Conductor Loss 
DC Resistance
R |
DC |
= ρ |
l |
= ρ |
l |
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l |
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tw |
A |
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12 in |
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RDC |
= 0.679 µΩ − in |
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= 0.6 |
Ω |
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t |
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(0.0014 |
in )(0.010 in ) |
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A |
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RDC |
= 0.679 µΩ − in |
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12 in |
= 2.3 |
Ω |
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w |
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(0.0007 |
in )(0.005 in ) |
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Skin Depth
δ=
δ=
δ=
ρ |
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•Current density drops to 37% (1/e) |
πfµ0 |
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•Ignore if t<2δ |
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0.0172 µΩm |
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= 660 nm = 0.03 mils |
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4πx10 |
−7 |
Ωs |
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π (10 GHz ) |
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m |
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0 .0172 µΩm |
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= 21 µm = 0 .8 mils |
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4πx10 |
−7 |
Ωs |
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π (10 MHz ) |
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m |
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Revision 4 |
Copyright Telephonics 2002-2005 |
35 |
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Loss due to Skin Effect & Roughness
Resistance, 5 mil Line |
Loss Variation, Roughness |
(on 1 oz and 0.5 oz copper) |
(1 oz, 11 mil width) |
Revision 4 |
Copyright Telephonics 2002-2005 |
36 |
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Time Delay
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Where: |
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td:time delay per unit length |
Lo:Inductance |
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= εr−effective =85 ε |
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t |
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= |
L C |
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ps/inch |
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εr-effective: Effective Relative |
per unit length |
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d |
r−effective |
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Co:Capacitance |
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o o |
c |
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Dielectric constant |
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per unit length |
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C: Speed of Light |
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Freespace |
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t |
W |
Freespace |
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εo (εr=1) |
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εo (εr=1) |
b |
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εr |
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εr |
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εr |
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h |
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Micro-Strip |
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Buried Micro-Strip |
Strip-Line |
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εr-effective(strip-line) = εr |
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ε |
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= |
εr |
+1 |
+ |
εr −1 |
1 |
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εr-effective(micro-strip) |
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_ effective |
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2 |
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2 |
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12h |
< |
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1 |
w |
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td =85 εr |
ps per inch |
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w |
≥1 |
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εr-effective(buried micro-strip) |
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when h |
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< |
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td |
=156 |
ps/inch |
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εr |
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td =180 |
ps/inch |
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(FR4, εr = 4.5, |
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(FR4, εr = 4.5) |
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w =18mils, h =10mils) |
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Revision 4 |
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Copyright Telephonics 2002-2005 |
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37 |
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Signal Dispersion
♦Frequency Dependant Dielectric Constant
-Propagation velocity is frequency dependant
-PWB acts as a dispersive Medium
♦Becomes Issue
-Long Trace Runs
-High Speed Clocks
-Critical Analog
Revision 4 |
Copyright Telephonics 2002-2005 |
38 |
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