Cascade Amplifier | types of cascade amplifier | configuration analysis , is a combination of

configuration analysis , is a combination of , Cascade Amplifier | types of cascade amplifier advantages pdf
Compound Configuration
Compound Configuration  The output from a single stage amplifier is usually insufficiest to drive an output device. consequently, additional amplification over two or three stages is necessary. to achieve this, the output of each amplifier stage is coupled in some way to the input of the next stage.
Darlington Amplifier
It consists of two emitter followers in cascaded mode as shown in fig. 1. the overall gain is closed to unity. the main advantage of darlington amplifier is very large increase in input impedance and an equal decrease in output imoedance.
DC Analysis
The first transistor has first V_BE drop and second transistor has second V_BE drop. the voltage divider produces V_TH to the input base. the DC emitter current of the second stage is
I_E2 = (V_TH – 2V_BE)/ (R_E)
The DC emitter current of the first stage that is the base current of second stage is given by I_E1 >> I_E2 / B₂
If R’_E(2) is neglected then input impedance of second stage is
Z_in(2)  = b₂R_E
This is the impedance seen by the first transistor. if R’_E(1) is also neglected then the input impedance of 1 becomes
Z_in(1) = b₁b₂R_E
Which is extremely high because of the products of two betas, so the approximate input impedance of darlington amplifier is
Z_in = R₁||R₂
Output Impedance
The Thevenin impedance at the input is given by
R_TH = R_S||R₁||R₂
Similar to single stage common collector amplifier, the output impedance of the two stages Z_OUT(1) and Z_OUT(2) are given by
Z_out1 = R’_E1 + R_TH/B₁
Z_out2 = R’_E2 + Z_out1 /B₂
= R’_E2 = R’_E1 + R_TH/B₁ / B₂
Therefore, the output impedance of the amplifier is very small.
Cascade Amplifier
To increase the voltage gain of the amplifier, multiple amplifiers are connected in cascade. the output of one amplifier is the input to another stage. in this way, the overall voltage gain can be increased, when number of amplifier stages are used in succession, it is called a multistage amplifier or cascade amplifier . the load on the first amplifier is the input resistance of the second amplifier. the various stages need not have the same voltage and current gain. in practice, the earlier stages are often voltage amplifiers and the last one or two stages are current amplifiers. the voltage amplifier stages assume that the current stages have the proper input swing. the amount of gain in a stage is determined by the load on the amplifier stage which is governed by the input resistance to the next stage. therefore, in designing or analyzing multistage amplifier, we start at the output and proceed towards the input.
An n-stage amplifier can be represented by the block diagram as shown in fig.
In fig. 2 the overall gain is the product of the voltage gain of each stage, i.e., the overall voltage gain is ABC.
To represent the gain of the cascade amplifier, the voltage gain are represented in dB. the two power levels of input and output of an amplifier are compared on a logarithmic scale rather than linear scale. the number of bels by which the output power p₂ exceeds the input power p₁ is defined as
Nunber of bels = log₁₀ (P₂/P₁)
Or         Nunber of dB = 10* NUnber of bels  = 10 log₁₀(p₂/p₁)
Since,                       p₁ = V₁² / R_in and  p₂ = V₂² / R_O
Where, R_in is the input resistance of the amplifie and R_O is the liad resistance.
dB = 10 log₁₀ (V₂²/R_O /V₁²R_in)
In case R_In and R_O are equal, then power gain is given by
dB = 10 log₁₀ (V₂/V₁)² = 20 log₁₀ (-V₂/V₁)
A_dB = A_dB1 + AdB₂ + ……………
Because of dB scale, the gain can be directly added when a number of stages are cascaded.
Types of Coupling
If a multistage amplifier, the output of one stage makes the input of the next stage. normally a network is used between two stages so that a minimum loss of voltage occurs when the signal passes through this network to the next stage. also the DC voltage at the output of one stage should not be permitted to go to the input of the next. otherwise, the biasing of the next stage are disturbed.
The three couplings generally used are

