ece 451 advanced microwave measurements amplifier

ECE 451 – Jose Schutt-Aine 1

ECE 451Advanced Microwave Measurements

Amplifier Characterization

Jose E. Schutt-AineElectrical & Computer Engineering

University of Illinoisjesa@illinois.edu

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• Tree fundamental types– Bipolar junction transistors (BJT)– Junction field effect transistors (JFET)– Metal-oxide semiconductor transistors (MOSFET)

• Technologies– Silicon– Compound Semiconductors (GaAs, InP, GaN)

Transistor TechnologyTransistors are semiconductor devices with 3 terminals. They are used to amplify signals and get voltage, current or power gain

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• Polarity– NPN, PNP for BJT– NMOS, PMOS for MOSFET– CMOS

Models for Transistors

NPN is favorites for BJTNMOS is favorite for MOSFET

B

C

E

base

collector

emitter

gate

drain

sourceNPN NMOS

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• Bipolar– Ebers-Moll– Gummel-Poon

• MOSFET– Shichman-Hodges– BSIM

Transistor Models

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MOSFET Amplifier

Common SourceTopology

Small‐Signal Model

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BJT Amplifier

Common EmitterTopology

Small‐Signal Model

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Amplifier Efficiency

A

AB

BC

, ,RF out RF inPAE

DC

P PP

,

,

RF outTotal

DC RF in

PP P

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Amplifier Efficiency

,RF outTotal PAE

DC

PP

For high‐gain amplifiers, PRF,in << PDC and

Efficiencies are typically between 25% and 50%

• Class A amplifier– Maintain bias so that the transistor is in the middle

of the linear range– Efficiency is reduced because of DC current– Best linearity– Choice for small signal (small input) amplification

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Amplifier Efficiency

Efficiency is improved by reducing DC power and moving bias point further down the DC load line as in class B, AB and C.

A

ABB

C

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Amplifier EfficiencyClass B, AB and C present impedance that is a function of the level of the RF signal.Class B, AB and C are generally not used for broadband applications because of stability concerns

AAB

BC

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Linear AmplifiersThe transducer power gain is defined as the power delivered to the load divided by the power available from the source. 

S os

S o

V Zb

Z Z

VS

2

21s

avsS

bP

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Linear Amplifiers

2 22

2 2

1

1

LdelT

avs s S

bPGP b

22 221

211 22 21 12

1 1

1 1

S L

T

S L S L

SG

S S S S

Non-touching loop rule for power available

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Linear Amplifiers

If we assume that the network is unilateral, then we can neglect S12 and get the unilateral transducer gain for S12=0.

2 2

221 2 2

2211

1 1

11

S L

TULS

G SSS

The first term (|S21|2) depends on the transistor. The other 2 terms depend on the source and the load.

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Linear Amplifiers

Gs affects the degree of mismatch between the source and the input reflection coefficient of the two‐port. 

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Linear Amplifiers

GL affects the degree of mismatch between the load and the output reflection coefficient of the 2‐port.

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Linear Amplifiers

Go depends on the device and bias conditions

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Linear AmplifiersMaximum unilateral transducer gain can be accomplished by choosing impedance matching networks such that.

*11S S *

22L S 2

212 211 22

1 11 1

UMAXG SS S

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Linear Amplifiers

For 

max max( ) ( ) ( ) ( )UMAX S o LG dB G dB G dB G dB

*11,S S GS is a maximum 

For  1,S GS is 0

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Linear Amplifiers

For arbitrary values of GS between these extremes, the solutions for |S| lies on a circle  Gain circles

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Classification of Amplifiers

Class A ‐ Amplifier is biased at current ICgreater than the amplitude of the signal. Transistor conducts for the entire cycle of the signal  conduction angle = 360o. 

Class A

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Classification of Amplifiers

In class B stage, the transistor is biased for zero dc current

Class B

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Classification of Amplifiers

The amplifier conducts for only half of the cycle of the input sine wave. Conduction angle = 180o Negative halves supplied by another transistor operating in class B

An intermediate class between A and B is called class AB

AB involves biasing the transistor at a nonzero DC current much smaller than the peak current

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Classification of Amplifiers

A

ABB

C

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Distortion and Nonlinearities

Distortion occurs when the output signal from an amplifier approaches the extremes of the load line and the output is no longer an exact replica of the input.The ideal amplifier follows a linear relationship. Distortion leads to a deviation from this linear relationship

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The 1dB compression point is the point where the difference between the extrapolated linear response exceeds the actual gain by 1dB. P1dB is the power output at the 1dB compression point and is the most important metric of distortion.

