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Texas Instruments Transmission Line RAPIDESIGNER Operation and Applications Application notes
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.
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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.
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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
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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.
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Find Co and Lo for a 75Ω microstrip on a substrate having er = 3.8.
4
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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
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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:
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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
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Email: ap.support@nsc.com
National Semiconductor
Japan Ltd.
Tel: 81-3-5639-7560
Fax: 81-3-5639-7507
National does not assume any responsibility for use of any circuitry described, no circuit patent licenses are implied and National reserves the right at any time without notice to change said circuitry and specifications.
AN-905
National Semiconductor
Corporation
Americas
Tel: 1-800-272-9959
Fax: 1-800-737-7018
Email: support@nsc.com
www.national.com
2. A critical component is any component of a life
support device or system whose failure to perform
can be reasonably expected to cause the failure of
the life support device or system, or to affect its
safety or effectiveness.
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