I have a transfer function of the following form:
\$\ T(jw)= a0 / (1+ s/w1) (1+ s/w2) (1+ s/w3) \$
where a0 = 3600 w1= 1MHz w2= 4MHz w3= 40MHz
I drew the the bode plot and double checked with matlab and I found some discrepancy. I found out the problem happens between 1MHz and 4MHz as the poles are close to each other (Less than 1 decade difference).
So since at 0 Hz, the gain is around 71 db, I expected that at 1MHz, the plot will start declining with 20db/dec. Between 4Mhz and and 1Mhz, there is ( \$\ log(4M/1M) = 0.6 \$ decade (not a full decade), and hence at 4MHz the gain is 71 - log(4M/1M)*20 = 71 - 12 = 59 dB.
However, in MATLAB, at 4MHz the gain is 69 db. Which means the gain dropped by 8dB not 12 dB. Can you please tell me where is the flow in my understanding?
I know that this problem happens because the poles are close to each other with less than 1 decade difference, and I am not sure how such cases are handled.
So the purpose of My main point is what's the gain at 4M (2pi) rad/s? Or in other words, how much the gain will fall between 2pi*1M rad/s and 2pi*4M rad/s and why?
My plot (The x axis is multiplied by 2pi and it is in rad/s):