The output from a single stage amplifier is usually insufficient to drive an output device. Inther words, the gain of a single amplifier is inadequate for practical purposes. 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. The resulting system is referred to as a multistage amplifier. It may be emphasized here that a practical amplifier is always a multistage amplifier. For example, in a transistor radio receiver, the number of amplification stages maybe six or more. In this chapter, we shall focus our attention on the various multistage transistor amplifiers and their practical applications.
A transistor circuit containing more than one stage of amplification is known as multistage transistor amplifier. In a multistage amplifier, a number of single amplifiers are connected in *cascade arrangement i.e. output of first stage is connected to the input of the second stage through a suitable coupling device and so on. The purpose of coupling device (e.g. a capacitor, transformer, etc.) is (i) to transfer a.c. output of one stage to the input of the next stage and (ii) to isolate the d.c. conditions of one stage from the next stage. Fig. 11.1 shows the block diagram of a 3-stage amplifier. Each stage consists of one transistor and associated circuitry and is coupled to the next stage through a coupling device. The name of the amplifier is usually given after the type of coupling used. e.g.
(i) In RC coupling, a capacitor is used as the coupling device. The capacitor connects the output of one stage to the input of the next stage in order to pass the a.c. signal on while blocking the d.c. bias voltages.
(ii) In transformer coupling, transformer is used as the coupling device. The transformer coupling provides the same two functions (viz. to pass the signal on and blocking d.c.) but permits in addition impedance matching.
(iii) In direct coupling or d.c. coupling, the individual amplifier stage bias conditions are so designed that the two stages may be directly connected without the necessity for d.c. isolation.
Regardless of the manner in which a capacitor is connected in a transistor amplifier, its behaviour towards d.c. and a.c. is as follows. A capacitor blocks d.c. i.e. a capacitor behaves as an “open**” to d.c. Therefore, for d.c. analysis, we can remove the capacitors from the transistor amplifier circuit. A capacitor offers reactance (= 1/2πfC) to a.c. depending upon the values of f and C. In practical transistor circuits, the size of capacitors is so selected that they offer negligible (ideally zero) reactance to the range of frequencies handled by the circuits. Therefore, for a.c. analysis, we can replace the capacitors by a short i.e. by a wire. The capacitors serve the following two roles in transistor amplifiers :
1. As coupling capacitors. In most applications, you will not see a single transistor amplifier. Rather we use a multistage amplifier i.e. a number of transistor amplifiers are connected in series or cascaded. The capacitors are commonly used to connect one amplifier stage to another. When a capacitor is used for this purpose, it is called a coupling capacitor. Fig. 11.2 shows the coupling capacitors (CC1; CC2 ; CC3 and CC4) in a multistage amplifier. A coupling capacitor performs the following two functions :
(i) It blocks d.c. i.e. it provides d.c. isolation between the two stages of a multistage amplifier.
2. As bypass capacitors. Like a coupling capacitor, a bypass capacitor also blocks d.c. and behaves as a short or wire (due to proper selection of capacitor size) to an a.c. signal. But it is used for a different purpose. A bypass capacitor is connected in parallel with a circuit component (e.g. resistor) to bypass the a.c. signal and hence the name. Fig. 11.3 shows a bypass capacitor CE connected across the emitter resistance RE. Since CE behaves as a short to the a.c. signal, the whole of a.c. signal (i e) passes through it. Note that CE keeps the emitter at a.c. ground. Thus for a.c. purposes, RE does not exist. We have already seen in the previous chapter that CE plays an important role in determining the voltage gain of the amplifier circuit. If CE is removed, the voltage gain of the amplifier is greatly reduced. Note that Cin is the coupling capacitor in this circuit.
In the study of multistage amplifiers, we shall frequently come across the terms gain, frequency response, decibel gain and bandwidth. These terms stand discussed below :
(i) Gain. The ratio of the output *electrical quantity to the input one of the amplifier is called it’s gain.
