Laser Predistortion

7/30/2019 Laser Predistortion

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Copyright by Michael G. Ellis, Ph.D.

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The word Predistortion originated from filter theory.

Lowpass filter with perfect inductors

Response of our perfect filter

http://michaelgellis.tripod.com/predistweb.html

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But the inductors are not infinite Q's, so that act like

they have resistors in series with them. This can

cause the response to be unacceptable.

A really unacceptable frequency response due to

using real inductors with finite Q's.


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Predistortion involves modifying the values of the

inductors and capacitors so that the resulting

frequency response is as close as possible to thedesired response using real inductors with finite Q's.

The results are never quite as good as using ideal

inductors, but usually the results are acceptable.


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Figure: A linear system


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Sine wave with only odd order distortion


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Sine wave with even order distortion


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A typical CATV laser transmitter contains a laser,

Mach-Zehnder modulator, and 50-870 MHz RF

input. The Mach-Zehnder is not linear.

The Mach-Zehnder produces both even and oddorder distortion.


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How do we apply the input signal so that the

Mach-Zehnder has no even order distortion?

or

or

This is called the Composite Second Order (CSO)

Control Loop


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Now the even order distortion problem is solved.


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The Entire Block Diagram


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The 3rd order predistortion circuit must have the

inverse function of the Mach-Zehnder to cancel it

out.

Notice that the 3rd-order predistortion network

cascaded with the Mach-Zehnder will produce a

linear transfer function.


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We need a circuit that provides more gain at the

positive and negative peaks of the RF input signal

than at the middle of the RF input signal.

How do we do this?


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With diodes, or course. A diode has less resistance

as the current through it is increased.

A working predistortion network.

The top 2 diodes have less and less resistance as the

input signal goes more and more positive, and thebottom two diodes have less and less resistance as

the input signal goes more and more negative.


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The Diode Equation

With a source resistance of Rs

and a load resistance

of RL, and M=2 for the number of diodes, the

transfer function becomes


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where

Deriving this may take an hour, a day, or longer,depending on your training in high school algebra


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We must

(1) solve the previous equation iteratively,

(2) cascade the output voltage, VL, with

, and

(3) take the Fourier transform of the Light Out to

look at any remaining 3rd, 5th, 7th, and 9th order

distortion.

This tells us if we have cancelled the 3rd order

distortion (linearized the Mach-Zenhder transfer

function) without increasing the 5th, 7th, and 9th

order products too much.


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The code for the Fourier transform

For harmon = 1 to 20twopi = 2*3.141592654

sine = 0: cosine=0

towpipt = twopi/pt

for i = 1 to pt

if i = 1 then

oldcos = 1

oldsin = 0

end if

x = i*twopipt

newcos = cos(x)

newsin=sin(x)sine=-(newcos-oldcos)*b(i)+sine

cosine=(newsin-oldsin)*b(i)+cosine

oldcos=newcos

oldsin=newsin

next iengy(harmon)=(sine^2+cosine^2)/(2*twopi)

next harmon


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Test Your Knowledge

Linearizer

Mach-Zenhder

Predistorting

3rd order

Composite Second Order

Staff of 20 people

2 years development time


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Intermission.

How long was the hundred years war?


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116 years.


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What was King George IV's first name?


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Albert


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Where are Panama hats made?


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In Equador


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Where do Chinese gooseberries come from?


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New Zealand


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What is a camel's hair brush made from?


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Squirrel's hair


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Intermission over.


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