Op-amps With Negative Feedback

Op-Amps with negative feedback

There are several basic ways in which an op-amp can be connected using negative feedback to stabilize the gain and increase frequency response.

The large open-loop gain of an op-amp creates instability because a small noise voltage on the input can be amplified to a point where the amplifier is driven out of the linear region.

Open-loop gain varies between devices.

Closed-loop gain is independent of the open-loop gain.

Closed-Loop voltage gain, Acl

It is the voltage gain of an op-amp with external feedback.

Gain is controlled by external components.

Noninverting Amplifier

The op-amp circuit shown below is a non-inverting amplifier in a closed-loop configuration.

Input signal is applied to the non-inverting input.

The output is applied back to the inverting input through feedback (closed loop) circuit formed by the input resistor Ri and the feedback resistor Rf.

This creates a negative feedback.

The two resistors create a voltage divider, which reduces Vout and connects the reduced voltage Vf to the inverting input.

The feedback voltage is:

Vf = Ri/(Ri + Rf)Vout

The difference between the input voltage and the feedback voltage is the differential input to the op-amp.

This differential voltage is amplified by the open loop gain, Aol, to get Vout­.

Vout­ = Aol(Vin – Vf)

Let B = Ri/(Ri + Rf). Thus Vf = BVout and

Vout = Aol(Vin – BVout)

Manipulate the expression to get:

Vout = AolVin - AolBVout

Vout + AolBVout = AolVin

Vout(1 + AolB) = AolVin

Overall Gain = Vout/Vin = Aol/(1 + AolB)

Since AolB >> 1, the equation above becomes:

Vout/Vin = Aol/(AolB) = 1/B

Thus the closed loop gain of the noninverting (NI) amplifier is the reciprocal of the attenuation (B) of the feedback circuit (voltage-divider).

Acl(NI) = Vout/Vin = 1/B = (Ri + Rf)/Ri

Finally:

Acl(NI) = 1 + Rf/Ri

Notice that the closed loop gain is independent of the open-loop gain.

Example

Determine the gain of the amplifier circuit shown below. The open loop gain of the op-amp is 150000.

Solution

This is a noninverting amplifier op-amp configuration. Therefore, the closed-loop voltage gain is

Acl(NI) = 1 + Rf/Ri = 1 + 100 k?/4.7 k? = 22.3

Voltage-Follower (VF)

Output voltage of a noninverting amplifier is fed back to the inverting input by a straight connection.

The straight feedback has a gain of 1 (i.e. there is no gain).

The closed-loop voltage gain is 1/B, but B = 1. Thus, the Acl(VF) = 1.

It has very high input impedance and low output impedance.

Inverting Amplifier (I)

The input signal is applied through a series input resistor Ri to the inverting input.

The output is fed back through Rf to the same input.

The noninverting input is grounded.

For finding the gain, let’s assume there is infinite impedance at the input (i.e. between the inverting and non-inverting inputs).

Infinite input impedance implies zero current at the inverting input.

If there is zero current through the input impedance, there is NO voltage drop between the inverting and noninverting inputs.

Thus, the voltage at the inverting input is zero!

- The zero at the inverting input is referred to as virtual ground.

Since there is no current at the inverting input, the current through Ri and the current through Rf are equal:

Iin = If.

The voltage across Ri equals Vin because of virtual ground on the other side of the resistor. Therefore we have that

Iin = Vin/Ri.

Also, the voltage across Rf equals –Vout, because of virtual ground. Therefore:

If = -Vout/Rf

Since If = Iin, we get that:

-Vout/Rf = Vin/Ri

Or, rearranging,

Vout/Vin = -Rf/Ri

So,

Acl(I) = -Rf/Ri

Thus, the closed loop gain is independent of the op-amp’s internal open-loop gain.

The negative feedback stabilizes the voltage gain.

The negative sign indicates inversion.

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