6.4
8.2
8.5
8.7
9.0
9.3
The Effect of VSWR
on Transmitted Power
VSWR
Return
Loss
(dB)
Trans.
Loss
(dB)
Volt.
Refl.
Coeff.
Power
Trans.
(%)
Power
Refl.
(%)
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
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
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
1.94
1.96
1.98
4.50
5.00
5.50
6.00
6.50
9.50
10.00
11.00
12.00
13.00
19.00
20.00
25.00
30.00
9.9
9.8
9.7
3.9
3.5
3.2
2.9
2.7
1.8
1.7
1.6
1.5
1.3
.9
.9
.7
.6
.468
.483
.497
2.255
2.553
2.834
3.100
3.351
4.626
4.807
5.149
5.466
5.762
7.212
7.413
8.299
9.035
.32
.32
.33
.64
.67
.69
.71
.73
.75
.76
.78
.79
.80
.81
.82
.83
.85
.86
.87
.88
.88
.89
.89
.90
.90
.92
.94
89.8
89.5
89.2
59.5
55.6
52.1
49.0
46.2
43.7
41.5
39.5
37.7
36.0
34.5
33.1
30.6
28.4
26.5
24.9
23.4
22.1
21.0
19.9
19.0
18.1
14.8
12.5
10.2
10.5
10.8
40.5
44.4
47.9
51.0
53.8
56.2
58.5
60.5
62.3
64.0
65.5
66.9
69.4
71.6
73.5
75.1
76.6
77.9
79.0
80.1
81.0
81.9
85.2
87.5
11
Dielectric Constant («r ) &
Loss Tangent (tan d) @ 3.0 GHz
«
Material
r
Air
Polystyrene Foam
PTFE
Vaseline
RT/Duroid 5880
®
Polyethylene
Polystyrene
1.000649
1.03
2.1
2.16
2.2
2.3
2.55
RO/Duroid 3003
3.0
Mica, Ruby
5.4
Quartz
®
Glass, Soda
Diamond (CVD)
RT/Duroid 6006
®
Beryllium Oxide (BeO)
Aluminum Nitride (AIN)
Alumina (AI2O3) 99.6%
RT/Duroid 6010
®
3.78
.0001
.0002
.00066
.0004
.0003
.00033
.0013
.00006
4.82
.0054
6.15
.0027
5.6
6.5
8.9
9.9
10.2
RT/Duroid is a registered trademark of Rogers Corporation
12
tan d
.0003
.0005
.004
.0005
.0001
.0028
Material Properties
Material
Conductivity,
s (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
PORT
1
2
COUPLED PORT 4
90˚ Crossover Hybrid
DIRECT PORT 3
3
4
1
2
ISO
-90˚
-90˚
0˚
IN
ISO
IN
0˚
Performance Parameters
-90˚
(
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
Vmax
Vmin
Phase Balance (0) = ±
(
4
0˚
0˚
-90˚
ISO
IN
ISO
)
VSWR+1
VSWR-1
( )
Pin
Pcoupled + Pdirect
Pin
)
Pisolated
Phasecoupled - Phasedirect
Amplitude Balance (dB) = 10 • Log
Amplitude Balance (dB) = 10 • Log
14
3
IN
(
(
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
Coupling
Ratio
Performance Parameters
Coupling Ratio (dB) = 10 • Log
(
( )
Pcoupled
Pin
)
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
Vmax
Vmin
(dB) - Cmean (dB)]
(dB) - Cmean (dB)]
max
min
(
VSWR+1
VSWR-1
( )
Pin
Pcoupled + Pdirect
( )
)
15
Normalized Dissipated Power
“T” Attenuator Network Design
Z in = 50V
R1
R2
R3
Z L = 50V
f Attenuator Network Design
Z in = 50V
R3
R1
R2
Z L = 50V
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
p
Attenuation
(dB)
Power Dissipation (watts)
R1
R2
R3
0.25
.014
.014
.028
0.75
.043
.037
.079
0.50
1.00
1.25
.029
.058
.072
.026
.046
.054
.054
.103
.124
1.50
.086
.061
.145
2.00
.115
.073
.182
.081
.214
1.75
2.25
.100
.068
.164
.129
.076
2.75
.157
.083
.229
3.25
.185
.088
.254
2.50
3.00
.143
.171
.086
.199
.242
3.50
.199
.088
.266
4.00
.226
.091
.285
3.75
4.25
.213
.240
.089
.090
.276
.294
17
Normalized Dissipated Power
in “T” & Attenuator Elements
(continued)
Attenuation
(dB)
Power Dissipation (watts)
R1
R2
R3
4.50
.253
.090
.302
5.00
.280
.089
.315
4.75
5.25
5.50
.267
.293
.306
.089
.087
.087
.309
.321
.325
5.75
.319
.085
.330
7.00
.382
.076
.342
6.00
8.00
9.00
.332
.431
.476
.084
.068
.060
.333
.342
.338
10.00
.519
.052
.329
14.00
.667
.027
.266
12.00
16.00
18.00
20.00
18
p
30.00
.598
.726
.776
.818
.939
.038
.018
.013
.008
.001
.301
.230
.195
.164
.059
Notes
19
Power Conversion Table
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
dBm
20
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
Watts
