Analysis of AC-coupled op amp circuits

反倒是fdsf

Analysis of AC-coupled op amp circuits [Copy link]

Here are the pictures first.

Where Z1 is the impedance of C1 and R1 in series, and Vdc is the DC component of the input signal Vin. I want to know how the calculation formula of Vout is obtained.

The first part of the formula looks like in-phase amplification:

This latter part looks like an inverted amplification:

Can we just add the last two numbers?
Please help me analyze it, thank you.

maychang

"I want to know how the calculation formula for Vout is derived"

List the equations according to the circuit, and then solve the equations using the "virtual short" of the op amp.

maychang

"Where Z1 is the impedance of C1 and R1 in series, and Vdc is the DC component of the input signal Vin"

For DC, Z1 is infinite, the previous item in the bracket is zero, and the item in the bracket is 1. Because of the capacitor C1, Vdc is zero, that is, no matter what kind of signal Vin is, its DC component does not affect the output of the op amp (this is only true in steady state, not in transient process).

maychang

"The first part of this formula looks like in-phase amplification, and the second part looks like inverting amplification. Can we just add the last two together?"

That’s right, just add them together.

反倒是fdsf

maychang posted on 2022-10-5 20:17 "The first part of this formula looks like in-phase amplification, and the second part looks like inverting amplification. Could it be that the last two are added together...

The result I calculated by virtual short is:

The calculation results of the previous part are the same, but there is a difference in the calculation of the inverting amplification part. Since the non-inverting amplification takes the capacitive reactance of C1 into account, why doesn't the inverting amplification take the capacitive reactance of C1 into account?

maychang

On the contrary, fdsf posted on 2022-10-5 21:59 The result I calculated by virtual short and virtual short is: The calculation results of the previous part are the same, and the calculation of the inverted amplification part is different...

"Since the in-phase amplification takes the capacitive reactance of C1 into account, why does the inverting amplification not take the capacitive reactance of C1 into account?"

The formula you posted in the first post is wrong. The latter term should also include the capacitive reactance of C1.

maychang

On the contrary, fdsf posted on 2022-10-5 21:59 The result I calculated by virtual short and virtual short is: The calculation results of the previous part are the same, and the calculation of the inverted amplification part is different...

There is also a problem with your calculation results. When calculating, you do not distinguish whether the signal is DC or AC, but mix them together. If you calculate them separately, then there is no need to consider capacitive reactance and inductive reactance when calculating DC: for DC, the capacitive reactance is infinite and the inductive reactance is zero.