Copyright by Michael G. Ellis, Ph.D.
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
to mean something else.
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?
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
Deriving this may take an hour, a day, or longer, depending on your training in high school algebra
(1) solve the previous equation iteratively,
(2) cascade the output voltage, VL, with
(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
x = i*twopipt
newcos = cos(x)
Test Your Knowledge
Composite Second Order
Staff of 20 people
2 years development time
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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