Amplifiers

THEORY

What is an amplifier?

The most common processing of analog (continuous-time) signals is the amplification. Under the term amplification we mean an increase in the level of a voltage or/and a current of a signal, which results in an increase in the level of the power of the signal.

Signal amplification is achieved by amplifiers, which are electronic circuits designed for this purpose. The amount of increase of the signal level is called gain of the amplifier.
An amplifier is placed between a signal source (vs , Rs) and a load (RL), as indicated in Figs.1 and 2. The input of the amplifier is driven by a signal from the signal source and delivers the amplified signal to the load.

Fig.1 An amplifier placed between a signal source and a resistive load

Fig. 2 Single-stage amplifier between a signal source and a resistive load

At least one active element e.g. a transistor, is necessary in order to obtain a simple, one stage amplifier, (Fig.2).

Gain definitions

The signal power gain is defined by

(1)

where, p_out is the power delivered to the load and p_in is the power at the amplifier input. Consequently,

expression (1) can be written as

(2)

(3)

where, A_v and A_i are the voltage and current gains respectively.

Why a dc power supply is needed ?

Fig.3 Bias current in a single stage amplifier

The dc voltage source V_cc, in the amplifier of Fig.3, is used to supply dc currents to the various branches of the amplifier in order to bias properly the transistors (active elements in general) in the active area of their output characteristics. Due to the nature of the active elements, only within their active area of I-V characteristics, a current amplification between the output (controlled) and the input (controlling) currents can take place, according to the relationship,

(4)

where h_fe is the ac current gain of the transistor.In equation (4) above,i_c represents the ac component of the dc collector current I_C, i.e.,

(5)

Equation(5) denotes that the ac output current i_c represents the variations of the dc current I_C as a result of the control operation imposed by the ac input current i_b=ΔI_B. Under this consideration the amplifier performs as a transducer of the dc bias current to an ac output current. The transducer power gain is defined by

(6)

where, P_out is the available power from the signal source, . When the signal source is properly matched to the input of the amplifier, ( ), the transducer gain factor becomes equal to the power gain of the amplifier.

Stages of an amplifier

Usually the gain required from an amplifier is higher than we can obtain with a single stage amplifier. In such a case, several stages of amplification are cascaded to obtain the desired result, (see multistage amplifiers).

Amplifier models Simple ohmic models, as indicated in Figs.4a and 4b, can easily model various wide band amplifiers within their frequency band of operation.

Fig.4 Small signal equivalent models of amplifiers

In the two models in Fig.4, R_i represents the input resistance of the amplifier, R_o represents the output resistance of the amplifier while A_vo and A_io represent the voltage and the current gain of the amplifier respectively, (see common emitter amplifier for definitions).

Example

Following a classical analysis for the two stage amplifier shown in fig.5 there where found:

· The input resistance R_i = 5KΩ

· The output resistance R_o= 23Ω

· The voltage gain for ( )

Fig.5 A two stage amplifier

Subsequently, the ac model of the amplifier is shown in Fig.6, within the frequency band of operation (pass band), is shown in Fig.6.

Fig.6 The ac model of the amplfier in Fig.5

Following some calculations the voltage gain for both circuits in Fig.5 and Fig.6, the voltage gain is found to be,

Summarizing, wide band amplifiers can be characterized by the following three factors a) the input resistance b) the output resistance, and c) the gain. This characterization applies regardless of the number of amplifying stages or the number of transistors employed.