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.
