# expo function of radio control transmitters

I always wondered what "expo" meant when talking about R/C radio transmitters (robbe Futaba, Graupner JR, Hitec, Turnigy/Eurgle and many others).

It's clear what it does, but what does "100%" actually mean?

So I finally decided to do a bit of research and with the help of a forum postat rcgroups , titled "What does x% expo mean?" I came up with my own function, the plot of which you can see above.

The main improvement I did was correct treatment of negative sign together with proper scaling, preventing the function from leaving the 100% envelope.

Please note that some manufacturers swap the sign of expo.

Also, the order of the function might not be 2 as in my case, but higher.

The "secret" is that you have a sum (or difference) of a linear function and a sign(x) * abs(x)^exponent function and the expo value says how much of each you use.

I wrote the Matlab code below. Should work with small changes in free alternatives:

clc

close all

clear all

% Jens Roesner, 2011

% improved from

% www.rcgroups.com/forums/showthread.php?t=452369

exponent=2; %

x=[-100:10:100];

k=[-100:50:100];

f=zeros(length(x),length(k));

for ik=1:length(k);

for ix=1:length(x);

f(ix,ik) = 100* ((1-k(ik)/100) * x(ix)/100 + k(ik)/100 * sign(x(ix)) * abs(x(ix)^exponent/100^exponent));

end

end

han=mesh(x,k,f');

xlabel('x = input [%]')

ylabel('k = expo [%]')

zlabel('z = output [%]')

titlecell={'Plotted expo ("exponential") function of radio transmitters'

'2011 Jens Roesner, improved from'

'http://www.rcgroups.com/forums/showthread.php?t=452369'

};

title(titlecell)

set(han,'meshstyle','row')

set(han,'FaceColor','none')

set(han,'LineWidth',2)

% Alternative, too extreme for negative expo

%

% for ik=1:length(k);

% for ix=1:length(x);

% y(ix,ik) = sign(x(ix)) * abs(x(ix)^(1+k(ik)/150))/ 100^(1+k(ik)/150);

% end

% end

%

% hold all

%

% mesh(x,k,y')

% xlabel('x')

% ylabel('k')

% zlabel('z')

%