Multistage Amplifiers

Multistage Amplifiers

AU : Dec.-02,03,09,10,12,14, May-03,05,09,10,11, Marks 16, May-15, Marks 2

• In practice, we need amplifier which can amplify a signal from a very weak source such as a microphone, to a level which is suitable for the operation of another transducer such as loudspeaker. This is achieved by cascading number of amplifier stages, known as multistage amplifier or Casceded amplifier.

 

1. Need for Caacading

• For faithful amplification amplifier should have desired voltage gain, current gain and it should match its input impedance with the source and output impedance with the load. Many times these primary requirements of the amplifier cannot be achieved with single stage amplifier, because of the limitation of the transistor/FET parameters. In such situations more than one amplifier stages are cascaded such that input and output stages provide impedance matching requirements with some amplification and remaining middle stages provide most of the amplification.

• In short we can say that,

• When the amplification of a single stage amplifier is not sufficient, or,

• When the input or output impedance is not of the correct magnitude, for a particular application two or more amplifier stages are connected, in cascade. Such amplifier, with two or more stages is also known as multistage amplifier.

Limitations of Multistage Amplifiers

1. The bandwidth of multistage amplifier is always less than that of the bandwidth of a single stage amplifier.

2. Nonlinear distortion is more in multistage amplifiers than single stage amplifiers.

 

2. Two Stage Cascaded Amplifier

• Fig. 8.1.1 shows the block diagram of two stage cascaded amplifier. These stages are connected such that the output of the first stage is connected to the input of the second stage.

• As shown in the Fig. 8.1.1 Vn is the input of the first stage and Vo2 is the output of the second stage.

• So that, we can say the voltage gain of multistage amplifier is the product of voltage gains of the individual stages.

• In the block diagram of two stage amplifier we have not considered the biasing arrangements for simplicity. Now, with primary understanding we will see the two stage amplifier with biasing arrangements and we will analyze its performance with the help of h-parameters.

 

Ex. 8.1.1 Let us consider the two stage amplifier circuit shown in Fig. 8.1.2. The first stage in the circuit is a common emitter amplifier and second stage is common collector amplifier.

Now, with the help of following transistor parameters at the corresponding quiescent point, calculate input impedance, output impedance, and individual as well as overall current and voltage gains.

h_ie = 2K, hf_fe = 50, h_re = 0, h_oe = 0

Sol. :

Fig. 8.1.3 shows the a.c. equivalent circuit for two stage amplifer shown in Fig. 8.1.2. It is drawn by shorting the d.c. supply.

• Before starting the analysis of multistage amplifier we should note that, in multistage amplifiers the output impendance of one stage is shunted by the input impedance of the next stage. Hence it is always advantageous to start analysis with the last stage. In addition, it is convenient to calculate, first, current gain, then input impedance, then voltage gain and finally the output impedance.

• The Fig. 8.1.4 shows the approximate h-parameter equivalent circuit

Analysis of first stage (CE amplifier)

a) Current gain (A₁₂) = 1 + h_fe = 1 + 50 = 51

b) Input resistance (R₁₂) = h_ie + (1 + h_fe ) R_E2 = 2 K + (1 + 50) × 47 × 10³ = 241.7 k Ω

 

3. n-Stage Cascaded Amplifier

• The gain of the amplifier can be further increased by connecting more number of stages in cascade, as shown in the Fig. 8.1.7.

Voltage gain :

• We have seen that the resultant voltage gain of the multistage amplifier is the product of voltage gains of the various stages.

A_v = A_v1 A_v2  … A_vn

• The voltage gain of the kth stage is given as,

A_vk = A_ikR_Lk / R_ik

where R_Lk is the effective load resistance of the k^th stage and R_ik is the input impedance of the k^th stage.

 

4. Gain in Decibels

• In many situations it is found very convenient to compare two powers on a logarithmic scale rather than on a linear scale. The unit of this logarithmic scale is called decibel (abbreviated dB). The number N decibels by which a power P2 exceeds the power Pj is defined by

N = 10 log P₂ / P₁           ...(8.1.4)

• Decibel, dB denotes power ratio. Negative values of number of dB means that the power P₂ is less than the reference power P₁ and positive value of number of dB means that the power P₂ is greater than the reference power P₁.

• For an amplifier, P₁ may represent input power, and P₂ may represent output power. Both can be given as

P₁  = V²_i / R_i and P₂  = V²_o / R_o

where Ri and Ro are the input and output impedances of the amplifier respectively. Then equation (8.1.4) can be written as,

• If the input and output impedances of the amplifier are equal i.e. R_i = R_o = R, then equation (8.1.5) simplifies to

Ex. 8.1.2 If the voltage gain of the amplifier is 100, calculate its gain on dB scale.