The gain of a multistage amplifier is equal to the product of gains of individual stages. For instance, if G1, G2 and G3 are the individual voltage gains of a three-stage amplifier, then total voltage gain G is given by :
*G = G1 × G2 × G3
It is worthwhile to mention here that in practice, total gain G is less than G1 × G2 × G3 due to the loading effect of next stages.
(ii) Frequency response. The voltage gain of an amplifier varies with signal frequency. It is because reactance of the capacitors in the circuit changes with signal frequency and hence affects the output voltage. The curve between voltage gain and signal frequency of an amplifier is known as frequency response. Fig. 11.4 shows the frequency response of a typical amplifier. The gain of the amplifier increases as the frequency increases from zero till it becomes maximum at fr , called resonant frequency. If the frequency of signal increases beyond fr , the gain decreases. The performance of an amplifier depends to a considerable extent upon its frequency response. While designing an amplifier, appropriate steps must be taken to ensure that gain is essentially uniform over some specified frequency range. For instance, in case of an audio amplifier, which is used to amplify speech or music, it is necessary that all the frequencies in the sound spectrum (i.e. 20 Hz to 20 kHz) should be uniformly amplified otherwise speaker will give a distorted sound output.
(iii) Decibel gain. Although the gain of an amplifier can be expressed as a number, yet it is of great practical importance to assign it a unit. The unit assigned is bel or decibel (db). The common logarithm (log to the base 10) of power gain is known as bel power gain i.e.
Advantages. The following are the advantages of expressing the gain in db :
(a) The unit db is a logarithmic unit. Our ear response is also logarithmic i.e. loudness of sound heard by ear is not according to the intensity of sound but according to the log of intensity of sound. Thus if the intensity of sound given by speaker (i.e. power) is increased 100 times, our ears hear a doubling effect (log10 100 = 2) i.e. as if loudness were doubled instead of made 100 times. Hence, this unit tallies with the natural response of our ears.
(b) When the gains are expressed in db, the overall gain of a multistage amplifier is the sum of gains of individual stages in db. Thus referring to Fig. 11.6,
However, absolute gain is obtained by multiplying the gains of individual stages. Obviously, it is easier to add than to multiply.
(iv) Bandwidth. The range of frequency over which the voltage gain is equal to or greater than *70.7% of the maximum gain is known as bandwidth.
The voltage gain of an amplifier changes with frequency. Referring to the frequency response in Fig. 11.7, it is clear that for any frequency lying between f 1 and f 2, the gain is equal to or greater than 70.7% of the maximum gain. Therefore, f 1 − f 2 is the bandwidth. It may be seen that f 1 and f 2 are the limiting frequencies. The former (f 1) is called lower cut-off frequency and the latter (f 2) is known as upper cut-off frequency. For distortionless amplification, it is important that signal frequency range must be within the bandwidth of the amplifier.
The bandwidth of an amplifier can also be defined in terms of db. Suppose the maximum voltage gain of an amplifier is 100. Then 70.7% of it is 70.7. ∴ Fall in voltage gain from maximum gain
Hence bandwidth of an amplifier is the range of frequency at the limits of which its voltage gain falls by 3 db from the maximum gain. The frequency f 1 or f 2 is also called 3-db frequency or half-power frequency. The 3-db designation comes from the fact that voltage gain at these frequencies is 3db below the maximum value. The term half-power is used because when voltage is down to 0.707 of its maximum value, the power (proportional to V2 ) is down to (0.707)2 or one-half of its maximum value.
Example 11.1. Find the gain in db in the following cases :
(i) Voltage gain of 30 (ii) Power gain of 100
Solution. (i) Voltage gain = 20 log10 30 db = 29.54 db
(ii) Power gain = 10 log10 100 db = 20 db
Example 11.2. Express the following gains as a number : (i) Power gain of 40 db (ii) Power gain of 43 db
Solution. (i) Power gain = 40 db = 4 bel If we want to find the gain as a number, we should work from logarithm back to the original number.
Example 11.3. A three-stage amplifier has a first stage voltage gain of 100, second stage voltage gain of 200 and third stage voltage gain of 400. Find the total voltage gain in db.
