How are the following two conclusions about op amps derived?

乱世煮酒论天下

How are the following two conclusions about op amps derived? [Copy link]

1. In the frequency range below the corner frequency, the open-loop gain decreases at a rate of 6dB/octave. What does this mean? How is it derived?

2. At any frequency, the product of the corresponding open-loop gain Avo and the frequency is a constant (for example, the open-loop gain at 100 Hz is 10000 V/V, and the product of the two is 1 MHz). This is the basic characteristic of the so-called constant value gain-bandwidth product operational amplifier, and all voltage feedback operational amplifiers have this characteristic. How is this theory derived? In the amplitude-frequency characteristic curve, if the amplification factor is horizontal at a low frequency, does this conclusion still hold? It means that if the amplification factors of the 1HZ and 10HZ amplitude-frequency curves are both 10^5, isn't this quantitative relationship wrong?

gmchen

first question

Because there is a low-frequency pole inside the op amp, after this pole frequency, the open-loop gain decreases at 6dB/octave.

How to derive: Assume that the signal is divided by a resistor and a capacitor, then the voltage at the dividing point relative to the input voltage can be written as vout/vin=(1/jwC)/(R+1/jwC), and the relationship between the modulus and the frequency is the same as above. You can calculate it yourself. If you don't know complex number operations, just pretend I didn't explain it to you.

gmchen

second question

The so-called constant gain-bandwidth product has two meanings. The first is that the gain-bandwidth product of any point on the curve above the pole frequency (before the next pole) remains unchanged.

The second meaning is that in an amplifier using conventional resistive feedback, the product of the amplifier's closed-loop gain and bandwidth is equal to the gain-bandwidth product mentioned above.

The specific analysis is a little complicated, so I won’t go into it here.

乱世煮酒论天下

gmchen posted on 2024-3-28 18:06 The second question is that the so-called gain-bandwidth product is constant, which has two meanings. The first one refers to the frequency greater than the pole mentioned above (the next pole...

I just don't understand how you derived it? Maybe you can tell me where to find it?

q1233

Operational circuit analysis, frequency domain analysis of operational amplifier circuit transfer function