Can anyone help me see how to write the transfer function of the following type of op amp circuit?

sunboy25

Can anyone help me see how to write the transfer function of the following type of op amp circuit? [Copy link]

Can that big guy teach me how to write the gain formula for an op amp circuit like this?

maychang

There are two R3s and two R1s in the figure. This is not allowed and can easily cause confusion. Each component should have a unique number.

maychang

There is a star resistor circuit between the upper end of the signal source, the inverting input end of the op amp, and the output end of the op amp, which consists of R1 (left), R5, and R1 (right). The star circuit is transformed from star to triangle. The transformed triangle circuit has a resistor in parallel with R3 (left), a resistor in parallel with R4 + R3 (right), and a resistor connected between the signal source and the output end of the op amp. Because the signal source is a voltage source, there is no need to consider the impact of the resistor on the output signal of the signal source.

Knowing the resistance from the op amp inverting input to the signal source and the op amp output, the gain of the amplifier circuit can be obtained. This amplifier circuit is a simple inverting amplifier circuit.

sunboy25

maychang published on 2020-11-22 15:49 Between the upper end of the signal source, the inverting input end of the op amp, and the output end of the op amp, there is a star-shaped resistor circuit consisting of R1 (left), R5, and R1 (right). In this regard...

Moderator, I know that what you did is right, but this picture is the simplified picture I took. The original picture is as shown below. The result in the book does not want to remove R5 but wants to remove R4. Can you help me take a look at it? In this case, how can I get the result of the circled part in the picture below?

maychang

sunboy25 posted on 2020-11-23 10:48 maychang posted on 2020-11-22 15:49 There is a star resistor between the upper end of the signal source, the inverting input end of the op amp, and the output end of the op amp...

The 4th floor picture is completely different from the 1st floor picture.

There are capacitors C1 and C2 in the diagram on the 4th floor. How can we ignore the capacitive reactance of the capacitors when writing the transfer function?

maychang

sunboy25 posted on 2020-11-23 10:48 maychang posted on 2020-11-22 15:49 There is a star resistor between the upper end of the signal source, the inverting input end of the op amp, and the output end of the op amp...

Figure 4 shows a tone control circuit. There are two potentiometers in the figure. When the positions of the two potentiometer sliding ends change, the transfer function of the circuit will also change.

sunboy25

As I said in the first sentence of the screenshot, at the high-frequency end of the audio, the capacitor is equivalent to a short circuit.

gmchen

There are two ways to calculate the gain of the circuit on the first floor:

The first method is to list the node equations honestly, and we can get two equations. One of the middle nodes is the connection point between R1 and R5. By eliminating the voltage of this middle node, we can solve VO/VI.

The second method is to transform the two R1 and R5 into a triangle network through star-to-delta transformation, and then merge them with other resistors; after merging, it is a triangle network, and then transform it back to star through star-to-delta transformation, and you can see a star network across the input, output and inverting input of the op amp. Since the op amp input does not take current, the resistor connected to the input can be ignored, and the ratio of the other two resistor values is the gain.

sunboy25

gmchen posted on 2020-11-24 13:11 There are two ways to calculate the gain of the circuit on the first floor: The first is to list the node equations honestly, and you can get two equations, one of which is an intermediate node between the two...

Could you help me confirm whether the formula result circled in red in my screenshot is correct? If it is, I can do it according to your instructions with a clear goal. Because I used the first algorithm you mentioned, but I couldn't get the same result as in the book after several calculations. I wonder if there is any trick involved?