In Op Amps for Everyone, there's a section on noise calculations "Op Amp Noise Theory and Applications" which is hard for me to follow. I see a few obvious errors, so I wonder if this section is just wrong.
Can someone go through each of these and confirm if the book is wrong or explain to me why I'm wrong?
- Twice it says "The output noise equals the input noise multiplied by the gain, which is 100 (40 dB)". But shouldn't it be multiplied by the non-inverting noise gain, which is 101? For this circuit it's a small difference, but for other circuits it's a big difference. This source says to multiply by the non-inverting gain: Part III: Resistor Noise And Sample Calculations
- The IC in Fig 10-15 and 10-16 should be a TLC2201, not TLE2201, which doesn't exist.
- The capacitor in Fig 10-15 and 10-16 should be 0.1 µF, not 0.1 F.
- Equation 10-23 is supposed to be the total output noise of the amplifier and the resistor divider, but I don’t think it’s correct:
- The noise of the two resistors is summed (5.73 µV² + 5.73 µV²), which would produce a total noise of 8.1 µV. But don’t the resistors load down each other’s noise sources, so the total contribution is equivalent to the resistors in parallel? It would be equal to a single 50 kΩ resistor producing 4.0 µV. A 1 MΩ resistor in parallel with a 1 Ω resistor produces the same noise as a lone 1 Ω resistor, not the noise of a lone 1 MΩ, right?
- The noise of the resistors (5.7 µV) that appears at the input of the op-amp is being summed with the output noise of the op-amp (1.13 µV x 100 = 113.1 µV). Shouldn’t the resistor noise be multiplied by the gain, too? It says “The amplifier noise is swamping the resistor noise”, but this isn’t true if you multiply the resistor noise by the gain, too.
- Equation 10-25 is not right.
- The left side of the equation is equal to 113.2, but the right side says 126.8. It was probably meant to include 57.3, not 5.73.
- The text says “Adding this [the 57.3 µV noise from the 10M] and the 100-kΩ resistor noise to the amplifier noise”. This is three terms (10 MΩ, 100 kΩ, op-amp), but there are only two in the equation.
- But again, these two resistors should be paralleled before the noise is calculated. The noise is actually that of a single 99 kΩ resistor, (5.707 µV).
- Again, the resistor noise is not multiplied by the gain, even though the text says it should be: “The noise associated with it appears as a voltage source at the inverting input of the op amp, and, therefore, is multiplied by a factor of 100 through the circuit.”
- If I understand correctly, I think the correct equation would be the noise of a 50 kΩ resistor (100k||100k) summed with a 99 kΩ resistor (10M||100k) and summed with the op-amp’s input noise, which is then multiplied by the non-inverting noise gain: √(4.06 µV² + 5.707 µV² + 1.131 µV²) × 101 = 716.3 µV
- A TINA-TI simulation of this circuit produces 633.44 µV, which is not quite the same, but the text gives only 126.8 µV
- Equation 10-27 has similar problems to the others.
- Because of the addition of the 0.1 µF cap, the resistor divider is being ignored. The equation then seems to be summing the 100 kΩ and 1 kΩ of the inverting side, but they should be in parallel instead (100 kΩ || 1 kΩ = 990.1 Ω → 0.5707 µV).
- If the 50 kΩ resistor is ignored, it becomes: √(0.5707 µV² + 1.131 µV²) × 101 = 127.9 µV
- A TINA simulation with the cap in place gives 112.3 µV
- So in this case the book’s answer of 113.2 µV is close to correct, but I think the derivation is not.