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Basic Interconnects at High Frequencies (Part 1)Dr. José Ernesto Rayas-Sánchez

March 24, 2020

1

1

Basic Interconnects at High Frequencies

(Part 1)

Dr. José Ernesto Rayas-Sánchez

2Dr. J.E. Rayas-Sánchez

Outline

Two-wire cables and coaxial cables

Stripline

Stripline geometry and field distribution

Characterizing striplines

Microstrip line

Microstrip geometry and field distribution

Characterizing microstrip lines

Embedded microstrips

Losses in striplines and microstrip lines


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Two-Wire Lines

Unsuitable for high-frequency applications

They have high radiation losses (large EMI)

(R. Ludwig and P. Bretchko, RF Circuit Design, Prentice Hall, 2000)


2-Wire Line – Transmission Line Parameters

H/m)(2

cosh 1

aD

L

F/m)()2/(cosh

'1 aD

C

(D. M. Pozar, Microwave Engineering, Wiley, 2005)

)tan1('''' jj

r' o r o

(F/m) 10854.8 120

(H/m) 104 7

0

Ω/m)(a

RR s

S/m)()2/(cosh

''1 aD

G

s

sR

1

where

surface resistivity

fs

1 skin depth


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Two-Wire Line – Z0 (Neglecting Losses)

)Ω(2

cosh73.376 1

r

0

aD

Z

H/m)(2

cosh 1

aD

L

F/m)()2/(cosh

'1 aD

C

)Ω('2

cosh1 1

0

aD

Z


Two-Wire Line – Transmission Line Parameters

H/m)(2

cosh 1

aD

L F/m)(

)2/(cosh'

1 aDC

0 5 10 15 20 25

D/2a

0

500

1000

1500

2000

L (

nH/m

)

2-Wire Cable Distributed Inductance

(e = 1.3)

0 5 10 15 20 25

D/2a

0

20

40

60

80

100

120

C (

pF/m

)

2-Wire Cable Distributed Capacitance

(e = 1.3)


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Two-Wire Line – Z0 (Neglecting Losses)

)Ω('2

cosh1 1

0

aD

Z

0 5 10 15 20 25

D/2a

0

100

200

300

400

500

Z0 (

ohm

s)

2-Wire Cable Characteristic Impedance

(e = 1.3)


Two-Wire Line – Practical Issues

The most common 2-wire TL is the “twin-lead” line

Typical Zo for twin-lead lines: 75, 300, and 400

They use copper for the wires, separated by a plastic (typically polyethylene) ribbon

(K. L. Kaiser, Transmission Line Matching and Crosstalk, CRC, 2005)

400- ladder twin-line

300- twin-line 300 to 75balun


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Coaxial Cables

Typical coaxial cables are used up to 10 GHz (high-end coaxial lines can be used up to 80 GHz)

They have no radiation losses (outer conductor is grounded)


Typical dielectrics: Polystyrene

(r = 2.5, tan = 0.0003*) Polyethylene

(r = 2.3, tan = 0.0004*) Teflon

(r = 2.1, tan = 0.0004*) * at 10 GHz


Coaxial Cables – Transmission Line Parameters

H/m)(ln2 a

bL

F/m)()/ln(

'2ab

C


)tan1('''' jj

r0' r o

(F/m) 10854.8 120

(H/m) 104 7

0

Ω/m)(11

2

baR

R s

S/m)()/ln(''2

abG

s

sR

1

where

surface resistivity

fs

1 skin depth


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Coaxial Cables – Transmission Line Parameters

H/m)(ln2 a

bL

F/m)(

)/ln('2ab

C

0 2 4 6 8 10

b/a

0

100

200

300

400

500

L (

nH/m

)

Coaxial Cable Distributed Inductance

(r = 2.5)

0 2 4 6 8 10

b/a

0

500

1000

1500

C (

pF/m

)

Coaxial Cable Distributed Capacitance

(r = 2.5)


Coaxial Cables – Z0 (Neglecting Losses)

)Ω('

ln21

0

ab

Z

F/m)()/ln(

'2ab

C

)Ω(ln2

73.376

r

0

ab

Z

H/m)(ln2 a

bL


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Coaxial Cables – Z0 (Neglecting Losses)