1. RC coupling
2. Impedance coupling
3. Transformer coupling

Bandwidth of an Amplifier
The gain is constant over a frequency range. the frequencies at which the gain reduces to 70.7% of the maximum gain are known as cut-off frequencies, upper cut-off and lower cut-off frequency. fig. 3, shows these two frequencies. the difference of these two frequencies is called band width (BW) of an amplifier.
At f₁ and f₂, the voltage gain becomes 0.707 Am (1/o2).
The output voltage reduces to 1/o2 of maximum output voltage. since, the power is proportional to valtage square, the output power at these frequencies becomes half of maximum power. the gain on dB scale is given by
20 log₁₀ (V_2/V₁) = 10 log₁₀ (V₂/V₁)² = 3 dB
20 log₁₀ (V₂/V₁) = 20 log₁₀ (0.707) = 10 log₁₀ (1/o2)²
= 10 log₁₀ (1/2) = – 3 dB
If the difference in gain is more than 3 dB then it can be detected by human. if it is less than 3 dB, it cannot be detected.
Direct Coupling
For applications, where the signal frequency is below 10 Hz, coupling and bypass  capacitors cannot be used. at low frequencies these capacitors can no longer be treated as AC short circuits, since they offer very high impedance. if these capacitors are used then, their values have to be extremely large, e.g., to bypass a 100 emitter resistor at 10 Hz, we need a capacitor of approximately 1600 mF lower the frequency, worse the problem becomes.
To avoid, this direct coupling is used. this means designing the stages without coupling and bypass capacitors, so that the direct current is coupled as well as alternating current. as a result, there is no lower frequency limit. the amplifier enlarges the signal no matter have low frequency including DC or zero frequency.
Intro Exercise – 4

1. Three identical amplifiers with each one having a voltage gain of 50 input resistance of 1 k and output resistance of 250 are cascaded. the open circuit voltage gain of the combined amplifier is

(a) 49 dB
(b) 51 dB
(c) 98 dB
(d) 102 dB

2. In the cascade amplifier shown in the figure, if the common-emitter stage ( Q₁) has transconductance g_m1 and the common-base stage (Q₂) has a tranconductance g (= I_O/V_I) of the cascade amplifier is

(a) g_m1
(b) g_m2
(c) g_m1 /2
(d) g_m2 /2

3. In the differential ampliffier of the figure, if the source resistance of the current source I_EE is infinite then the common mode gain is

(a) zero
(b) infinite
(c) indeterminate
(d) V_{in 1} + V_in2 /2V_T

4. In the silicon BJT circuit shown below, assume that the emitter area of transistor Q₁ is half that of transistor Q₂. The value of current I_O is approximately

(a) 0.5 mA
(b) 2 mA
(c) 9.3 mA
(d) 15 mA

5. The cascade amplifier is a multistage configuration of

(a) CC-CB
(b) CE-CB
(c) CB-CC
(d) CE-CC

6. In an ideal differential amplifier shown in the figure.large value of (R_E)

(a)  increases both the differential and common mode gains
(b) increases the common mode gain only
(c) decreases the differential mode gain only
(d) decreases the common mode gain only
Answers with Solutions

1. (c)

A_V = V₄/V₁          A_V = V₄ /V₃ x V₃/V₂ x V₂/V₁
Voltage across 1 k after 1 st stage = 1000 x 50 /1250 = 40
Similarly,       V₃/V₂ = 40
A_V = 40 x 40 x 50
A_V = 8 x 10⁴
A_V in dB = 20 log (8 + 10⁴) = 96 dB

2. (a) g_m = I_OV_II_O ~= I_E2 = I_C1

f_c1 = BI_B, I_E2 = I_C1
I_O = BI_B1,V_I = I_B1
I_O/V_I = BI_B1 /I_B1 = g_m1 = I_C1/V_i                 (as I_C1 = BI_B1)

3. (a) Common-mode gain

V_C = A_CV_I(V_i1 = V_i)
If R_E is infinite then because of symmetry of figure V_C becomes zero.
I_e1 = I_e2 = 0
I_b2 << I_c2
so,                        I_c2 ~= I_e2

4. (b) The given circuit is a current mirror circuit in which the output current is a mirror image of the input current, if both the transistors are identical.

