Hello everyone!

I’m trying to solve a problem that asks for the total noise spectral density observed at the output of an operational amplifier. I have some questions regarding the calculation and would appreciate some help.
Regarding the bias current noise of the operational amplifier, should I consider both resistors in the circuit (R1 and R2) when calculating the input current error? Or should I treat each resistor separately
I’m using the following formula to calculate the total noise spectral density: \[ S_V(f)_{\text{total}} = \sqrt{(en)^2+(in_{er1} \times R_1)^2 + (in_{er2} \times R_2)^2 + 4.1 \times\sqrt { \frac{R1}{1k}} + 4.1 \times\sqrt{ \frac{R2}{1k}} } \]
But I'm not sure if im doing correctly the analysis. The problem provides the values for the input voltage noise (En=7.9nV/sqrt(Hz)) and input current noise (in=0.5fV/sqrt(Hz)), that 4.1 is the spectral density for 1kΩ in 1 hz, and also mentions that the BW=100Hz.
Could anyone confirm if my approach is correct, or if there’s anything I should adjust?
Thanks in advance for your help!

 

The noise in:
the 5k resistor,
the input voltage,
the op-amp voltage noise
and he op-amp current noise
are all multiplied by the gain of the circuit
The noise in the 50k resistor is multiplied by 1.
I'm not sure where you get 4.1x√(R1/1k) but I presume it must be related to the Johnson noise equation.
I would have used vn=√(4KTfR)

 

The noise in:
the 5k resistor,
the input voltage,
the op-amp voltage noise
and he op-amp current noise
are all multiplied by the gain of the circuit
The noise in the 50k resistor is multiplied by 1.
I'm not sure where you get 4.1x√(R1/1k) but I presume it must be related to the Johnson noise equation.
I would have used vn=√(4KTfR)

Hi Ian, thanks for the answer. The exercise provided this information:

"MAX4256 Specifications in terms of noise:
7.9 V/√Hz
In = 0.5 (A/√Hz)
These values are assumed to be constant over the entire frequency range of interest (the noise was increased by 1/f).

Reminder:
Each resistor generates thermal noise (4.1 nVeff at Iko to IH).
An effective bandwidth of 100 Hz is considered. "

So, I use the relation provided in the reminder to calculate the noise.
Therefore, should I not consider the bias current noise for the 50kΩ resistor in the final density calculation? I also exclude the thermal noise? . Im sorry, i did nor understand why.