Example 11.4. (i) A multistage amplifier employs five stages each of which has a power gain of 30. What is the total gain of the amplifier in db ? (ii) If negative feedback of 10 db is employed, find the resultant gain.
It is clear from the above example that by expressing the gain in db, calculations have become very simple.
Example 11.5. In an amplifier, the output power is 1.5 watts at 2 kHz and 0.3 watt at 20 Hz, while the input power is constant at 10 mW. Calculate by how many decibels gain at 20 Hz is below that at 2 kHz ?
Solution. db power gain at 2 kHz. At 2 kHz, the output power is 1.5 W and input power is 10 mW.
Example 11.6. A certain amplifier has voltage gain of 15 db. If the input signal voltage is 0.8V, what is the output voltage ?
Example 11.7. An amplifier has an open-circuit voltage gain of 70 db and an output resistance of 1.5 kΩ. Determine the minimum value of load resistance so that voltage gain is not more than 67db.
Example 11.8. An amplifier feeding a resistive load of 1kΩ has a voltage gain of 40 db. If the
input signal is 10 mV, find (i) output voltage (ii) load power.
Example 11.9. An amplifier rated at 40W output is connected to a 10Ω speaker. (i) Calculate the input power required for full power output if the power gain is 25 db. (ii) Calculate the input voltage for rated output if the amplifier voltage gain is 40 db.
Example 11.10. In an amplifier, the maximum voltage gain is 2000 and occurs at 2 kHz. It falls to 1414 at 10 kHz and 50 Hz. Find : (i) Bandwidth (ii) Lower cut-off frequency (iii) Upper cut-off frequency.
Solution. (i) Referring to the frequency response in Fig. 11.8, the maximum gain is 2000. Then 70.7% of this gain is 0.707 × 2000 = 1414. It is given that gain is 1414 at 50 Hz and 10 kHz. As bandwidth is the range of frequency over which gain is equal or greater than 70.7% of maximum gain, ∴ Bandwidth = 50 Hz to 10 kHz
(ii) The frequency (on lower side) at which the voltage gain of the amplifier is exactly 70.7% of the maximum gain is known as lower cut-off frequency. Referring to Fig. 11.8, it is clear that : Lower cut-off frequency = 50 Hz
(iii) The frequency (on the higher side) at which the voltage gain of the amplifier is exactly 70.7% of the maximum gain is known as upper cut-off frequency. Referring to Fig. 11.8, it is clear that: Upper cut-off frequency = 10 kHz Comments. As bandwidth of the amplifier is 50 Hz to 10 kHz, therefore, it will amplify the signal frequencies lying in this range without any distortion. However, if the signal frequency is not in this range, then there will be distortion in the output. Note. The db power rating of communication equipment is normally less than 50 db.
The power gain expressed as a number is called ordinary power gain. Similarly, the voltage gain expressed as a number is called ordinary voltage gain.
1. Properties of db power gain. The following are the useful rules for db power gain :
(i) Each time the ordinary power gain increases (decreases) by a factor of 10, the db power gain increases (decreases) by 10 db. For example, suppose the ordinary power gain increases from 100 to 1000 (i.e. by a factor of 10).
This property also applies for the decrease in power gain. (ii) Each time the ordinary power gain increases (decreases) by a factor of 2, the db power gain increases (decreases) by 3 db. For example, suppose the power gain increases from 100 to 200 (i.e. by a factor of 2).
2. Properties of db voltage gain. The following are the useful rules for db voltage gain : (i) Each time the ordinary voltage gain increases (decreases) by a factor of 10, the db voltage gain increases (decreases) by 20 db. For example, suppose the voltage gain increases from 100 to 1000 (i.e. by a factor of 10).
(ii) Each time the ordinary voltage gain increases (decreases) by a factor of 2, the db voltage gain increases (decreases) by 6 db. For example, suppose the voltage gain increases from 100 to 200 (i.e. by a factor of 2).
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