MULTISTAGE AMPLIFIER

CHAPTER 4

1. Introduction • The basic purpose of multistage amplifier is

to increase the overall voltage gain.• Multistage amplifier is used when power

gain or voltage gain of single stage amplifier is not sufficient

• A cascade amplifier is any amplifier constructed from a series of amplifiers, where each amplifier sends its output to the input of the next amplifier

• The output of one stage serves as input of the next stage

• The overall voltage gain, A’v, of cascaded amplifiers, is the product of the individual voltage gains. A’v = Av1 × Av2 × Av3 × . . . . . . Avn

n= number of stages

Input

Output

• Amplifier voltage gain is often expressed in decibels (dB)

Av(dB) = 20 log Av

 

Av1Av2 Av3 Avn

• When the voltage gain is expressed in decibels (dB), then the overall decibel gain of the multistage amplifier is equal to the sum of the dB gains of the individual stage. A’v(dB) = Av1(dB) + Av1(dB) +…….. + Avn(dB)

ExampleA certain cascaded amplifier arrangement has the following voltage gains: Av1 = 10, Av2 = 15, Av3 = 20. What is the overall voltage gain? Also express each gain in decibels (dB) and determine the total voltage gain in dB.Solution: A’v = Av1 Av2 Av3 = (10)(15)(20)= 3000

Av1(dB) = 20 log 10 = 20.0 dB

Av1(dB) = 20 log 15 = 23.5 dB

Av1(dB) = 20 log 20 = 26.0 dB

A’v1(dB) = 20.0 dB + 23.5 dB + 26.0 dB = 69.5 dB

2. Feedback Amplifier

• A feedback amplifier is one that provides a path from the amplifier output back to the input.

• The purpose of this path is to “feed” a portion of the output signal back to the amplifier input.

Feedback Amplifier Block Diagram

• With the feedback network (circuit or path) connecting the output of the amplifier back to the output, a small portion of the output signal is fed at the amplifier input.

• The effect that this feedback signal has on the amplifier depends on the type of feedback used.

• There are 2 basic types of feedback:i) Negative feedbackIi) Positive feedback

• NEGATIVE feedback also called DEGENERATIVE feedback is provided when the feedback signal is 180° out of phase with the input signal. Negative feedback is frequently used in amplifier circuits.

• POSITIVE feedback also called REGENERATIVE feedback is provided when the feedback signal is in phase with the input signal. Positive feedback is used mostly in a special type of circuit called an oscillator.

• The difference between these two types is whether the feedback signal is in phase or out of phase with the input signal.

• Positive feedback occurs when the feedback signal is in phase with the input signal. Notice that the feedback signal is in phase with the input signal. This means that the feedback signal will add to or "regenerate" the input signal. The result is a larger amplitude output signal than would occur without the feedback.

• Negative feedback occurs when the feedback signal is out of phase

with the input signal. This means that the feedback signal will subtract from or "degenerate" the input signal. This results in a lower amplitude output signal than would occur without the feedback.

•

For an ordinary amplifier i.e. one without feedback, the voltage gain is given by the ratio of the output voltage Vo and input voltage Vi. As shown in the block diagram below, the input voltage Vi is amplified by a factor of A to the value Vo of the output voltage.

 

∴ A = Vo /Vi

This gain A is often called open-loop gain. 

Suppose a feedback loop is added to the amplifier. If Vo´ is the output voltage with feedback, then a fraction β* of this voltage is applied to the input voltage which, therefore, becomes (Vi ± βVo´) depending on whether the feedback voltage is in phase or anti phase with it.

Assuming positive feedback, the input voltage will become (Vi + βVo´). When amplified A times, it becomes A(Vi + βVo´).

The term ‘βA’ is called feedback factor whereas β is known as feedback ratio. The expression (1 ± βA) is called loop gain. The amplifier gain A´ with feedback is also referred to as closed loop gain because it is the gain obtained after the feedback loop is closed.

(a) Negative FeedbackThe amplifier gain with negative feedback is given by

Obviously, A´ < A because | 1 + βA | > 1. 

Suppose, A = 90 and β = 1/10 = 0.1

Then, gain without feedback is 90 and with negative feedback is

• As seen, negative feedback reduces the amplifier gain. That is why it is called degenerative feedback. A lot of voltage gain is sacrificed due to negative feedback. When | βA | » 1, then

  

• It means that A´ depends only on β. But it is very stable because it is not affected by changes in temperature, device parameters, supply voltage and from the aging of circuit components etc.

• Since resistors can be selected very precisely with almost zero temperature-coefficient of resistance, it is possible to achieve highly precise and stable gain with negative feedback.

 

(b) Positive Feedback• The amplifier gain with positive feedback is given by

• Suppose gain without feedback is 90 and β = 1/100 = 0.01, then gain with positive feedback is

 

• Since positive feedback increases the amplifier gain. It is called regenerative feedback. If βA = 1, then mathematically, the gain becomes infinite which simply means that there is an output without any input! However, electrically speaking, this cannot happen. What actually happens is that the amplifier becomes an oscillator which supplies its own input. In fact, two important and necessary conditions for circuit oscillation are

i) The feedback must be positive,ii) Feedback factor must be unity i.e. βA = +1.

