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**Single stage BJT & MOSFET Amplifiers study notes for Electronics and communication**

**➤ Introduction to Amplifier: **

An amplifier is an electronic circuit designed by using an active device like bipolar junction transistor (BJT), field effect transistor (FET), that changes, usually increases the amplitude of the input signal (usually voltage or current). The relationship between the input and the output signals of an amplifier is expressed as a function of input frequency, commonly known as transfer function of amplifier.

Based upon the value of signal variation, amplifier can be classified in two types**(i) Small signal Amplifier(ii) Large signal Amplifier**

From the characteristic curve of BJT, it can be seen that BJT is a nonlinear device. But in small signal amplifier BJT exhibits piece wise linearly or it simply behave as a linear element, that’s way small signal amplifier output signal will be distortion less. Small signal amplifier is used as voltage amplifier.

**➤ ****Small-Signal variations**

Consider the BJT circuit shown in figure 1. Various small signal parameters for the circuit is described below.**(i) Collector Current and the transconductance**

If a signal v_{be} is applied as shown in Figure 1, The total instantaneous base-emitter voltage v_{BE} becomes

v_{BE} = V_{BE} + v_{be}

Instantaneous collector current becomes

or,

So,

Thus, the instantaneous collector current is composed of the dc bias value I_{C} and a signal component i_{C}. So, signal current in the collector is:

i_{c }= (I_{C}/V_{T})v_{be}

It can be rewritten as

i_{c} = g_{m}V_{be}

where g_{m} = I_{C}/V_{T} is called the transconductance.

**(ii) Base Current and input Resistance at the Base**

To determine the resistance seen by v_{be}, first evaluate the total base current i_{B} using equation (V) as follows

The small signal input resistance between base and emitter, looking into the base, is denoted by r_{π} and is defined as

or r_{x }= βV_{T}/I_{C}

**(iii) Emitter Current and the input Resistance at the Emitter**

Total Emitter current iE can be determined from equation (V) as

or i_{E} = I_{E} + i_{e}

So, we have the signal current,

If we denote the small signal resistance between base and emitter, looking into the emitter, by r_{e}, it can be defined as

**➤ ****Small Signal Hybrid - Π Equivalent Circuit of BJT:**

A bipolar junction transistor can be treated as a two-port network as shown in figure 2. Small time-varying signals is superimposed at Q-point. Since the sinusoidal signals are small, the slope at Q-point is treated as constant, which has the units of conductance. The inverse of this conductance is the small-signal resistance defined as r_{π}. The small-signal input base current is related to the small-signal input voltage by

v_{be} = i_{b }r_{π}

where 1/r_{π} is equal to the slope of the i_{B} – v_{BE} curve. r_{π} can be found as given below,

(**Note: **The resistance r_{π} is called diffusion resistance or base-emitter input resistance. r_{π} is a function of Q-point parameters.)

While considering the output characteristics of bipolar transistor. Initially consider the case in which the output collector current is independent of the collector-emitter voltage, then the collector current is a function only of the base-emitter voltage. Then it can be written as,

Also,

Then,

Then term IS exp (V_{BE}/V_{T}) evaluated at Q-point is just the quiescent collector current. The term I_{CQ}/V_{T} is conductance. Since this conductance relates a current in the collector to a voltage in the B-E circuit, the parameter is called transconductance and is written as

Using these new parameters, a new simplified small-signal hybrid-π equivalent circuit can be developed for npn transistor, as shown in Figure 3(a).

The small-signal collector current is related to the small-signal base current as

and is called an incremental or ac common-emitter current gain.

It can be written as,

The small-signal equivalent circuit of bipolar transistor in Figure 3(b) uses this parameter.

Note: If rπ and gm is multiplied, then

**➤ ****Methodology to Analyse a BJT Amplifier:**

In linear amplifier circuits, superposition theorem is applicable, means the ac and dc analysis can be performed separately. The analysis of the BJT amplifier proceeds as follow:**Step 1:** Determine the dc operating point of the BJT and in particular the dc collector current I_{c}.**Step 2:** Calculate the values of the small signal model parameter,

g_{m} = I_{C}/V_{T}, r_{π} = β/g_{m}**Step 3:** Eliminate the dc sources by replacing each dc current source with an open circuit.**Step 4: **Replace the BJT with one of its small signal equivalent circuit models. Although any one of the models can be used, one might be more convenient than the other for the particular circuit being analysed.**Step 5:** Analyse the resulting circuit to determine the required quantities (eg. Voltage gain, input resistance etc.).

**➤ ****Basic Transistor Amplifier Configurations:**

As it is already discussed, the bipolar transistor is a three-terminal device, so three basic single-transistor amplifier configurations can be formed, depending on which of the three transistor terminals is used as signal ground. These three basic configurations are appropriately called common emitter, common collector (emitter-follower) and common base. Which configuration or amplifier is used in any particular application depends on whether the input signal is voltage or current and whether the desired output signal is voltage or current. The characteristics of these three types of amplifiers will be determined to show the conditions under which each amplifier is most useful. Each of the three basic transistor amplifiers can be modelled as a two-port network in one of four configurations as shown Table 1.

**➤ ****Frequency Response of Common Emitter Amplifier:**

In common emitter amplifier circuit of figure 4(a) , it was assumed that the coupling capacitors C_{c1 }and C_{c2} and the bypass capacitor C_{E} were acting as perfect short circuits at the signal frequencies of interest, also there is neglected the internal capacitances of the BJT that is, C_{π} and C_{μ} of the BJT high frequency model. It was assumed to be sufficiently small to act as open circuit at all signal frequency of interest. So, it is observed that the gain is almost constant over a wide frequency band, called the mid-band.

Figure 4(b) shows that the gain fall off at signal frequencies below and above the mid-band. The gain fall-off in the low frequency band is due to the fact that even though C_{C1}, C_{C2} and C_{E} are large capacitance, as the signal frequency is reduced their impedance increase and they no longer behave as short circuit. On the other hand, the gain falloff in the high frequency band as result of C_{gs} and C_{gd}, which though very small, their impedance at sufficiently high frequency decrease, thus they can no longer be considered as open circuits.**(i) Cut-off Frequency**

For a given circuit with equivalent resistance (R_{eq}) and equivalent capacitance (C_{eq}), the 3-dB cut-off frequency is given by

Thus, we calculate 3 dB frequencies due to C_{C1}, C_{C2}, C_{E} as below.

- The effect of C
_{C1}is determined with C_{E }and C_{C2}assumed to be acting as perfect short circuit as shown in figure 5(a). So, - The 3dB frequency due to C
_{C2 }is given by - The 3dB frequency due to C
_{E}is given by

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