adding bode plots together? I am trying to understand the bode plot result I have obtained.



The blue, green, and red plots are $a$, $ b$, and $a+b$ respectively.  

What I'm having a hard time understanding is how a+b is formed.  Looking at the magnitude of $a$, it is in the range of $500 dB$ or $$10^{25}$$.  Whereas, looking at $b$, it is a negative dB gain, so a number of small magnitude.  Although I do expect to see the gain of $a+b$ to be lower than that of $a$, I can't explain why the drop is so significant.  

Am I missing something fundamentally important here? or is this fishy to anyone else?

If it makes any difference, I directly got this plots in matlab using

bode(a,b,a+b)


TIA
This question is old, but for the benefit of the next person stumbling across it:
You have to multiply transfer functions in order to "add" them in the bode plot.