laser predistortion
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Copyright by Michael G. Ellis, Ph.D.
More Tutorials
The word Predistortion originated from filter theory.
Lowpass filter with perfect inductors
Response of our perfect filter
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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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