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What is Feedback in an Amplifier Circuit?
Feedback: Let A be the amplification of a voltage amplifier shown in Fig. If the input and output voltages are Vs and V0 respectively, then
A = \(\frac{V_o}{V_s}\) i.e., V0 = A Vs ….. (1)
Now a feedback circuit is connected between the points P and Q in this amplifier circuit [Fig.]. Voltage between P and Q is so controlled that a part of the output voltage V0 (say, β V,sub>0) is again fed back to the input through the feedback circuit. This phenomenon is known as feedback. β is known as feedback ratio, where β < 1.
In this case, effective input voltage of the amplifier circuit,
Vi = Vs + βV0
So, the output voltage,
V0 = AVi = A(Vs + βV0) = AVs + AβV0
or, V0 – AβV0 = AVs or, V0(1 – Aβ) = AVs
So, the effective amplification of the amplifier circuit,
Af = \(\frac{V_o}{V_s}\) = \(\frac{A}{1-A \beta}\) ……….. (2)
In general, the self amplification A of the amplifier is called open loop gain and the effective amplification Af due to feed back is called closed loop gain. Gain Aβ is known as loop gain.
Negative feedback: If loop gain Aβ be real and negative, then according to equatIon (2) (1 – Aβ) > 1 and Af < A. Due to such feedback the effective amplification A becomes less compared to self amplification A. This is called negative feedback. In spite of the lowering of amplification, negative feed back has great utility due to some special advantages:
- The amplification can be kept at a stable value.
- The distortion in output signal with respect to the input signal can be removed.
- The internal noises of the amplifier can be minimised.
- The effective bandwidth [see the chapter ‘Communication System’] increases and so on.
[Further discussion on negative feedback is out of syllabus]
Positive feedback: Borkhausen criterion: If the loop gain Aβ is real, positive and less than 1, then (1 – Aβ) < 1 and Af > A. Consequently, the effective amplification Af becomes greater with respect to self amplification A of the amplifier. It is called positive feedback.
Generally, the reactive components, like inductors or capacitors are used in feedback and amplifier circuits. As a result A and β both become complex, instead of being real, which means that an addition to the numerical values, these quantities include a phase factor.
Let us assume that the components of an amplifier and positive feedback circuit are so chosen that the following condition is satisfied:
Aβ = 1 …… (3)
Then from equation (2), Af = ∞, i.e., the effective amplification of the amplifier becomes infinity. Hence, the amplifier produces an output signal without any externally applied input signal. Thus, the amplifier becomes an oscillator. This condition is called the Barkhausen criterion of oscillation.
This condition means that |Aβ| = 1 and the phase difference for a complete feedback cycle is zero or an integral multiple of 2π. If the components used in the feedback circuit remain unchanged, then it is observed that for a certain frequency (say f0) the condition (3) is satisfied. Only for this specific frequency (f0), the magnitude and phase of the feedback voltage becomes equal to those of the input voltage. So, the feedback voltage itself behaves effectively as input signal. Hence, no external input signal is required to obtain output signal.
Thus an oscillator can generate output signal of a particular frequency without any externally applied input signal. Due to this, an oscillator may also be called a self-sustaining device.
Output can be generated without input—this is true for the signal only. In view of the law of conservation of energy, to get a stable alternating voltage or alternating current of a specific frequency as an output, we should connect an energy source at the input. Generally, any dc source or ac source of unregulated frequency is used for this purpose.
Definition: The system which can convert a dc or unregulated ac signal to ac signal of a certain frequency is called an oscillator.
Classification of Oscillators: Depending on the active arrangements of components to generate oscillation, oscillators can be classified as
- feedback oscillator and
- negative resistance oscillator.
On the other hand, according to the range of frequencies generated by an oscillator, it can also be classified as
- audio frequency oscillator or AF oscillator,
- radio frequency oscillator or RF oscillator etc.
In case of sinusoidal oscillators, depending on the particular circuit used as the frequency-determining circuit, oscillators are named as LC oscillator, RC oscillator, crystal oscillator etc.
LC feedback oscillator: In the feedback amplifier town in Fig., an LC circuit has been used as a feedback circuit.
From ac analysis, t will be observed that such a type of circuit will generate alternating voltage or alternating current of a constant frequency. The frequency is given by
f0 = \(\frac{1}{2 \pi \sqrt{L C}}\) …. (4)
Now, if a dc source is applied at the input, it can be observed that such type of dc source, whatever may be its stability in magnitude, always contains some amount of distortions or ripples mixed with it. These are called noise, Ripples of each noise can also be analysed as combination of many sinusoidal waves. Each of such sinusoidal waves reaches the output point Q after getting amplified by the amplifier A . Then the LC feedback circuit brings back the wave of frequency f0 [as shown in equation (4)] to the point P. For all other frequencies except f0, LC circuits act as rejector circuits.
Hence, no feedback of the frequencies other than f0 takes place to the input. Thus the wave of frequency f undergoes repeated feedback and amplification and ultimately attains stability at the output. Outputs for all other frequencies become negligible. So, it can be said that the LC feed-back oscillator generates an alternating wave of a constant frequency fo. This frequency-determining LC circuit is called tank circuit.
It may be noted that the noise at the input is the source of the output wave of a constant frequency.
If the magnitude of the components of LC circuit in Fig. is changed, then according to equation (4), the magnitude of will also he changed. Thus by changing the magnitudes of the components of LC circuit, alternating waves of other frequencies can also be generated.
Particularly, if It is so arranged that the magnitude of Capacitor C can be changed continuously, then the LC feedback oscillator is converted to a variable frequency oscillator.
Besides generating sinusoidal waves, if an oscillator is used to generate square waves, triangular waves and other types of complex waves, then this oscillator is termed as multivibrator.
Designing of an oscillator using transistor ampli-fier: Fig. shows, how an n-p-n transistor can be used as an oscillator (Resistors which are used for biasing of the transistor have not been shown here).
In this oscillator, a frequency-determining tank circuit has been used. This tank circuit is a combination of a capacitor C and a mutual inductor M (L and L’ are constituent self inductors of this mutual inductor). This combination of C and M acts as the feedback circuit across collector output and base input.
We know, in case of common-emitter (CE) configuration of transistor, there is a phase difference of 180° between input and output. The components of the tank circuit are so selected that due to feedback, it again generates a phase shift as 180°, which means the feedback voltage is in same phase as the input voltage. Such an oscillator is called tuned collector oscillator. Generally, this type of oscillator is used for generating alternating output of high frequency of the order of 1 MHz . There are some other varieties of oscillators made of transistors which find different applications.