We are going to look at the 2nd Op-Amp Circuit, the inverting amplifier. As before we will assume the amplifier is ideal and of those assumptions, the most important today is the assumption that the amplifier has infinite input resistance and draws no input current. To analyze this circuit we will use Kirchhoff’s current law to look at the current going into and out of the junction I have labelled “Node 1”.

Remember Kirchhoff’s current law is simply stated: “What goes in must come out”, but is usually stated: “The sum of the current into a node equals zero.” As shown on the diagram: I in + I out -I oa = 0. Since the current into our ideal op-amp equals 0 this drops out of the formula and it simply becomes I in = – I out.

Now, we need to think back and remember that the Op-Amp is going to put out a very large Voltage if the voltages at the inputs are different values because it is assumed in our ideal op-amp that the gain is infinite. This means that if the amplifier is satisfied (my terminology is the amplifier is “happy”) then V inverting input (-) = V non-inverting input (+). Because the non-inverting input is wired to 0 Volts the inverting input must also be 0 volts. Now we are able to calculate the current I in and I out.

I in = Vin / Rg

I out = Vout /Rf

Substituting these into the relationship derived from Kirchhoff’s law gives us:

Vin/Rg = -Vout/Rf

With a little formula manipulation we can get the gain formula”

Vout/Vin = -Rf/Rg

Again this will be very accurate with real Op-Amps as long as the resistors are in the 10KΩ range.

We have one more standard circuit, the summing amplifier. Since we have multiple inputs the equation for it cannot be written as a gain formula. The equation will be Vout on one side of the equal sign and all the V inputs and resistors on the other side of the equation. The analysis is done exactly the same as the inverting amplifier. For now I will leave that analysis for you to do and will provide my answer in a future post. (Why should I have all the fun?) Seriously, it follows exactly the same procedure as done above just a little more complicated.

On the next post we also will start getting real and deal with some actual data sheets and start complicating our lives with reality.

Gary

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