Amplifier Fundamentals

 Introduction To Amplifiers:

Amplify or Amplifiers, what comes to your mind when you hear these words? I think it will increase the sound levels. This is the first impression of the word amplifier in a common man’s mind. But from an engineer's perspective amplifiers are not only the sound levels, but it is also much more. Radio, television and computers all use amplifiers. In this post, I will explain amplifiers, their types, and important parameters. The article provides knowledge of amplifiers on the system level. It means I suppose an amplifier is a block, I am not interested in its internal circuitry or component. At the system level, you can think of an amplifier as a two-port network. It has two input terminals and two output terminals.

Outline:

• Amplification and amplifiers

• Ideal amplifier characteristics

• Need for linearity

• Imperfections in practical amplifier

• Distortion

• Noise

• Loading effect

• Slew rate

• Design parameters

• Bandwidth

• Frequency response

• Gain or transfer ratio

• Explanation Of Power Gain In Amplifiers: (How does an amplifier increase the power gain?)

• Efficiency

• Input impedance

• Output impedance

Amplification and Amplifiers:

Amplification is the process of boosting a signal or strengthening a signal. For example, increasing the volume of sound etc. 

The amplifier is an electronic device that is used to enlarge the input signal. 

There is a small signal at the input of the amplifier, it processes the signal and produces a larger signal at the output. A transistor is the simplest amplifying device.

Ideal amplifier characteristics:

An ideal amplifier is perfectly linear. At any instant output current, voltage or power is constantly proportional to input current, voltage or power. There are several characteristics of an ideal amplifier

• The gain (Av, Ai) of an ideal amplifier remains the same irrespective of the applied input signal amplitude (vin, vout)

• Gain must be independent of the frequency of the signal. The signal of all frequencies must be amplified by the same amount

• The ideal amplifier is free from noise

• Temperature stability for an amplifier should be very important. It works well in high temperatures as well

• Time stability, another performance parameter of an ideal amplifier. It should be stable over a period of time

Need For Linearity:

During the amplification process, it is desirable to process a signal so that the information contained in it must remain unchanged. The output of an amplifier should be a replica of the input signal, except the magnitude. Or in other words, the output and input waveforms are exactly similar in shape but different in magnitudes.

Now come to the imperfections. Almost all the amplifiers are linear up to some part of their operating range. However, some of them deviate from linear behaviour at higher frequencies. No real amplifier is an ideal amplifier. A real system must have imperfections, we engineers are here to minimize them. 

Imperfections in a practical amplifier:

Distortion

The purpose of an amplifier is to reproduce the exact signal with some gain. Any change in signal shape is referred to as Distortion. It is an undesirable effect. Practically it won't reproduce the exact signal. The output signal might be distorted in three ways: amplitude, phase and frequency.

Amplitude distortion:

This type of distortion is linear and is due to the bandwidth of the amplifier. The input of an amplifier is alternating and of course the output as well. Signals of smaller amplitude amplify properly because they can swing freely on either side. But signals of larger amplitudes drive the amplifier (transistor-based amplifiers) into a non-linear region and hence the edges of the signal attenuate. This type of distortion not only affects the gain but also results in distorted amplitude. 

Harmonic distortion

It is nonlinear distortion caused by device characteristics. In this type of distortion, the output signal contains harmonic components as well, which are not part of the input signal. Lower harmonics are more dominant These harmonics appear at the output and give rise to distorted output. 

Phase distortion

This type of distortion is also non-linear. When a signal flows through inductors and capacitors, there is a phase shift. The output signal appears after a delay as compared to the input signal. The amount of phase shift is related to frequency.

Noise

An unwanted signal, superimposed on an electrical signal.  Noise may be added from the outside of the circuits or it may be added by the circuit components. In amplifiers, transistors are responsible for producing noise. Low noise transistors are available. The amount of noise produced is somewhat related to the amount of current. So, keep the current low in your design.

Loading effect:

When you are understanding the concepts of amplifiers you must come across the term “loading effect”. What is the loading effect and how to minimize it? Consider a situation, your amplifier output resistance is 1k and you have attached a load of resistance 100 ohms in parallel with output. What is going to happen? The effective output resistance decreases and hence gain decreases. To avoid this there's a technique known as impedance matching or impedance transformation is used. 

Slew rate

The ability of an amplifier to change the output voltage with respect to rapid change in input. It is measured in V/s. 

Slew rate = ∆V/∆t

Design Parameters:

Each amplifier has three important design parameters. Gain, input impedance and output impedance.

