Closed Loop Gain Of An Inverting Operational Amplifier
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Closed Loop Gain Of An Inverting Operational Amplifier (a) What is an ideal amplifier and what is an op-amp?
(b) What is an open loop op-amp?
(c) What is a closed loop op-amp?
(d) What is an ideal op-amp?
(e) Show that the inverting amplifier closed-looped gain equals -RF/Rs. Where RF is the feedback impendance and Rs is the impedance associated with the voltage source.
(f) An inverting amplifier uses two 10% tolerance resistors: RF = 33kΩ and Rs = 1.2 kΩ.
(i) What is the nominal gain of the amplifier?
(ii) What is the maximum value of |Av|?
(iii) What is the minimum value of |Av|?

The strings: S7P5A51 (change - physical).

The math:
Pj Problem of Interest is of type change (change - physical).  (a) An amplifier (figure 8.1.3) is an electronic device use to amplify low level electric signals (e.g. voltage and currents). For example, the sound produced by a loud speaker is the result of amplication. Basically an ideal amplifier recieves a signal vs(t) and outputs a signal:
vo(t)= Avs(t) (also called the load voltage)-------(1)
Where A is called the gain of the amplifier.
An operational amplifier (op-amp) is an integrated circuit (an aggregation of many electronic and electric circuits on a wafer of a semi-conductor such as silicon). The op-amp amplifies the difference between two input signals. In figure 8.1, vd is the difference signal. The relationship between the difference voltage that is input and the output voltage is as follows:
vo = AOLvd-------(2)
Where AOL is called the open-loop gain.

(b) The op-amp of figure 8.2.1 is open looped. That is, the output signal is not fed back as input.

(c) The inverting op-amp (output signal is inverted) of figure 8.2 is closed looped. That is, output signal is fedbacked as input. This is why iF is called the feed back current.

(d) An op-amp is ideal if it satifies the following characteristics:
- The open-loop voltage gain is negatively infinite.
- The input current iinm = 0 which implies input impedance Rin is infinitely large.
- The output impedance R0 = 0, which implies the output voltage is independent of the load.

(e) Consider figure 8.2. By KCL, i1 + iF = iin-------(3)
So. (vs - vd)/R1 + (vo - vd)/RF = vd/Rd------(4)
By eq (2), vd = vo/AOL
So, substituting vo/AOL in eq(4) and allowing AOL tend to - infinity, we have:
vs/R1 + Vo/RF = 0
So, inverting amplifier closed loop gain, Av = vo/vs = - RF/R1.
This derivation uses the first characteristics of the ideal op-amp: that open loop gain AOL tends to - infinity.
If we use the characteristic that iin = 0, we gat the same result thus:
iin = 0, implies i1 = iF
So, vs/R1 + vo/RF = 0
So, Av = vo/vs = -RF/R1. (fi) Nominal gain = Av = -RF/R1 = - -(33/1.2) = -27.5

(fii) Max value of |Av| = (33 + 10% of 33)/(1.2 - 10% of 1.2) = 36.3

(fiii) Min value of |Av| = (33 - 10% of 33)/(1.2 + 10% of 1.2) = 22.5

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