# Voltage gain of this OPA circuit with AC input

The aim is to attenuate 10 times and cutoff frequency of at least 10 MHz. I understood that the green section of the circuit reduces the voltage gain. I have noticed that increasing the orange section's resistance leads to voltage amplification, which I initially thought was the denominator of the gain but turned out to be amplifying. I'm not quite sure how to calculate the gain of this circuit. I made the circuit by myself, so it might be wrong.

1. How can I calculate the voltage gain of this circuit? without using spice software

2. Is the AC input voltage gain calculated as Vout / ((Vpin) - (Vvin))?

• I rolled back your question because the question already has answers, and you should not edit a question in a way that undermines those answers. Commented Sep 24, 2023 at 19:28
• Actually, I should have rolled back to revision 4. Commented Sep 24, 2023 at 19:32
• Louis - Hi, (a) As you're new here, please see the main site rules in the tour & edit as they differ from typical forums. (b) We have been alerted that the question has been changed after you received answers. Stack Exchange (with its Q&A format) does not work well when questions change after answers have been written - it can make the answers look wrong or incomplete, since they were answering a different, earlier, question. Although another site member tried to explain this above, you have changed the question again. The changes to this question must stop. Commented Sep 24, 2023 at 19:53
• (continued) I'm going to roll-back the question to (as far as I can tell) the state when it was answered i.e. rev 3. Then, if the original question has been answered, you can consider "áccepting" your choice of the best answer given as the answer to that one, to effectively signal that it is complete. If you need to ask a follow-up question then ask it separately, explain how it is different & include a link to this one for context (note that any new follow-up question must be self-contained and should not rely on people reading this one). Please don't change this question again. Thanks. Commented Sep 24, 2023 at 19:53
• Louis - As you edited the question to remove useful details yet again, despite my previous request not to do that, the question has now been locked to prevent further editing. Commented Sep 27, 2023 at 14:37

This is a differential amplifier. Google "op amp differential amplifier" and you'll find billions of resources.

NOTE: One thing my eyes caught is that the Vref (3V) will appear in both DC and AC i.e. it'll be amplified so the output will have a DC offset, if this is really want you want.

EDIT

From the OP's comment under the answer:

yeah, I will want to have a Vref appear as a DC offset because the OPA doesn't have a negative supply.

So the design needs to be revised. The idea is to isolate the DC reference from the AC analysis (i.e. no DC amplification) and have unity gain at DC. Here's the circuit:

simulate this circuit – Schematic created using CircuitLab

At DC, the capacitors show very high resistance (ideally open circuit), so the circuit turns into a buffer:

simulate this circuit

I removed the resistors as they basically have almost no effect since the op amp's inputs draw virtually zero current.

So the DC gain is:-

$$V_{OUT-DC}=V_{ref}$$

At AC, the capacitors come into play (By default I selected 10 uF but can be changed). DC reference voltage becomes practically zero-volt source (ground) so the circuit turns into a differential amplifier:

simulate this circuit

Notice the resistance values i.e. they are equal in groups of two. So the AC gain is:-

$$V_{OUT-ac}=V_{diff} \ \frac{R_b}{R_a}$$

From superposition, the total gain of the circuit will be:-

$$V_{OUT}=V_{OUT-DC}+V_{OUT-ac}=V_{ref}+V_{diff} \ \frac{R_b}{R_a}$$

This is practically an AC signal with a DC offset.

Few things worth to note:

• Using an op amp as an attenuator (Gain < 1) instead of an amplifier may not be a good idea. You can still select resistors to have a gain of less than unity. But personally, I'd use the differential amplifier with unity gain (i.e. Ra = Rb) and use a voltage divider then use a buffer (optionally, for lowest output impedance if required).
• I intentionally didn't put any capacitors to narrow the bandwidth. Theoretically, from the definition of GBW one can think that using the op amp as an attenuator may increase the bandwidth but this may not always be possible in practice. Ideally, you should use an op amp with maximum GBW (gain-bandwidth product) such as LT6202 as shown in the question. If you really want to limit the BW you can place one capacitor across the output and inverting input (in parallel with top-side Rb), and another one across the non-inverting input and ground.
• The coupling caps (Cc) interact with Ra resistors i.e. together they bring a low-cut and that'll determine the low-bound of the pass band.
• yeah, I will want to have a Vref appear as a DC offset because the OPA doesn't have a negative supply. What about when calculating the Voltage gain? Is it should be Vout/Vpin or Vout / ((Vpin) - (Vvin))? Commented Sep 19, 2023 at 9:35
• @Louis see my edit. Commented Sep 19, 2023 at 13:01

The two input R1's are equal in value. Therefore:

For a true differential amplifier that delivers common mode voltage rejection or attenuation, along with a clearly defined gain equation, the orange combination of {R3 R3 R2} in parallel should equal R2.

https://en.wikipedia.org/wiki/Differential_amplifier#Symmetrical_feedback_network_eliminates_common-mode_gain_and_common-mode_bias

• What about when calculating the Voltage gain? Is it should be Vout/Vpin or Vout / ((Vpin) - (Vvin))? Commented Sep 19, 2023 at 9:35