Advantages and disadvantages of negative feedbackDISADVANTAGE

• The primary disadvantage of using negative feedback is that is reduces the effective gain of the amplifier

ADVANTAGES

• Stabilized the gain of amplifier• Increases bandwidth of the amplifier so that it provides

nearly constant gain for large frequency range of the input signal.

• Reduce the noise / distortion in the amplifier output• Series negative feedback increases the input

resistance of the amplifier. This avoid loading of the source of the amplifier.

• Voltage negative feedback decrease the output resistance of the amplifier. This avoid loading of amplifier itself when driving on output load.

• Negative feedback also stabilizes operating point.

Feedback ConceptGain Stability

The voltage amplifier gain with negative feedback is given by,

Reduction in noise and non linear distortion

The amount of noise signal (such as power supply hum) and non linear distortion are reduced by a factor of when negative feedback is used.

This is because the feedback network feed back only a portion of the output voltage, but also a portion of the distortion in the opposite phase, which appears in the output after amplification and reduces the amount of the distortion present in the output. The distortion after negative feedback is expressed as

Where D is the distortion without feedback.

Bandwidth Extension When negative feedback is applied, the

frequency response of an amplifier is increased. The lower half power frequency f1 is decreased by a factor of , the upper half-power frequency f2 is increased by a factor of . Hence, these two frequencies with feedback are given by

Hence, the bandwidth of the amplifier f1f - f2f increases by negative feedback as shown below.

3. Multistage Amplifier Analysis

Amplifier Coupling

• All amplifiers need some coupling network. Even a single-stage amplifier has to be coupled to the input and output devices. In the case of multistage systems, there is interstage coupling.

• The type of coupling used determines the characteristics of the cascaded amplifier. In fact, amplifiers are classified according to the coupling network used.

3.1 Resistance –Capacitance (RC) Coupling

Figure below shows a two-stage RC-coupled amplifier which consists of two single-stage transistor amplifiers using the CE configuration. The

resistors R2 and R3 and capacitor C2 form the

coupling network. R2 is collector load of Q1 and R4 is

that of Q2. Capacitor C1 couples the input signal

whereas C3 couples out the output signal. R1 and R3

provide dc base bias.

Circuit Operation

• The input signal is amplified by Q1. It is phase reversed (usual with CE connection);

• The amplified output of Q1 appears across R2;

• The output of the first stage across R2 is coupled to the input at R3 by coupling capacitor C2. This capacitor is also sometimes referred to as blocking capacitor because it blocks the passage of dc voltages and currents;

• The signal at the base of Q2 is further amplified and its phase is again reversed; the ac output of Q2 appears across R4;

• The output across R4 is coupled by C3 to load resistor R5;

• The output signal v0 is the twice-amplified replica of the input signal vi. It is in phase with vi because it has been reversed twice.

 

Direct Coupled Amplifier

• These amplifiers operate without the use of frequency-sensitive components like capacitors, inductors and transformers etc. They are especially suited for amplifying:

(a) ac signals with frequencies as low as a fraction of a hertz,(b) change in dc voltages.

Circuit Operation• Amplifier which uses two similar transistors each

connected in the CE mode. each connected in the CE mode. Both stages employ direct coupling.

• Collector of Q1 is connected directly to the base of Q2 and load resistor R2 is connected to the collector of Q2.

• The resistor R1 establishes the forward bias of Q1 and also indirectly that of Q2. Any signal current at the base of Q1 is amplified β1 times and appears at the collector of Q1 and becomes base signal for Q2.

• Hence, it is further amplified β2 times. Obviously, signal current gain of the amplifier

Transformer-Coupled amplifier

• TRANSFORMER COUPLING uses a transformer to couple the signal from one stage to the next. Transformer coupling is very efficient and the transformer can aid in impedance matching.

• T1 is the coupling transformer whereas T2 is the output transformer. C1 is the input coupling capacitor whereas C2, C3 and C4 are the bypass capacitors. Resistors R1 and R2 as well as R4 and R5 form voltage divider circuits whereas R3 and R6 are the emitter-stabilizing resistors

Circuit Operation • When input signal is coupled through C1 to the base of

Q1, it appears in an amplified form in the primary of T1.

• From there, it is passed on to the secondary by magnetic induction. Moreover, T1 provides dc isolation between the input and output circuits.

• The secondary of T1 applies the signal to the base of Q2 which appears in an amplified form in the primary of T2.

• From there, it is passed on to the secondary by magnetic induction and finally appears across the matched load R7.

 

Darlington Pair The Darlington Amplifier is a special-case emitter follower

that uses two transistor to increase the overall values of circuit current (Ai) and input impedance (Zin). The two transistors are connected as shown below.

The emitter of the first is tied to the base of the second, and the collector terminals are tied together.

• It is the name given to a pair of similar transistors so connected that emitter of one is directly joined to the base of the other. Obviously, the emitter current of Q1 becomes the base current of Q2.

• Darlington pairs are commercially mounted in a single package that has only three leads : base, collector and emitter. It often forms a double CC stage in multistage amplifiers. It is so because a Darlington connection can be considered equivalent to two cascaded emitter followers.