# What is this opamp configuration?

I am trying to understand the function of this input stage of a filter I am using.

The input current source is a 2uA peak-to-peak with zero offset.

(This specific stage is followed by an active bandpass with a gain of 40 and an active low pass with a gain of 30.)

Quick summary:

My first question before simulating it in Multisim was "Where is the input resistor?" and hence "How much is the gain?". Although my question still remains, I figured that the output voltage could be derived by adding the voltage drop across R2, to the non-inverting reference voltage 1.65 V. Specifically, the current passing through the feedback network is 1.65/47k =35uA (+- 1uA due to input current) and therefore Vout =1.65 + 35uA*36kΩ = 2.91 V.

However, I could not find any relationship between the input Vin(pp) of 359 nV (probe1) and Vout(pp) of 71.8 mV. In fact, Vout(pp) remains constant despite changes in R1, but is linearly proportional to a change in R2 ( if R2'=2*R2, Vout,pp'= 2* Vout,pp). So I assume there is no R2/R1 type of relationship to calculate gain. Then where does the gain of (71.8 mV)/(359 nV)~ 200,000 come from?

Another thing that I did not like is that Vout(dc) is different than the reference voltage 1.65 V. I know I just explained above how this dc output voltage V(dc) of probe2 is derived, but, up until now I thought the whole point of a reference voltage in the non-inverting pin is to perform level shifting so that the ac signal in the output will be centered around that reference voltage.

After this realization (that vout(dc) does not equal the reference voltage), I went on examining other possible level shifting circuits, like this for example ,

where I would think that Vout= Vref + (1+R1/R2)*Vin. However by doing the math (superposition), I get: Vout=(1+R1/R2)*Vin-(R1/R2)*Vref.

Questions:

1. Is there a formula for calculating the ac gain of this active low pass configuration in the first picture?

2. If not, is the ~200,000 times gain of the ac signal intentional? Or did the the designer just aim for the low pass functionality and remained satisfied with this huge gain that is somehow provided?

3. Please help me demystify opamp level shifting once and for all. Is the formula derived above for the opamp of the second picture correct? Vout=(1+R1/R2)*Vin-(R1/R2)*Vref. If it is, then how is level shifting achieved for the non inverting configuration?

**for an inverting configuration it can be achieved as explained by Spehro Pefhany in this post.

• I'm puzzled by your supply connections to the op-amp. I expect to see the higher potential at the top connection and negative or ground potential at the bottom. – Russell Borogove May 5 '18 at 1:01
• @RussellBorogove It simply is because of the way multisim places the supply pins on the opamp symbols. The positive supply pin is closer to the non-inverting input and the negative suppy is closer to the inverting input. – George May 5 '18 at 12:38