# Non-inverting Amplifier

The non-inverting amplifier is essentially a voltage follower with a voltage divider between the output and the inverting input.

 An op-amp non-inverting amplifier. The voltage gain (AV) is calculated by the formula below the diagram. Example of operation

In the above example (bottom illustration), the input voltage is +2 volts (assume all voltages are positive unless otherwise specified). This is going directly to the non-inverting input. The op-amp will make the output voltage whatever it takes to make the inverting input also +2 volts. It may look like the feedback network is a combination series-parallel circuit, but it isn't. No current can flow into the inverting input. The impedance is too high. This leaves only one current path in the feed back network, the definition of a series circuit. Since the two feedback resistors are in series, and they have the same resistance, they must have the same voltage across them. The left side of R1 is connected to ground (0 volts) and the right side has +2 volts. That shows that there are 2 volts across R1. R2 must also have 2 volts across it. We start at ground, gain two volts across R1 and gain two more volts across R2. The output of the op-amp must have +4 volts.

Let's increase the value of R2 to 2 k.

 R2 has been increased to 2 k.

R1 and R2 are in series and R2 has twice the resistance as R1. Therefore, R2 must have twice the voltage as R1. The voltage across R1 will not change. Why not? Because, when we change the value of R2, the op-amp will adjust its output voltage to whatever it takes to keep the voltage at the inverting input at +2 volts. That puts 2 volts across R1. Now, we start at ground, gain 2 volts across R1 and gain 4 more volts across R2. The output of the op-amp must be +6 volts.

Notice that when the resistors have a 1:1 ratio (R2 to R1) that the gain was 2. When we changed the ratio to 2:1, the gain became 3. The gain is always the ratio of R2 to R1 plus 1.

You may often see diagrams of non-inverting amplifiers with a resistor between circuit input and the non-inverting input of the op-amp, as shown below. Recall that, although the op-amp tries to make the inputs equal, it may not be able to do so. Some op-amps have zener diodes between the inputs to limit the voltage difference when the op-amp cannot compensate. If these diodes are triggered by a high voltage differential between the inputs, high current may flow into the non-inverting input. This resistor limits such current.

 The resistor on the non-inverting input limits input current if the voltage difference between the inputs triggers internal zener diodes.

## AC operation

Op-amps work with AC as well as DC. Since the polarity of an AC signal is constantly changing, polarity is not a consideration with AC operation. Remember that AC is simply DC that changes at regular intervals. At any moment in time, the instantaneous output of the op-amp will be the instantaneous input voltage multiplied by the gain of the amplifier.

Let's put a 2 VP-P signal on the input of a non-inverting amplifier. This amplifier has equal resistors in the feedback network, so it has a gain of 2. The 2 VP-P input signal starts at 0 volts and at that moment the output voltage is also at 0 volts. A moment later the input voltage reaches its positive peak of +1 V, at which time the output is +2 V. When the signal reaches its negative peak of -1 V, the output is at -2 V. The input is 2 VP-P and the output is 4 VP-P.

 AC operation: The amplifier has a gain of 2. Therefore the AC output is two times the AC input.

If there is a DC offset of the AC voltage (a mix of AC and DC), think of the AC and DC components of the signal as if they are treated separately. Let's say you have an input voltage that is a sine wave with a negative peak of +0.5 volts and a positive peak of +3.5 volts. This is a 3-volt swing, peak-to-peak, centered on +2 volts. The signal is 3 volts peak-to-peak with a +2-volt DC offset.

 The input (left) is 3 VP-P with a +2-volt DC offset. The amplifier has a gain of 2. The output (right) is 6 VP-P with a +4-volt DC offset.

At any instant of time, the output voltage will be 2 times the input voltage. When the input voltage is at its lowest point of +0.5 volts, the output is at its lowest point of +1 volt. When the input voltage is at its highest point of +3.5 volts, the output is at its highest point of +7 volts. The input is centered on a +2-volt DC offset and the output is centered on a +4-volt DC offset. Therefore, the input is 3 VP-P with a +2 volt DC offset and the output is 6 VP-P with a +4-volt DC offset. Everything is multiplied by 2.

## Troubleshooting

Myth:

The voltage at the non-inverting input and the voltage at the inverting input of a working op-amp will always be the same.

There is a common misconception that the two inputs of a working op-amp will always have the same voltage. It is clearly shown in the previous pages that this not true. A perfectly good op-amp can have different input voltages if conditions make it impossible to produce an output voltage that makes the inputs equal. Therefore, checking the input voltages for equality is not a valid test for a good or bad op-amp.

Let's say you have a non-inverting amplifier powered by dual 10-volt power supplies. The non-inverting input is at +2 volts, the inverting input is at 0 volts and the output is at +9.5 volts.

Clearly, something is not right. Is it a bad op-amp? Notice that the non-inverting input is at a higher voltage than the inverting input. This should be driving the output higher. In fact, the output is as high as it can go. The op-amp is doing exactly what it is expected to do; the non-inverting input is higher than the inverting input and the output is jammed against the positive supply voltage. The circuit appears to be acting like a comparator instead of a non-inverting amplifier. A comparator has no connection from the output to the inverting input. This circuit should have a connection from the output to the inverting input through R2. Maybe R2 is open.

R2 could be open, or maybe it just has too much resistance. Let's say that R2 has a resistance of 4 k instead of 1 k. That would give the amplifier a gain of 5 (the gain is the resistor ratio plus 1 or 1+R2/R1). With an input of +2 volts, the output would be +10 volts. That's not going to happen with a 10-volt positive power supply. The best it can do is about +9.5 volts. It looks like R2 is either open or has too much resistance. The op-amp is acting exactly as it should.

 The voltages are not as expected because R2 is open. The op-amp is acting exactly as expected.

Or is R2 the problem? Is there something else that could cause this situation? What if R1 were shorted? This would hold the inverting output at groundâ€”0 voltsâ€”and the output will jam itself against the positive supply voltage trying to bring it up. Again, the op-amp is doing exactly what it is expected to do.

 Same voltages as above, but this time it's because R1 is shorted.

An op-amp may also appear to be shorted-out if there is a failure in the feedback network. In the following example, both inputs and the output have the same voltage. This is not because the op-amp is shorted, but because R1 is open. The circuit is acting like a voltage follower instead of a non-inverting amplifier (no current flows through R2, so there is no voltage drop across R2). The same thing would happen if R2 were shorted. 100% of the output voltage would be at the inverting input and the circuit will also act as a voltage follower.

 This op-amp looks shorted but R1 is open. Same voltages as above, but this time because R2 is shorted.

When troubleshooting, be sure to examine the op-amp to see if it is acting as it should. Don't be quick to change-out the op-amp circuit if the input voltages are unequal. First, see if the op-amp is doing what it should if the input voltages are unequal.

Operational Amplifiers No. 3 - Voltage Followers