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
dBm
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
Watts
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
dBm
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
Watts
Power Conversion Table
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
dBm
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
Watts
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
dBm
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
Watts
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
dBm
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
Watts
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 (DT) 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:
1
22
P=
KA • DT
x
Thermal Discussion
P = dissipated power, (W)
where:
K = thermal conductivity of material,
DT = T2 - T1
T2 = temperature of source, (˚C)
W
cm˚C
T1 = reference temperature (heat sink), (˚C)
x = length of heat flow path, (cm)
A = area of heat source, (cm2)
u = thermal resistance (˚C/W)
Thermal Resistance
Rearranging equation 1 will yield an equation
that will relate power dissipation and temperature
differences.
2
therefore:
DT x
=
P
KA
The term, x , is called the thermal resistance (u),
KA
3
Pu = DT
which will give the temperature rise when the element is
dissipating power.
23
Thermal Discussion
(continued)
Calculating Thermal Resistance
Examining u =
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.
4
u=
1
L 2x + W
• In
2K(L - W)
W 2x + L
(
)
And when the source is square, L = W
5
24
u=
x
KL(L + 2x)
Thermal Conductivity
METALS
Silver
Copper
Gold
Aluminum
Beryllium
Tungsten
Rhodium
Molybdenum
Brass
Chromium
Nickel
Platinum
Tin
Tantalum
Lead
Titanium
Manganese
(cmWatts˚C)
(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
(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)
(BeO)
(AlN)
(HBN 500º)
(Al2O3)
(Al2O3)
(Al2O3)
BONDING
Gold Germanium 88/12
Gold Tin 80/20
Tin Lead Solder
Indium 100%
Silver Filled Epoxy
Epoxy
MISC.
Thermal Grease
26
(Sn62)
(cmWatts˚C)
•
10.0 - 16.0
2.61
1.70
0.59
0.46
0.36
0.26
0.13
0.015
.0043 - .0062
.00026
.8834
.6824
.4921
.2386
.0156
.0099
.0042 - .0049
Thermal Conductivity
Conversion Factors
Thermal Conductivity
To Convert
Watt
m • ˚K
cal • cm
sec • cm 2 • ˚C
To
Multiply By
Watt
cm • ˚C
4.1868
Watt
cm • ˚C
3.674e-5
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
Watt
cm • ˚C
BTU • in
ft 2 • h • ˚F
cal • cm
sec • cm 2 • ˚C
Watt
inch • ˚C
Watt
cm • ˚C
.002397
2.54
1.422 - 3
(AT 20°C)
27
Thermal Conductivity
Conversion Factors (continued)
Power
To Convert
Calories
sec
BTU
hr
28
To
Multiply By
Watts
4.186
Watts
.293
(AT 20°C)
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
TEMPERATURE CONVERSION TABLE
˚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
Celsius to Kelvin
Fahrenheit to Celsius
Kelvin to Celsius
TF = 1.8 TC + 32
TK = TC + 273.15
TF - 32
= .5556 (TF - 32)
1.8
TC = TK - 273.15
TC =
29
Voltage vs. Power
10.0
1E-10
(50 ohm system)
POWER (milliwatts)
1E-8
1E-6
1E-4
.01
1
100 1000
1.0
0.1
VOLTAGE (rms)
0.01
.001
1E-4
1E-5
1E-6
1E-7
-110 -100
30
-90
-80
-70
-60
-50
-40
- 30
LEVEL (dBm)
-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
m
n
p
f
a
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
.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%
0%
SAFE OPERATING AREA
25
50
85
75
HEAT SINK TEMPERATURE IN °C
100
125
Standard Derating Curve for Resistors
and Terminations
100%
PERCENT
OF
RATED
POWER
50%
0%
36
SAFE OPERATING AREA
25
50
75
100
HEAT SINK TEMPERATURE IN °C
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.