Sol. : Gain in dB = 20 log 10 100 = 20 × 2 = 40 dB

a. Gain of Multistage Amplifier in dB

• The gain of a multistage amplifier can be easily calculated if the gain of the individual stages are known in dB, as shown below.

• Thus, the overall voltage gain in dB of a multistage amplifier is the sum of the decibel voltage gains of the individual stages. It can be given as

A_vdB = A_vldB + A_v2dB + …+ A_vndB        … (8-1-8)

 

Ex. 8.1.3 Two amplifiers having gain 20 dB and 40 dB are cascaded. Find the overall gain in dB.

AU : Dec.-09, Marks 2

Sol. : Overall gain in dB = 20 + 40 = 60 dB.

b. Advantages of Representation of Gain in Decibels

Logarithmic scale is preferred over linear scale to represent voltage and power gains because of the following reasons :

• In multistage amplifiers, it permits to add individual gains of the stages to calculate overall gain. (Use of logarithms changes multiplication into an addition).

• It allows us to denote, both very small as well as very large quantities of linear scale by considerably small figures.

• For example, voltage gain of 0.0000001 can be represented as -140 dB and voltage gain of 1,00,000 can be represented as 100 dB.

• Many times output of the amplifier is fed to loudspeakers to produce sound which is received by the human ear. It is important to note that the ear responds to the sound intensities on a proportional or logarithmic scale rather than linear scale. Thus use of dB unit is more appropriate for representation of amplifier gains.

 

5. Methods of Coupling Multistage Amplifiers

• In multistage amplifier, the output signal of preceding stage is to be coupled to the input circuit of succeeding stage. For this interstage coupling, different types of coupling elements can be employed. These are :

1. RC coupling

2. Transformer coupling

3. Direct coupling

a. RC Coupling

• Fig. 8.1.8 shows RC coupled amplifier using transistors. As shown in the Fig. 8.1.8 the output signal of first stage is coupled to the input of the next stage through coupling capacitor and resistive load at the output terminal of first stage.

• The coupling does not affect the quiescent point of the next stage since the coupling capacitor CC V blocks the d.c. voltage of the first stage from reaching the base of the second stage. The RC network is broadband in nature. Therefore, it gives a wideband frequency response without peak at any frequency and hence used to cover a complete AF amplifier bands. However its frequency response drops off at very low frequencies due to coupling capacitors and also at high frequencies due to shunt capacitors such as stray capacitance.

• Fig. 8.1.9 shows the frequency response of RC coupled amplifier.

b. Transformer Coupling

• Fig. 8.1.10 shows transformer coupled amplifier using transistors. As shown in the Fig. 8.1.10 the output signal of first stage is coupled to the input of the next stage through an impedance matching transformer.

• This type of coupling is used to match the impedance between output and input cascaded stage. Usually, it is used to match the larger output resistance of AF power amplifier to a low impedance load like loudspeaker. As we know, transformer blocks d.c., providing d.c. isolation between the two stages. Therefore, transformer coupling does not affect the quiescent point of the next stage.

• Frequency response of transformer coupled amplifier is poor in comparison with that of an RC coupled amplifier. Its leakage inductance and interwinding capacitances does not allow amplifier to amplify the signals of different frequencies equally well. Interwinding capacitance of the transformer coupled may give rise resonance at certain frequency which makes amplifier to give very high gain at that frequency. By putting shunting capacitors across each winding of the transformer, we can get resonance at any desired RF frequency. Such amplifiers are called tuned voltage amplifiers.

• These provide high gain at the desired of frequency, i.e. they amplify selective frequencies. For this reason, the transformer-coupled amplifiers are used in radio and TV receivers for amplifying RF signals.

• As d.c. resistance of the transformer winding is very low, almost all d.c. voltage applied by V_CC is available at the collector. Due to the absence of collector resistance it also eliminates unnecessary power loss in the resistor.

• Fig. 8.1.11 shows the frequency response of transformer coupled amplifier.

• Fig. 8.1.13 shows direct coupled amplifier using transistors. As shown in the Fig. 8.1.13 the output signal of first stage is directly connected to the input of the next stage. This direct coupling allows the quiescent d.c. collector current of first stage to pass through base of the next stage, affecting its biasing conditions.

• Due to absence of RC components, its low frequency response is good but at higher frequencies shunting capacitors such as stray capacitances reduce the gain of the amplifier.

• The transistor parameters such as VBE and p change with temperature causing the collector current and voltage to change. Because of direct coupling these changes appear at the base of the next stage, and hence in the output. Such an unwanted change in the output is called drift and it is serious problem in the direct coupled amplifiers.

d. Comparison between Various Cascading Methods