An internally compensated op amp is specified to have an open-loop dc ...
Given parameters:
Open-loop dc gain (Aol) = 106 dB
Unity gain bandwidth (fT) = 3 MHz
To find:
a) Open-loop gain (Aol) at 15 Hz and 103 dB
Solution:
We know that the frequency response of an op amp can be modeled as:
Aol(f) = Aol(0) / (1 + jf/fT)
Where f is the frequency, Aol(0) is the open-loop dc gain and fT is the unity gain bandwidth.
For the given problem, we need to find Aol at 15 Hz and 103 dB. Let's substitute the values in the above equation:
Aol(15Hz) = Aol(0) / (1 + j15/3x10^6)
Taking the magnitude of the above equation, we get:
|Aol(15Hz)| = Aol(0) / √(1 + (15/3x10^6)^2)
Now, substituting the given values, we get:
|Aol(15Hz)| = 106 dB / √(1 + (15/3x10^6)^2)
|Aol(15Hz)| = 103 dB (approx.)
Hence, option A is correct.
b) Open-loop gain (Aol) at 30 Hz and 103 dB
We can repeat the above steps with f = 30 Hz:
|Aol(30Hz)| = Aol(0) / √(1 + (30/3x10^6)^2)
|Aol(30Hz)| = 103 dB (approx.)
Hence, option B is incorrect.
c) Open-loop gain (Aol) at 15 Hz and 51.5 dB
We can repeat the above steps with the given values:
|Aol(15Hz)| = 51.5 dB / √(1 + (15/3x10^6)^2)
|Aol(15Hz)| = 49.5 dB (approx.)
Hence, option C is incorrect.
d) Open-loop gain (Aol) at 30 Hz and 51.5 dB
We can repeat the above steps with the given values:
|Aol(30Hz)| = 51.5 dB / √(1 + (30/3x10^6)^2)
|Aol(30Hz)| = 49.5 dB (approx.)
Hence, option D is incorrect.
Therefore, the correct answer is option A.