How is this TOI output solved graphically ?

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STOIKOV

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graphical solution

how is solved TOIoutput graphically ? Read that intermodulation products rise 3 times faster than IF tones (so slopes rate is 3) but do not have clear why TOIoutput=1.5*m1-0.5*m2
 

Re: graphical solution

it's only a simple solution of linier equation

for 1st line which slope =1
YTO1 - m1 = XTO1 - X1

for 2nd line which slope = 3

YTO1 - m2 = 3 (XTO1 - X1)

where (XTO1, YTO1) is the intersection point of 1st and 2nd line.

from those two equations, an elimination can be done.
YTO1 -m1 = (YTO1-m2)/3
2/3*YTO1 = m1 - 1/3*m2

YTO1 = 3/2*m1 - 1/2*m2

hopefully it helps

regards
 

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    STOIKOV

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Re: graphical solution

thanks masadi, your process to get TIOoutput is clear. This equation is in function of m1 and m2, I tried to obtain TOIinput also in function of m1 and m2 (without involving other variables) but cannot get it so far :|. Can help with it ?
Regards,
 

Re: graphical solution

well, found in books that TOIinput=½(m1-m2)+PIN
also assuming that slopes ratio is 1:3 (see figure)
but wonder if can be obtained only in function of m1 and m2.
 

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