Answer :
The total rms noise, Vn,rms, of an opamp with FL = 0.2 Hz, FH = 12 Hz, FC = 0.8 Hz, and Vnw= 10 nV/√Hz is 3.9 nV.The correct answer is option b.
To calculate the total RMS noise voltage (Vn, rms) of an operational amplifier (op-amp) using the given parameters, we need to consider the various noise sources and their contributions.
The total RMS noise voltage can be calculated as follows:
Vn, rms = √(4 * k * T * FL + [tex](e_n)^2[/tex] * (FH - FL) + [tex](i_n)^2[/tex] * (FC - FH))
Where:
- k is Boltzmann's constant (1.38 x [tex]10^{-23}[/tex]J/K)
- T is the temperature in Kelvin
- FL is the low-frequency corner (-3dB) of the op-amp noise
- FH is the high-frequency corner (-3dB) of the op-amp noise
- FC is the corner frequency of the 1/f noise
- (e_n) is the voltage noise density (in volts per square root of hertz)
- (i_n) is the current noise density (in amperes per square root of hertz)
Given values:
- FL = 0.2 Hz
- FH = 12 Hz
- FC = 0.8 Hz
- Vnw = 10 nV/√Hz (voltage noise density)
Assuming room temperature (T = 298 K), we can plug in the values and calculate the total RMS noise voltage:
Vn, rms = √(4 * (1.38 x [tex]10^{-23}[/tex] J/K) * (298 K) * 0.2 Hz + [tex](10 nV)^2[/tex] * (12 Hz - 0.2 Hz) + [tex]0^2[/tex] * (0.8 Hz - 12 Hz))
Vn, rms = √(4 * 1.38 x [tex]10^{-23}[/tex] J * 298 K * 0.2 Hz + (10 x [tex]10^{-9}[/tex] V[tex])^2[/tex] * 11.8 Hz)
Vn, rms = √(2.7636 x [tex]10^{-19}[/tex] J + 1.32 x[tex]10^{-16}[/tex]J)
Vn, rms = √(1.32 x [tex]10^{-16}[/tex] J)
Vn, rms ≈ 3.64 x [tex]10^{-9}[/tex] V
Since the voltage noise density (Vnw) is given in nV/√Hz, we need to convert the RMS noise voltage to nV by multiplying by √Hz:
Vn, rms ≈ 3.64 x [tex]10^{-9}[/tex] V * √Hz
Now, let's convert the value to nV:
Vn, rms ≈ 3.64 x [tex]10^{-9}[/tex] V * [tex]10^{9}[/tex] nV/1 V
Vn, rms ≈ 3.64 nV
Therefore, the closest option to the calculated total RMS noise voltage is option (b) 3.9 nV.
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