Waveguide Characteristics and Measurement Errors€¦ · Waveguide • Waveguide = hollow metal...

Keith AndersonAgilent Technologies

© Copyright 2011 Agilent Technologies, Inc.

Waveguide Characteristicsand Measurement Errors

IMS2011 in Baltimore: A Perfect Match

Agenda

• Background• Characteristics• Conclusion

Waveguide• Waveguide = hollow metal pipe• Rectangular, 2:1 aspect ratio• Advantages

– Conducts millimeter signals– Low loss– High power– Good shielding– Can "flare" end into horn antenna

•Disadvantages– Bandwidth < 1 octave– Rigid, heavy, large– Expensive– No DC connection– Dispersive

a

b a = 2 * b

Waveguide dimensions

Millimeter Bands

Propagation Modes

• Electromagnetic wave modes• TEM• TE & TM• Hybrid

• Rectangular waveguide• Supports TE and TM• For TEmn, m & n give the "order" of mode • Mode propagates above its "cutoff frequency"

a

b

x

y

TE10 electric field(end view)

Waveguide Frequencies

• Standard millimeter waveguide is 2:1• Fcutoff1 = c / (2 * a)

• No propagation below Fcutoff1• TE10 propagates between Fcutoff1 and 2*Fcutoff1• Other modes propagate above 2*Fcutoff1

• Operating range• Fmin = 1.25 * Fcutoff1• Fmax = 1.89 * Fcutoff1• FLinearMean = 1.57 * Fcutoff1• FGeometricMean = 1.54 * Fcutoff1

a

b

x

y

TE10 electric field(end view)

Dispersion

• Wave propagation depends on frequency• Below Fcutoff1, no propagation• Above Fcutoff1, the wave "ping-pongs"

Fcutoff1

Low frequencypropagation

High frequencypropagation

Agenda


Propagation Velocity• Wave velocity: Free space propagation• Group velocity: Energy propagation • Phase velocity: Phase propagation

V /

c

f / Fcutoff1

Vgroup

Vwave

Vphase

Vphase

Vwave

Vgroup

fcutoff1

f1

2Vphase = c

fcutoff1

f1

2Vgroup = c *

c2 = Vphase * Vgroup

Vwave = c

Fmin Fmax

1.67

1.18

0.600.85

FGMean

0.76

1.34

Group Delay

• GD is infinite at Fcutoff1 & approaches GDfreespace

GD = GDfreespace

GD = (Physical Length) / Vgroup 1.671.181.34

FGMean

GD = 1ns / foot, in free spaceG

D /

GD

frees

pace

Fcutoff1

f1

2

f / Fcutoff1 Fmin Fmax

Guide Wavelength

• λguide is infinite at fcutoff1 & approaches λfreespace

λguide = λfreespace

λ g/ λ

frees

pace

λguide = Vphase / f

f / Fcutoff1Fmin Fmax

1.67

1.18λfree space = 1mm @ 300GHz

Fcutoff1

f1

2

Impedance

• ZTE is infinite at Fcutoff1 & approaches Zfreespace

• Network analyzers assume Zo = "1"

ZTE = Fcutoff1

f1

2

Zfreespace

Z TE

/ Zfre

espa

ce

f / Fcutoff1

ZFreespace = 377Ω

Fmin Fmax

628Ω

444Ω

LossLoss is due to skin effect & surface roughness

Loss in perfect copper

Agenda


Conclusion

• Waveguide is dispersive• Zo = 444Ω - 628Ω•Set Zo = "1" in VNA• Group delay is 18~67% longer than free space• Wavelength is 18~67% longer than free space• Skin effect loss is high (6.5dB/meter for WR7)

Waveguide Characteristics and Measurement Errors€¦ · Waveguide • Waveguide = hollow metal...

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