Bandwidth:

It is a range of frequencies over which an amplifier gives its best results. An amplifier is designed to operate over a selected frequency range. This range is called bandwidth.

Frequency response:

It is an actuarial representation of output voltage versus the frequency of the amplifier. It shows the effect of frequency on the output of the amplifier. Look at the graph, at lower frequencies, the output decreases because of capacitive reactances of coupling and bypass capacitors. At higher frequencies, the output voltage drops because of transistor Internal capacitances and stray wiring capacitances. The middle range of frequencies is called the mid-band. Over this frequency range, amplifiers produce maximum output. An amplifier with a larger bandwidth has a smaller gain.

To design an amplifier we must select a suitable range of frequencies according to the design requirements.

Critical Frequency:

The frequency at which output voltage reaches 0.707 of Vmax. There are usually two critical frequencies in an amplifier frequency response. These are lower critical frequency f1 and upper critical frequency f2. The middle part of the graph shows the range of frequencies where the amplifier produces maximum output. Usually, amplifiers operate in this range of frequencies.

Gain or Transfer ratio

The ability of an amplifier to enhance the input signal. It is the ratio of output signal divided by input signal. It is expressed in decibel dB. The three gains in an amplifier system are given below.

• Voltage gain

• Current gain

• Power gain

Voltage Gain:

It is the voltage amplification factor and denoted by AV. If the output voltage (vo) of an amplifier is greater than the input voltage (vi) then it is a voltage gain. Therefore, it is the ratio of output voltage to the input voltage.

\[A_v = \frac {v_o}{v_i}\]

It is important to note that voltage gain is the ratio, not the difference. Some amplifiers produce the inverted output and it is denoted by a 'minus sign. The voltage gain as a function of current gain can be expressed as,

\[A_v = \frac {i_o*R_L}{v_i*r_i}\]

\[A_v =A_i \frac {R_L}{r_i}  ..equation 1\]

Where, 

ri = input resistance seen from the signal

RL = output resistance

Equation 1 holds for any type of structure of an amplifier. An important consideration in this context is that input and output currents are entering the positive terminals.

\[A_v = \frac {-i_o*R_L}{v_i*r_i}\]

-io is the output current leaving the positive terminals.

Current Gain:

Like the voltage gain, it is the current amplification factor and denoted by Ai. If the output current is greater than the input current then it is a current gain. Therefore, it is the ratio of the output current to the input current.

\[A_i = \frac {i_o}{i_i}\]

Power Gain:

It is the power amplification factor and denoted by AP. If the output power is greater than the input power then it is the power gain. Therefore it is the ratio of the output power to the input power. 

\[A_P = \frac {p_o}{p_i}\]

Where, 

\[p_o = v_o*i_o\]

\[p_i = v_i*i_i\]

\[A_P = \frac {v_o*i_o}{v_i*i_i} = A_vA_i\]

Explanation Of Power Gain In Amplifiers: (How does an amplifier increase the power gain?)

Look at the schematic and connections. There are two DC voltage sources V+ and V- to drive the transistor. vi is the input signal to be amplified. 

It is important to note that an amplifier increases the signal power. In comparison with the transformers, the applied power (input power) is almost equal to or less than the power delivered (output power).

The reason behind this additional power is the external DC supplies. To operate an amplifier external DC source is required. Additional power delivered and heat dissipated (due to internal circuit) is provided from the power supply. 

\[P_{DC} = P_1+P_2\]

\[P_{DC} +P_I = P_L+P_{dissipated} ..equation 2\]

V1  and V2 are necessary for operating an amplifier. P1 and P2 are the power obtained from voltage sources V1  and V2. PDC is the total DC power input to the circuit. Equation 2 is the power balance equation.

Efficiency:

Efficiency is always an important performance parameter for the system. In power amplifiers (that enhance voltage and current of the signal) efficiency is important.

\[\eta = \frac { P_L}{P_DC}\]

The real-life signal is very small (signals obtained from the transducers are usually in millivolts), so power drawn from the signal source is not considered while calculating the efficiency.

Input impedance Zin

It is a design parameter of the amplifier. It is the impedance offered by input terminals. There is no single element that creates input impedance. Input impedance is the combined effect of source internal resistance and biasing resistors and any other resistance in the path of the signal. 

Output impedance

It is also a design parameter of the amplifier. Same as the input impedance, there is no single component that creates output impedance. It is a little bit difficult to explain where the output impedance comes from. It is the equivalent impedance of signal source at the amplifier output, load resistor and any other resistance in the path of output signal flow.