Operational Amplifier
Analysis of Inverting Amplifier
Having an amplifier with enormous gain is useful, and we will certainly exploit that eventually, but let's first look at an op-amp circuit that has a much lower gain. The circuit that is shown is called an 'inverting' amplifier. We'll see why it's called that later on.
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In the circuit there is one input voltage source and one load resistor. In addition, it has two other resistors. Notice that one of the resistors is connected between the output of the op-amp and the inverting input. Because this resistor is feeding some of the output of the op-amp back into an input it's called a 'feedback' resistor.
Let's now develop a mathematical model for this circuit. We'll assume that we're using an ideal op-amp.
The first thing to notice is that the non-inverting input is grounded. What does that tell us about the voltage at the inverting input?
- Answer
The non-inverting input must also be at zero volts.
With that in mind, let's now figure out the current that's flowing through resistor R1. We can use Ohm's law to calculate the current flowing through the resistor.
The next step in our analysis is to do KCL at the node labeled 'A'. The current i1 is flowing into node A; assume a current is flowing out of the node through the resistor R2. What about the last branch connecting to node A the inverting input to the op-amp? How much current is flowing in that branch?
- Answer
The answer in this case is zero. Recall that the current flowing into either of the inputs of an ideal op-amp approaches zero.
So that means the current flowing out of node A must equal the current flowing into node A.
Finally, Kirchoff's voltage law (KVL) can be used to create one additional equation. The loop will start at node A and end at the load resistor RL which is specified to have the voltage Vo across it.
Why can we start the KVL loop at node A?
- Answer
It's because the non-inverting input to the op-amp is grounded - which in turn means that the inverting input of the op-amp (node A) is also effectively grounded.
This results in the given equation vo + i2R2
The quantity that is of particular interest is the ratio of the output voltage to the input voltage or Av = vo/vin. This is formally called the closed-loop gain of the circuit ('closed' because of the presence of the feedback resistor), but we'll call it just the gain of the circuit.
Two things in particular should be noted. The first is that the gain sis simply the negative of the ratio of the resistors Rf/Ri. Because resistors come in many different standard fixed as well as variable values it should be apparent that any desired gain including fractional values can be arranged. The other important thing to notice is that the gain is negative. This means that the output voltage will be of opposite polarity to the input voltage. The name of the circuit, i.e., an 'inverting' amplifier, comes from this characteristic.
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