waveguide-based measurements at terahertz frequencies

WMI: Making Reliable Measurements at Millimeter and Submillimeter Wavelengths

Waveguide-Based Measurements at Terahertz Frequencies

Robert M. Weikle, IIGuoguang Wu

Huilin Li

Charles L. Brown Department of Electrical and Computer EngineeringUniversity of Virginia

Jeffrey L. Hesler

Virginia Diodes, Inc.Charlottesville, VA

Anthony R. Kerr

Central Development LaboratoryNational Radio Astronomy Observatory



OVERVIEW

Scattering-Parameter Measurements at Submillimeter Wavelengths

Flange Alignment and Repeatability

Flange Alignment and Calibration

• Four-Port and Six-Port Approaches• Six-Port Reflectometer Operation• WR-2.8 Six-Port Reflectometer• In-Situ Measurement with Embedded Six-Ports

• Waveguide Flange Types• Ring-Centered Flange Repeatability

• Calibration Standards Resistant to Misalignment• Calibration by Null Double Injection



Waveguide Scattering Parameter Measurements atSubmillimeter Wavelengths



Waveguide-Based Scattering Parameter Measurements

VDI WR-1.5 Frequency Extension Module(500—750 GHz)

VDI Frequency Extenders with a Rhodeand Schwarz ZVA 40 Network Analyzer



Basic S-Parameter Measurement Architectures



Intersection of Circles determinesratio b3/b4

“true” Γ related by bilinear transform:requires four-port calibration

Six-port to four-port reduction requiresknowledge of five “network constants:”

1. w1 (real)2. w2 (complex)3. ρ (scalar)4. ζ (scalar)

Determination of complex ratio w = b3/b4



Constraining Relation between b3 , b4 , b5 , and b6 :

a + b ζ + c ρ + (c – a – b) ζ + (b – a – c) ρ

+ (a – b – c) ζ ρ + a(a – b – c) + b(b – a – c) ζ

+ c(c – a – b) ρ + abc = 0

P3P4

( )2 P5P4

( )22 2 P6P4

( )2 P3P5P4

( )2P3P6

P4( )2

P5P6P4

( )2P3P4

P5P4

P6P4

Where,

a = w1 – w22 b = w2

2 c = w12

Sliding Load Method (G. Engen)



Constrain Γ to lie on a circle (i.e., sliding termination) maps into circle in w-plane

Quadratic Surface in P-space maps out an ellipse:

A + 2 B + C + 2 D + 2 E + F = 0P3P4

( )2 P5P4

( )2 P3P4

( ) P5P4

( )P3P5P4

( )2

Where,

w – Rc2 = R2

A = a B = ζ (c – a – b)/2C = ζ 2bD = [R2(b – a – c) + a(a – b – c)]/2E = ζ [R2(a – b – c) + b(b – a – c)]/2F = [R4 + R2(c – a – b) + ab]

a = w1 – Rc2

b = Rc2

c = w12

ζ = 1/| K |2



General Calibration Strategy :

1. Measure Response of Power Detectors to Sliding Load2. Plot Power Ratios Against One-Another Ellipse in P-plane3. Determine Five Coefficients via Least-Squares Fit,

4. Algebraically Determine Six-Port Reduction Coefficients5. Calibrated Effective Four-Port Using One of Several Standard Methods

AF

BF

CF

DF

EF, , , ,

Note:

1. Only five detectors used thus far 5 port reflectometer2. Several sign ambiguities are encountered in intermediate steps determining

a, b, c, ζ, and R2



Comparison of Four-Port and Six-Port Approaches

Four-Port Architecture Six-Port Architecture

Measurement of Magnitude/PhaseLarger Dynamic RangeEasier Calibration Procedure

Increased Complexity and Cost

(Heterodyne Approach) (Power Detection Approach)

Measurement of Magnitudes OnlyDynamic Range limited by detectorsComplex Calibration Procedure

Simple Hardware ImplementationRelatively Inexpensive and Low-Profile



Example: WR-2.8 Six-Port Reflectometer



Example: WR-2.8 Six-Port Reflectometer(response to offset shorts)



Example: WR-2.8 Six-Port Reflectometer(calibrated measurements of delayed shorts and

waveguide match)

285 GHz 335 GHz



Example: WR-15 In-Situ Six-Port Reflectometer



Example: WR-15 In-Situ Six-Port Reflectometer(detector response)



Example: WR-15 In-Situ Six-Port Reflectometer(comparison with HP 8510C)

Waveguide Coupler

Horn Antenna



Example: WR-15 In-Situ Six-Port Reflectometer(VDI Frequency Doubler Chain)



Waveguide Flange Alignment and Repeatability



Waveguide Flange Misalignment and Repeatabilitystandard MIL spec 0.75” round (UG-387)



Waveguide Flange Misalignment and RepeatabilityAnti-Cocking flange



Waveguide Flange Misalignment and RepeatabilityBoss-and-socket flange (Lau and Denning)



Waveguide Flange Misalignment and RepeatabilityRing-Centered flange (A.R. Kerr)

Prototype WR-5 (140—220 GHz) ring-centered flange sections with anti-cocking rim and extended boss to permit mating with alignment ring (seen on the right boss)



Waveguide Flange Misalignment and Repeatability



Waveguide Flange Misalignment and Repeatability

140 GHz 180 GHz 220 GHz

Anti-cockingflange

Ring-centeredflange



Waveguide Flange Alignment and Calibration



Four Calibration Standards:

1. Flush Short Circuit2. Two offsets with unknown (but

different) phases3. Open Waveguide Flange

NOTE: None of these standards require precise alignment of waveguides

Waveguide Calibration: Flange Misalignment



Effects of Waveguide Misalignment on Calibration Standards

Simulated return loss of misaligned matchedload (7% offset in E-plane)

Simulated phase error of misaligned matcheddelayed short (7% offset in E-plane)

Measured return loss of purposely misaligned matched load (~7% offset in E-plane)



Measured load is offset short verification standard

Comparison of Various Calibration Schemes



Comparison of Various Calibration Schemes

Measured component is waveguide E-H tuner



Six-Port Calibration by Null Double InjectionConcept: Simultaneously Drive Source and Measurement Ports with Pair of

Phase-Locked Sources

b5 = Kb3 + Lb4

b6 = Mb3 + Nb4

Adjust Sources to Null b4 :

Adjust Sources to Null b3 :

b5 = Kb3

b6 = Mb3

P5P3

= |K|2 =

P6P3

= |M|2 =

1ζ

1ρ

b5 = Lb4

b6 = Nb4

P5P4

= |L|2 =

P6P4

= |N|2 =

w1

ζ

2

w2

ρ

2



Six-Port Calibration by Null Double Injection (cont’d):Adjust Sources to Null b5 :

Kb3 + Lb4 = 0P4 KP3 = = L 2

w12

P6P4

= |M|2 LK

NM

2– +

21 w1 – w2ρ=P6P4

b6 = M b3 + N b4



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waveguide-based measurements at terahertz frequencies

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