1. Lecture on Feedback Amplifiers
Text Book: Jacob Millman, Cristos C. Halkias, “Integrated Electronics: Analog and Digital Circuits and Systems”, 34th Reprint 2004, Tata-McGraw-Hill. (yellow covered book).

2. (c) Trans-conductance amplifier, and (d) Trans-resistance amplifier.
Amplifier: An amplifier is a circuit that receives a signal at its input and delivers an undistorted large version of the signal at its output.
Used of Amplifier: Amplifiers are used in wireless communications and broadcasting, and in audio equipment of all kinds.
Classification of amplifiers:
Based on the voltage level, amplifiers can be classified into two categories, as:
(a) Weak-signal amplifiers: Weak-signal amplifiers are used in wireless receivers, audio tape players, and compact disc players. A weak-signal amplifier is designed to deal with exceedingly small input signals, in some cases measuring only a few nanovolts (units of 10-9 volt).
(b) Power amplifiers: Power amplifiers are used in wireless transmitters, broadcast transmitters, and hi-fi audio equipment. A power amplifier is designed to deal with large input signals, in some cases measuring only a few volts.
Based on the magnitudes of the input and output impedances of an amplifier relative to the source and load impedances, respectively, amplifiers can be classified into four broad categories as:
(a) Voltage amplifier,
(b) Current amplifier,
(c) Trans-conductance amplifier, and
(d) Trans-resistance amplifier.

3. Voltage amplifier: A voltage amplifier is defined as an amplifier, which provides an output voltage proportional to the input voltage, and the proportionality factor is independent of the magnitudes of the source resistance (Rs) and load resistance (RL).
Figure 13-1 shows a Thevenin’s equivalent circuit of a two-port network, which represents an amplifier.
Fig Thevenin’s equivalent circuits of a voltage amplifier.
Here, Vs= source voltage,
Vi= amplifier input voltage,
Vo= output voltage,
Rs= source resistance,
Ri= amplifier input resistance,
Ro= amplifier output resistance,
RL= external load resistance.
If Ri is larger compared with Rs (Ri>> Rs), then Vi  Vs.
If the external load resistance RL is large compared with the output resistance Ro of the amplifier (Ro<< RL), then Vo  AvVi AvVs. Hence, the output voltage is proportional to input voltage.
The symbol in Fig Av represents Av=Vo/Vi with RL=, and hence represents the open-circuit voltage amplification, or voltage gain.

4. Current amplifier: A current amplifier is defined as an amplifier, which provides an output current proportional to the input current, and the proportionality factor is independent of the magnitudes of the source resistance (Rs) and load resistance (RL).
Fig Norton’s equivalent circuits of a current amplifier.
Figure 13-2 shows a Norton’s equivalent circuit of a current amplifier.
Here, Is= source current,
Ii= amplifier input current,
Io= IL= output or load current,
If the amplifier input resistance Ri is smaller compared with the source resistance Rs (Ri<<Rs), then Ii  Is.
If the external load resistance RL is smaller compared with the output resistance Ro of the amplifier (Ro>> RL), then Io  AiIi AiIs. Hence, the output current is proportional to input current.
An ideal current amplifier must have zero input resistance (i.e. Ri =0) and infinite output resistance (i.e. Ro = ).
The symbol Ai in Fig represents Ai=Io/Ii with RL=0, and hence represents the short-circuit current amplification, or current gain.

5. Trans-conductance amplifier: A trans-conductance amplifier is defined as an amplifier, which provides an output current proportional to the input voltage, and the proportionality factor is independent of the magnitudes of the source resistance (Rs) and load resistance (RL).
Fig A trans-conductance amplifier is represented by a Thevenin’s equivalent in its input circuit and a Norton’s equivalent in its output circuit.
Figure 13-3 shows a trans-conductance amplifier, which is represented by a Thevenin’s equivalent in its input circuit and a Norton’s equivalent in its output circuit.
If the amplifier input resistance Ri is larger compared with the source resistance Rs (Ri>> Rs), then Vi  Vs.
If the external load resistance RL is smaller compared with the output resistance Ro of the amplifier (Ro>> RL), then Io  GmVi GmVs. Hence, the output current is proportional to the input voltage.
An ideal trans-conductance amplifier must have infinite input resistance (i.e. Ri = ) and infinite output resistance (i.e. Ro = ).
The symbol Gm in Fig represents Gm=Io/Vi with RL=0, and hence represents the short-circuit transfer conductance (trans-conductance) or gain.

