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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

 


 

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.


Predistortion involves modifying the values of the inductors and capacitors so that the resulting frequency response is as close as possible to the desired 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.

 

 


 

Within the past 2 decades, a group of optics engineers have temporarily "borrowed" the use of the word

 

"PREDISTORTION"

 

to mean something else.

 


Definition:

 

A system is linear if the output voltage is proportional to the input voltage.

 

Figure:  A linear system


If a system is non-linear, it can produce both even and odd order distortion.


The sine wave below has NO even order distortion because the top and the bottom half of the sine wave is distorted in the same manner.

 

 Sine wave with only odd order distortion


The sine wave below is distorted differently on the top and bottom half cycles, so it contains even order distortion.

 

Sine wave with even order distortion

 


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 odd order distortion.

 


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

 

 

 

Now the even order distortion problem is solved.


The Entire Block Diagram

 


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.


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?

 


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 the bottom two diodes have less and less resistance as the input signal goes more and more negative.

 

 


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


where

 

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

 


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.


The code for the Fourier transform

 

For harmon = 1 to 20

twopi = 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 i

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

next harmon


Test Your Knowledge

 

Linearizer

 

Mach-Zenhder

 

Predistorting

 

3rd order

 

Composite Second Order

 

Staff of 20 people

 

2 years development time


Intermission.

     

How long was the hundred years war?

 


116 years.


What was King George IV's first name?


Albert


Where are Panama hats made?


In Equador


Where do Chinese gooseberries come from?


New Zealand


What is a camel's hair brush made from?


Squirrel's hair


 

Intermission over.

 

 

 

 

A subtractor


An example of expansive predistortion

 

(This is what we want).

 

 

 


An example of compresive predistortion

 

(This is what we don't want).

 


Expansive or Compressive?

 

 

 

____________


Expansive or Compressive?

 

__________

 

This is a hyperbolic arctangent circuit

 

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