# Theory of Op-Amps and Voltage/Signal Amplification

LECTURE NOTES

TABLE OF CONTENT

1.INTRODUCTION2

1.1Signals2

1.2Classification of Signals4

1.2.1Digital vs. Analogue4

1.2.2Continuous-time vs. Discrete-time5

1.2.3Hazy Part of the Classification5

1.3System Response6

1.4Linearity vs Non-linearity6

2.AMPLIFIERS7

2.1Types of Amplifiers8

2.1.1Signal Amplifier8

2.1.2Power Amplifier8

2.2Amplifier Circuit Symbol8

2.3Amplifier Gain9

2.3.1Voltage Gain9

2.3.2Current Gain10

2.3.3Power Gain10

2.3.4Decibel values of Voltage, Current and Power Gains10

2.3.5DC Supply to An Amplifier11

2.3.6Amplifier Saturation12

1.INTRODUCTION

1.1Signals

A signal can be defined as detectable transmitted energy that can be used to carry information. Put in another way, a signal is a time-dependent variation of a characteristic of a physical phenomenon, used to convey information. For example, a signal could be the current flowing through a light dependent resistor (LDR), giving information about the amount of illumination in the LDR's environment. Another signal could be the colour of a methyl orange solution indicating the pH of the solution. Signals discussed in this course will be restricted simply to voltage signals and current signals. Hence, in this course, a signal will be either a voltage or a current. There are two common ways in which signals are represented:

i.Time-domain representation; and

ii.Frequency-domain representation.

The time-domain representation is the representation which you are more likely than not most familiar with. Here, the signal is represented as a function of time. The plot of the signal is a plot of its magnitude against time. Figure 1.1 shows a time-domain representation of a signal. The signal in figure 1.1 is

Figure 1.1: Time-domain representation of a signal

Mathematically, the signal is represented as to show that it is a time-domain signal. We may represent this same signal in the frequency-domain. When it is represented in the frequency-domain as a function of frequency f, it is represented mathematically as . Representations in the frequency-domain are often not represented in terms of f. Often times the representation is made in terms of the angular frequency, ? or the complex Laplace variable, s. The frequency-domain representation of a signal is a representation of the magnitudes of the individual frequency components which the signal has in it. The Fourier series decomposition or Fourier transform of a time-domain signal gives the frequency components of the signal. For example, a sine wave is a signal which has only one frequency. Hence, the signal is a signal which has an angular frequency of ? or a frequency of f (). can be expressed in the frequency-domain as shown in figure 1.2.

Figure 1.2: Frequency-domain representation of

Every periodic signal can be represented as a sum of sinusoidal waves. For example, a square wave, whose peak-to-peak amplitude is 2A (i.e. -A/+A) can be represented as

Equation 1.1

Equation 1.1 is called the Fourier series expansion of the square wave. Figure 1.3 shows the time domain and frequency-domain representation of .

Figure 1.3: Frequency-domain representation of the square wave signal When the frequency-domain representation of a signal has discrete values only at discrete frequencies, the plot is usually made with arrows as shown in figures 1.2 and 1.3. This is usually the case for periodic signals. Non-periodic signals can often not be represented as a sum of sinusoids, but their frequency-domain representation can be found by finding their Fourier transform. The frequency-domain representation for non-periodic signals is often made with line plots. An example is the frequency-domain for a low-pass filter shown in figure 1.4.

Figure 1.4: Frequency-domain representation of a Low-Pass Filter We will leave the full discourse about Fourier series and Fourier transforms to EEE 306...

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