6. Trans-resistance amplifier: A trans-resistance amplifier is defined as an amplifier, which provides an output voltage proportional to the input current, and the proportionality factor is independent of the magnitudes of the source resistance (Rs) and load resistance (RL).
Fig A trans-resistance amplifier is represented by a Norton’s equivalent in its input circuit and a Thevenin’s equivalent in its output circuit.
Figure 13-4 shows a trans-resistance amplifier, which is represented by a Norton’s equivalent in its input circuit and a Thevenin’s equivalent in its output circuit.
If the amplifier input resistance Ri is smaller compared with the source resistance Rs (Ri <<Rs), then Ii  Is.
If the external load resistance RL is large compared with the output resistance Ro of the amplifier (Ro<< RL), then Vo  RmIi RmIs.
An ideal trans-conductance amplifier must have zero input resistance (i.e. Ri =0) and zero output resistance (i.e. Ro = 0).
The symbol Rm in Fig represents Rm=Vo/Ii with RL=, and hence represents the open-circuit transfer resistance (trans-resistance), or gain.

7. Table 13-1 represents the characteristics and the parameters values in the ideal case.

8. Feedback: Feedback is a portion of the output is returned to the input to form part of the system excitation.
There are two types of feedback:
(a) Negative (degenerative) feedback and
(b) Positive (regenerative) feedback.
Negative (degenerative) feedback: If the signal fed back is of opposite polarity or out of phase by 180 (or odd integer multiples of 180) with respect to the input signal, the feedback is called negative feedback.
The feedback signal reduces the magnitude of the amplifier input signal.
It decreases the voltage gain.
It is principally applied in amplifiers.
Positive (regenerative) feedback: If the signal fed back is of the same polarity or in phase with the input signal, the feedback is called positive feedback. So, the feedback signal increases the magnitude of the amplifier input signal.
It increases the voltage gain and causes the instability of an amplifier.
It is mainly used in oscillators.
A feedback amplifier is sometimes referred to as a closed-loop amplifier because the feedback forms a closed loop between the input and output.

9. (a) Signal source, (b) Feedback network with reverse transmission,
A feedback amplifier consists of a basic amplifier and a feedback network.
The representation of any single-loop feedback connection around a basic amplifier is shown in Fig
The basic parts of a single-loop feedback connection around a basic amplifier are as follows:
(a) Signal source, (b) Feedback network with reverse transmission,
(c) Sampling network, (d) Comparator or mixer network, and
(e) Basic amplifier with forward transfer gain.

10. Signal Source: Feedback Network: Sampling Network:
Signal source is either a signal voltage Vs in series with a resistor Rs (a Thevenin’s representation) or a signal current Is in parallel with a resistor Rs (a Norton’s representation).
Feedback Network:
The feedback network is usually a passive two-port network which may contain resistors, capacitors, and inductors.
Sampling Network:
Two types of sampling networks can be used. These two sampling networks are:
Voltage or node sampling: In this type of sampling system the output is sampled by connecting the feedback network in shunt across the output. Fig. 13-6(a) shows the representation of voltage or node sampling network.
Current or loop sampling: In this type of sampling system the output is sampled by connecting the feedback network in series with the output. Fig. 13-6(b) shows the representation of current or loop sampling network.

11. Comparator or mixer network:
Mixer network circuit is either series (loop) input or shunt (node) input connections.
Figs. 13 –7 (a) and (b) show the representation of series and shunt connections, respectively.
A differential amplifier is often also used as the mixer.
Such an amplifier has two inputs and gives an output proportional to the difference between the signals at the two inputs.

12. Transfer Ratio, or Gain:
The symbol A in Fig represents the ratio of the output signal to the input signal of the basic amplifier.
The transfer ratio V/Vi is the voltage amplification, or the voltage gain, AV.
The transfer ratio Io /Ii is the current amplification, or the current gain, AI.
The transfer ratio I/Vi is the trans-conductance, GM. and V/Ii is the trans-resistance, RM.
Although GM and RM are defined as the ratio of two signals, one of these is a current and the other is a voltage waveform.
Hence the symbol GM or RM does not represent an amplification in the usual sense of the word.
Nevertheless, it is convenient to refer to each of the four quantities AV, AI, GM, and RM as a transfer gain of the basic amplifier without feedback and to use the symbol A to represent any one of these quantities.
The symbol Af is defined as the ratio of output signal to the input signal of the amplifier configuration of Fig and is called the transfer gain of the amplifier with feedback.
Hence Vo/VsAVf, Io/IsAIf, Io/VsGMf, and Vo/IsRMf,

13. Advantages of Negative feedback
In negative feedback system, the gain Af with feedback is lowered in comparison with the transfer gain A of an amplifier without feedback.
So the voltage gain in a negative feedback is reduced.
While negative feedback results in reduced overall voltage gain, a number of improvements are obtained, among them being:
1. Higher input resistance,
2. Lower output resistance,
3. Better stabilized voltage gain under the variation of
parameters,
4. Improved frequency response,
5. More linear operation,
6. Reduced Noise, and
7. Reduced non-linear distortion.