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Transmission Lines and S-Parameters

Prof. Bhaskar Banerjee

EE 7V82 - RF IC Design

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Transmission Lines

Transmission line theory is basic for any high frequency design

Microstrip

h

w

Coplanar

w1

w2

WaveguideTwisted-pair Coaxial

b

ah

w

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Basic Concepts on Transmission Lines

A portion of the power generated by a source (Gen.) is delivered to aload (Z L) by means of a transmission line (TL) Voltage , current , and power can be considered to be in the form

of waves traveling in both directions along the transmission line Incident and reected voltages on a TL results in a standing

voltage wave on the line

TL(Zo)

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Termination of Transmission Lines

Waves on TL with different termination impedances

For reection, a transmission line terminated in Zo behaveslike an innitely long transmission line

For reection, a transmission line terminated in a shortor open reects all power back to source

Standing wave pattern does not go to zero aswith short or open

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Power Transfer on Transmission Line Low frequencies : wavelength >> wire length

Current (I) travels down wires easily for efcient power transmission Measured voltage and current not dependent on position along wire

High frequencies : wavelength

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Power Transfer on Transmission Line Maximum power transfer

It should be considered in a transmitter of RF system

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Power Transfer on Transmission Line

Maximum power transfer

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50 Transmission Lines

Why 50 ?

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Network Characterization Two-port network parameters

Open-circuit parameters (Z-parameters) Short-circuit parameters (Y-parameters) Hybrid parameters (H-parameters) Transmission parameters (ABCD-parameters)

Features Based on voltage (V) and current (I) Requires open and short terminations

Z11 =V1I1 I2=0

Z21 =V2I1 I2=0

Z12 =V1I2 I1=0

Z22 =V2I2 I1=0

H11 =V1I1 V2=0

H12 =I2I1 V2=0

H12 =V1V2 I1=0

H22 =I2V2 I1=0

Y11 =I1V1 V2=0 Y21 =

I2

V1 V2=0Y12 =I1V2 V1=0 Y22 =

I2V2 V1=0

A =V1V2 I2=0

B =V1

- I2 V2=0C =

I1V2 I2=0

D =I1

- I2 I1=0

Open termination

Short termination

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Why S-Parameters?

Problems on traditional network parameters when moving tohigher frequencies Equipment is not readily available to measure total voltage

and total current at the ports of the network Short and open circuit are difcult to achieve over a broad

band of frequencies

Active devices, such as transistors and tunnel diodes, very often will not be short and open circuit stable

Therefore, some method of characterization is necessary toovercome these problems Scattering parameters (S-parameters)

The logical variables to use at high frequencies are traveling waves rather than total voltages and currents

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Two-port S-parameters Derivation

Generalized scattering parameters have been dened by K. Kurokawa Refer K. Kurokawa, Power waves and the scattering matrix, IEEE Trans.

MTT, Vol. 13, No. 2. Mar. 1965

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Multiple-Port S-parameters

Two-port S-parameter concept can be extended to multi-port

Required proper termination for other ports

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S-parameters Measurement

S 11 = Reected Incident

=b

1a 1 a 2 = 0

S 21 =Transmitted

Incident =

b2

a 1 a 2 = 0

S 22 = Reected Incident =b

2a 2 a 1 = 0

S 12 =Transmitted

Incident =

b1

a 2 a 1 = 0

Incident TransmittedS 21

S 11Reflected

b 1

a 1

b 2

Z 0Load

a 2 = 0DUTForward

1IncidentTransmitted S 12

S 22Reflected

b 2

a 2

b

a 1 = 0

DUTZ 0Load Reverse

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S-parameters Measurement

Equipment: Vector Network Analyzer (VNA)

Agilent PNA 2008

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S-parameters Measurement

Vector Network Analyzer (VNA) operation

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Smith Chart

Smith Chart maps rectilinear impedance plane onto polar plane

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Smith Chart

Impedance plot over frequency

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Device Characterization Parameters

Reflected

Incident

REFLECTION

SWR

S-ParametersS11,S22 Reflection

Coefficient

Impedance,Admittance

R+jX,G+jB

ReturnLoss

,

A

R=

Transmitted

Incident

TRANSMISSION

Gain / Loss

S-ParametersS21,S12

GroupDelay

TransmissionCoefficient

InsertionPhase

,

B

R=

R

A

Incident

Reflected

BTransmittedDUT

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Device Characterization Parameters

Reection parameters S11 and S22 Reection coefcient ( ) Return Loss (RL) (dB) Voltage Standing Wave Ratio (VSWR)

E max

E min

Standing wave

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Device Characterization Parameters

Transmission parameters S21 and S12 Transmission coefcient ( T ) Insertion Loss (IL) or Gain Group delay