To calculate I_i,
9.3 I_I + 0.7 = 0 – (- 10) = 10
I_I = 1 mA
Since, the emitter area of transistor Q₁ is half that of transistor Q₂ So, I_i = 10/2
Therefore,     I_O = 2 mA

5. (b)
6. (d) Only common mode gain depends on R_E and differential mode gain is independent of R_E.

Transistorized Audio Power Amplifiers
Transistorized Audio Power Amplifiers  A transistorized audio power amplifiers converts the medium-level medium impedance AC signal into a high-level amplified signal that can drive a low impedance audio transducer such as a speaker.
A practical amplifier always consists of a number of stages that amplify a weak signal until sufficient power is avilable to operate a loudspeaker or other output device. the first few stages in this multistage amplifier have the function of only voltage amplification. however, the last stage is designed to provide maximum power. this final stage is known as power stage.
The term audio means the range of frequencies which our ear can hear. the range of human hearing extends from 20 Hz to 20 kHz. therefore, audio amplifiers amplify electrical signals that have a frequency range corresponding to the range of human hearing i.e., 20 Hz to 20 kHz. fig. 1 shows the block diagram of an audio amplifier. the early stages build up the voltage level of the signal while the last stage build up power to a level sufficient to operate the loudspeaker. in this chapter, we shall talk about the final stage in a multistage amplifier – the power amplifier.
Transistor Audio Power Amplifier
A transistor amplifier which raises the power level of the signals that have audio frequency range is known as transistor audio power amplifier.
In general, the last stage of a multistage amplifier is the power stage. the power amplifier differs from all the previous stages in that here a concentrated effort is made to obtain maximum output power. a transistor that is suitable for power amplification is generally called a power transistor. it differs from other transistors mostly in size. it is considerably larger to provide for handling the great amount of power.
Difference Between Voltage and power Amplifiers
The distinction between voltage and power amplifiers is somewhat artificial since, uesful power (i.e., product of voltage and current) is always developed in the load resistance through which current flows. the difference between the two types is really one of degree. it is a question of how much voltage and how much power? a voltage amplifier is designed to achieve maximum voltage amplification however, it is not important to raise the power level. on the other hand a power amplifier is designed to obtain maximum output power.

1. Voltage Amplifier

The voltage gain of an amplifier is given by
A_V = B x R_C/R_in
In order to achieve high voltage amplification, the following features are incorporated in such amplifiers :

1. The transistor with high B (> 100) is used in the circuit. in other words, those transistors are employed which have thin base.
2. The input resistance R_in of the transistor is sought to be quite low as compared to the collector load R_C.
3. A reatively high load R_C is used in the collector. to permit this condition, voltage amplifiers are always operated at low collector currents (~ 1 mA). if the collector current is small, we can use large R_C in the collector circuit.
4. Power Amplifier

A power amplifier is required to deliver a large amount of power and as such it has to handle large current. in order to achieve high power amplification, the following features are incorporated in such amplifiers :

1. The size of power transistor is made considerably larger in order to dissipate the heat produced in the transistor during operation.
2. The base is made thicker to hasdle large currents. in other words, transistors with comparatively smaller B used.
3. Transformer coupling is used for impedance matching.

The comparison between voltage and power amplifiers is given below in the tabular form.
Example 1. A power amplifier operated from 12 v battery gives a output of 2 w. find the maximum collector current in the circuit.
Sol. Let I_C be the maximum collector current.
power = battery voltage x collector current
2 = 12 x I_C
I_C = 2 / 12 = 1/6 A = 166.7 mA
This example shows that a power amplifier handles large power as well as large current.