)Ω('

ln21

0

ab

Z

0 2 4 6 8 10

b/a

0

20

40

60

80

100

Z0 (

ohm

s)

Coaxial Cable Characteristic Impedance

(r = 2.5)


Coaxial Line – Practical Issues

Typical Zo for coaxial lines: 50, 75 and 93

The most common type is the RG-6 cable (TV, 75)

Detailed technical data-sheets are available for each type

(http://en.wikipedia.org/wiki/Coaxial_cable#References, 2009)

RG-59 Connectors


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Striplines

A stripline trace is immersed in a dielectric and sandwiched between two metallic planes

The electric and magnetic fields are confined to the dielectric (TEM propagation if losses are small)


TEM Propagation

The electric and magnetic fields in the direction of propagation are zero



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Stripline Geometry and Field Distribution


re e

p

cv

Mm/s300c


Characterizing Striplines (Zero Thickness)

)44.0(30

bWb

Zer

o

where We is the effective width given by

35.0for )35.0(

35.0for 0

2

bW

bW

bW

bW

bWe



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Characterizing Striplines (Non Zero Thickness)

(S. C. Thierauf, High-Speed Circuit Board Signal Integrity, Artech, 2004)



35.0for

854.8

15.94

tb

wC

kbw

Z

r

fr

o

and Cf is the fringing capacitance given by


where

bt

k

1

1

(pF/m) )1ln()1()1ln(2854.8 2 kkkkC r

f


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35.0for 4

ln60

tbw

db

Zr

o


where

2

51.04

ln112 w

ttw

wtw

d





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Microstrips

A microstrip trace is sandwiched between two very different dielectrics

Due to this non-homogeneous media, microstrips propagate in non TEM mode

Using the effective dielectric constant approach, microstrips can be modeled as if they had an homogeneous media (quasi TEM propagation if the losses are small)


Microstrip Geometry and Field Distribution


Substrates with higher r reduce field leakage and cross couplingSubstrates with smaller r reduce dielectric losses


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Potential and E Field Distributions (Open Box)

Substrate: Air (r = 1)


Potential and E Field Distributions (Open Box)

Substrate: FR4 (r = 4.5)


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Microstrip Geometry (cont.)

Exposed microstrip:

Embedded microstrip:

solder mask



Characterizing Exposed Microstrip Lines

e

p

cv

Mm/s300c

)/10(121

21

whrr

e



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Characterizing Exposed Microstrip Lines (cont.)

Zo neglecting thickness (t = 0)

Ω 4

8ln

60 , 1 if

hw

wh

Zhw

e

o

Ω

144.042.2

1120 , 1 if 6

wh

wh

hw

Zhw

e

o

(C.S. Walker, Capacitance, Inductance and Crosstalk Analysis; Artech, 1990)

Model 1: Walker’s formulae



Ω 4

8ln

60 , 1 if

hw

wh

Zhw

e

o

Ω 444.1ln667.0393.1

1120 , 1 if

hw

hw

Zhw

e

o

(K.C. Gupta et. al, Computer-Aided Design of Microwave Circuits; Artech, 1981)

Model 2: Gupta’s formulae


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0 0.5 1 1.5 2 2.5 3 3.5 40

50

100

150

200

250

300

350

400Characteristic Impedance of a Microstrip Line

w/h

Zo (

ohm

s)

r = 4.5

r = 2.2

r = 9

r = 1

GuptaWalker



Effects of t 0 on Zo



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Zo considering thickness (t 0)

Ω 8.098.5

ln60

, 2 if

twh

Zhw

e

o

Ω 444.1ln667.0393.1

1120 , 2 if

hw

hw

Zhw

e

o



50- Stripline and 50- Embedded Microstrip

w = 5milt = 0.65milh = 6.1mil


w = 5milt = 0.65mil


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Losses in Transmission Lines

The total loss t is the sum of the conductor and dielectric losses

Conductor losses c are due to the resistive losses in the signal trace and the return path (produced by a conductive current)

Dielectric losses d are due to the energy lost in the dielectric layers (produced by a displacement current)

dct


50- Stripline and 50- Embedded Microstrip


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