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GENERALIZED AMPLIFIER CIRCUIT MODEL

Amplifier System

What is the best way to model the amplifier?

Input stage

Ideally, the amplifier should have no effect on the source of the input signal. In other words,

it should not draw any input current. This is, however, impossible. In actual fact, a small

amount of current flows into the input terminals of the amplifier. This can be modelled as an

input impedance.

Output stage

Ideally, the voltage amplifier should be able to supply an infinite amount of current to the

load connected to it. In other words, it should be an ideal voltage source. Since this is not

possible the output stage is generally modelled as a Thevinin equivalent source which

includes an ideal controlled voltage source of the appropriate value in series with a

Thevinin equivalent resistance, Ro.

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Complete Amplifier Circuit Model

Resistive input

Thvenin equivalent output circuit

Thvinin voltage is a "dependent" voltage source the magnitude of which depends upon the input voltage

Amplifier System Model

Text:- Examples 14.1 14.3 for problems related to this topic

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Operational Amplifiers

Circuit Symbol

Properties

An 'ideal' operational amplifier has:

infinite voltage gain

zero output impedance

infinite input impedance

infinite bandwidth

Its normal implementation is in the form of an integrated circuit.

'Real' operational amplifiers have a

voltage gain of around 50,000

input impedance of megohms or hundreds of megohms

output impedance of hundreds of ohms

open-loop 3 dB bandwidth is around 50 Hz, a far cry from the ideal value of infinity.

Negative feedback is often used to make the characteristics of real operational

amplifier circuits closer to those of the ideal operational amplifier.

Note

The circuit symbol for an operational amplifier normally does not show the

connections to the dc power supplies required to make the amplifier operate.

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IDEAL vs REAL OPERATIONAL AMPLIFIERS

The 741 operational amplifier is the most common and the one which will be used in this

course. See text Sect. 16.5 to 16.5.9 for a discussion on real 741 characteristics summarized

in the table below.

Characteristic Ideal Voltage

Amplifier

Real 741 Operational Amplifier

Voltage Gain Infinite 106 dB (2 x 105)

Input Impedance Infinite 80 Mto 1012

Output Impedance Zero 75to 2k

3 dB Bandwidth Infinite Tens of Hertz

Cost Zero $0.50

Most of the "real" operational amplifier characteristics become closer to the "ideal"

amplifier characteristics if negative feedback is used.

741 OP-AMP OPEN-LOOP FREQUENCY RESPONSE

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EXAMPLE OF NEGATIVE FEEDBACK

Op-amp inverting amplifier

Redrawn, the circuit is

For this circuit make the following assumptions:

1. The forward gain A is very large (for the 741 it is 50,000) 2. No current is drawn by the input of the amplifier (ie the input impedance of the

op-amp is very large)

3. The feedback circuit does not affect the output voltage Vo (the output impedance of the op-amp is very small)

The result of these assumptions is the following two rules:

Rule (1): the difference in voltage between the two input terminals of the op-amp is very small and can be neglected

Rule (2): the signal current that flows into the op-amp terminals is very small and can be considered to be equal to zero.

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NEGATIVE FEEDBACK (continued)

INVERTING AMPLIFIER (also called parallel voltage feedback).

The currents through Z1 and Z2 are i1 and i2 , respectively, and V+ = 0.

Rule 1 gives V- = 0.

Rule 2 gives i1 + i2 = 0, because the signal currents into the amplifier terminals are

negligible. Thus,

(Vi - V-)/Z2 + (Vo - V-)/Z1 = 0 from Kirchoff's current law or

(Vi - 0)/Z2 + (Vo - 0)/Z1 = 0

The circuit gain with feedback (Vo/Vi) is then,

A = -Z1 /Z2.

The circuit input impedance (defined as Vi /i1) is equal to Z2. The circuit output impedance is

approximately (ZoZ1)/(AolZ2),

where Zo is the amplifier output impedance without feedback.

Aol is the open-loop gain of the amplifier, and

(Z2/Z1) is the feedback factor

(This result is not obvious. However, there is a table in the Week 5 notes giving formulae

for the input and output impedances of inverting and non-inverting amplifiers.).

Inverting Amplifier

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NON-INVERTING AMPLIFIER

(also called series voltage feedback)

Rule 1 gives V- = Vi , i2 = (0 - Vi)/Z2 and i1 = (Vo - Vi)/Z1 by Ohm's law

Rule 2 again gives i1 + i2 = 0.

Thus,

A = V0/Vi = (Z1 + Z2)/Z2 = (1 +Z1/Z2)

Non-inverting Amplifier

The input impedance of this circuit is of the order of one hundred megohms and the output

impedance is reduced by the factor (1 + Aol) to Z0/(1+ a), where = Z2/Z1.and a = open-loop gain of the amplifier

UNITY GAIN or BUFFER AMPLIFIER

An important special case of the non-inverting amplifier circuit is the unity-gain follower,

when Z1 = 0 and therefore A = 1. A "unity follower" has constant voltage gain (equal to

unity), and negligible phase shift, over a wide range of frequencies. In addition, it has very

high input impedance and very low output impedance. It is used as an impedance

transformer and buffer amplifier.

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SUMMING AMPLIFIER

In general, there can be any number of inputs.

Rule 1 gives V- = 0.

Rule 2 gives the algebraic sum of all the currents at the inverting input = 0.

Thus, we have the result that V1/ R1 +V2/ R2 +..+Vx/Rx +V0/ RF = 0.

The output voltage is then given by the weighted sum of the inputs, with weighting factors

given by the ratio of the feedback resistor to the appropriate input resistor.

-V0 = (RF / R1)V1 + (RF / R2)V2 + ..... + (RF / Rx)Vx

Or

V0 = -RF.[(V1/R1) + (V2/R2) + ..... + (Vx/Rx)]

Summing Amplifier.

[Note that the notation is different to that in the course text. However, the circuit is a more

general circuit, and the equations are valid. The summing amplifier is seen later in the

course, when data acquisition circuits are studied Digital-to-Analogue Converter (DAC or D/A), and Analogue-to-Digital Converters (ADC or A/D)]