4 - 40
Mounting Torque
10 - 24
18 inch - lbs
6 - 32
8 - 32
6 inch - lbs
8 inch - lbs
12 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
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
Liquidus
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 50 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
Ω
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:
DdB - Total amount of compensation required
DT - Total amount of temperature change in the system.
dBnom - Nominal Attenuation
Temp. (C˚)
-55
25
125
Atten. (dB)
4
3
1.8
DT = 180
DdB = 2.2
TCA = DdB / dBnom. / DT
= 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
}
DdB
125, 1.8
1.5
DT
1
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)
Skin Depth
(eq 9)
Conductor Loss
(eq 10)
Dielectric Loss
(eq 11)
Coaxial Line Loss
(eq 12)
b
Z O = 59.959 . In a
«r
=­
VP =
c
«r
=­
l=
f=
«r . Lf
-360 =­
c
TD =
fC =
c
f
«r . L
=­
c
c
p (a + b)=­
mr ­
«r
­
2 p«o « r
In b
a
momr
. In b
L´ =
a
2p
C´ =
dS =
a C = 13.6
a a = 27.3
1
=­­­­
pfmomrs
dS=­
«r .1+ ba
lb . In ab
«r .
=­
tan (d)
l
aT = a C + a a
49
Symbols for Coaxial
Transmission Lines
Symbol
b
a
«r
«o
c
mr
mo
f
Units
Outside radius
of center conductor
meter
Permittivity of free space
(8.854 x 10 -12)
Farad /meter
Relative permeability
1
Inside radius
of outer conductor
Relative permittivity
(dielectric constant)
meter
1
Velocity of light in free space meter/second
(299.7925 x 10 6)
Permeability of free space
(4p x 10 -7)
Henry/meter
Cutoff frequency
Hertz
Frequency
Hertz
f
Phase length
degree
VP
Velocity of propagation
fC
TD
50
Description
Time delay
second
meter/second
Symbols for Coaxial
Transmission Lines
Symbol
Zo
C´
L´
ds
s
ac
ad
a
T
l
tan d
Description
Characteristic impedance
Units
ohm
Capacitance per unit length Farad /meter
Inductance per unit length
Henry/meter
Conductivity
Mho/meter
Attenuation constant,
dielectric
dB/meter
Skin depth
Attenuation constant,
conductors
Attenuation constant,
total
Wavelength in free space
Loss tangent
meter
dB/meter
dB/meter
meter
meter
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
h
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 mm
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
g-rays
Cosmic rays
Sterilization
Medical diagnosis
Cancer therapy, astrophysics
Astrophysics
ENGINEERING REFERENCE GUIDE
8851 SW Old Kansas Ave.
Stuart, FL 34997
(800) 544-5594
(772) 286-9300
Fax: (772) 283-5286
Website: www.rflabs.com
www.emct.com
email: info@rflabs.com
CERT.
NO. 19.2523
CERT. NO.
The name FLORIDA RF LABS and LOGO are Registered Trademarks of Florida RF Labs.
The name EMC Technology and LOGO are Registered Trademarks of EMC Technology.
ENGINEERING
REFERENCE
GUIDE