Distortion and Nonlinearities

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Distortion and Nonlinearities

AM‐AM Distortion

P1dB

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AM‐PM Distortion

Distortion and Nonlinearities

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AM‐AM distortion is generally more significant

Distortion is a result of nonlinearities in the response of an amplifier. One possible model for the response is:

When the input signal is large enough the higher order terms become significant.

Distortion and Nonlinearities

2 31 2 3 ...o i i iv k v k v k v

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Single‐Tone Excitation

2 31 2 3o i i iv k v k v k v

1 1cosiv t a t

22 1

22 1 1

3

21

3 1

1

1

1 3 1

1 c

3 cos4

os31 cos 22

12

4

o k a k a tv

k a t

t k

k a t

a

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Single‐Tone Excitation

Single-tone excitation produces harmonics of input frequency

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If the input is a sine wave, the output will contain harmonics of the input. That is the output will have frequency components that are integer multiples of the fundamental (CW) sine wave input signalWhen the input signal is a two‐tone signal (modulated signal), additional tones will appear at the output and we say that the distortion produces intermodulation products (IMP)

Distortion and Nonlinearities

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Two‐Tone Excitation2 3

1 2 3o i i iv k v k v k v

1 1 2 2cos cosiv t a t a t

2 2 2 21 2 1 1 2 2

1 1

3 31 1 2 2

23 1 2 2 1 2 1

21 2

1 2 2

2

1 2

1 2 1

2 1

2

1 2 1 2

1 1cos3 cos34 4

1

1 1

3 cos 2

1cos2 cos

co

cos 24 4

3 cos 2 cos 24

22 2 2

cos cos

s coso

a t a t

k a a t

a a t

a a a t a tk

a a t a a t

k a t at tv

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Two-tone excitation produces intermodulation

Two‐Tone Excitation

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If f1 and f2 are the frequencies associated with the two signals, the output will have components at f3 and f4where

3 1 22f f f and 4 2 12f f f

are known as the lower and upper IM3 respectively.

Distortion and Nonlinearities

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At low power, before compression the fundamental has a response with 1:1 slope with respect to the input

The IP3 response varies as the cube of the level of input tones. The IP3 has a 3:1 logarithmic slope with respect to the input.

Distortion and Intermodulation

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The point of intersection of the extrapolated linear output (of power Po) and third order (IP3) of power PIP3 is called the third‐order intercept point which is a key parameter

• Harmonics can be filtered out by filters• Intermodulation distortion cannot be filtered out because they are in the main passband

Distortion and Intermodulation

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Distortion and Intermodulation

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• Methods– Load Pull– X-Parameters

Power Transistor CharacterizationBecause of nonlinearities, scattering parameters cannot be used to characterize power devices.  Other techniques must be used. 

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Load-Pull Measurements• Varying (“pulling”) load impedance ZL

seen by an active device under test

• Measuring performance metrics of DUT at each ZL point:

– Transducer Gain (as shown)– Power-added Efficiency– 1-dB Gain Compression Point– Noise Figure– …

• Not needed for linear devices– Performance with any ZL determined by

measuring small-signal S-parameters

• Important for characterizing devices operating in large-signal (nonlinear) mode

– Operating point (and thereby performance) may change for different loads

Nonlinearmode

2-dB GT gain drop contours (52 points measured)

Optimal ZL

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Manual Load-Pull Setup• First set up source tuner for maximum gain, then fix its position• For each (X,Y) position of the load tuner:

1. Measure injected power Pinj, delivered power Pm

2. Measure S-parameters of source and load circuitry (shaded boxes)3. Move the reference plane to the DUT input and output:– Calculate input and output power loss (due to mismatch) from measured S-parameters– Obtain Pin, Pout by correcting Pinj, Pm for power losses4. Solve for transducer gain GT=Pout/Pin

• Done at a constant input frequency f0 - harmonic measurements also possible• Large number of points needed for each frequency

– Measurements are usually automated