FUNDAMENTALS OF MIXED SIGNALS AND SENSORS Course Description This course covers operational amplifiers, signal converters, power switching devices, and the construction and operation of sensors and transducers for converting physical parameters into electrical signals and vice versa. The course focuses on the application of these devices in developing signal conversion circuits that allows measurement, processing, and control of physical parameters by digital processing systems such as a finite state machine or a digital computer. Chapter 01: Introduction / Overview of Signals Objectives: At the end of the module, the students would be able to: Analyze analog and digital signals Differentiate the time domain and frequency domain representation Describe the differential amplifier and its operation Evaluate Operational Amplifiers and its application Discuss the modes of signal operation Describe single-ended and double ended differential input operation Determine common-mode operation Define and determine the common-mode rejection ratio (CMRR) Discuss how negative feedback affects op-amp impedances Analyze the amplifier impedances An analog signal is a smoothly and continuously varying voltage or current. Signals of which amplitude changes continuously with respect to time with no breaks or discontinuities. Some typical analog signals are shown in the figure below. A sine wave is a single-frequency analog signal. Voice and video voltages are analog signals that vary in accordance with the sound or light variations that are analogous to the information being transmitted. Digital Signals Digital signals, in contrast to analog signals, do not vary continuously, but change in steps or in discrete increments. Signals that are described as discrete; their amplitude maintains constant level for a prescribed period of time and then it changes to another level with respect to time with no breaks or discontinuities. Most digital signals use binary or two-state codes. Binary Signal-Digital signal with only two levels possible. *Note: Many transmissions are of signals that originate in digital form, e.g., telegraphy messages or computer data, but that must be converted to analog form to match the transmission medium. An example is the transmission of digital data over the telephone network, which was designed to handle analog voice signals only. If the digital data is converted to analog signals, such as tones in the audio frequency range, it can be transmitted over the telephone network. Analog signals can also be transmitted digitally. It is very common today to take voice or video analog signals and digitize them with an analog-to-digital (A /D) converter. The data can then be transmitted efficiently in digital form and processed by computers and other digital circuits. Modulation and Multiplexing Modulation and multiplexing are electronic techniques for transmitting information efficiently from one place to another. Modulation and multiplexing techniques are basic to electronic communication Modulation makes the information signal more compatible with the medium Multiplexing allows more than one signal to be transmitted concurrently over a single medium. Signal Analysis- Is the mathematical analysis of the frequency, bandwidth, and voltage level of a signal. Time Domain versus Frequency Domain Time Domain are variations of signals such as voltage, current, or power with respect to time(amplitude with respect to time). A signal waveform shows the shape and instantaneous magnitude of the signal with respect to time but does not directly indicate its frequency content. Time Domain versus Frequency Domain Frequency Domain Representation A description of signal with respect to its frequency(amplitude with respect to frequency). Essentially, no waveform is displayed on the CRT. Instead, an amplitude-versusfrequency plot is shown. The horizontal axis represents frequency and the vertical axis amplitude. Therefore, there is a vertical deflection for each frequency present in the waveform. The vertical deflection(height) of each line is proportional to the amplitude of the frequency that it represents. A frequency-domain representation of a wave shows the frequency content but not necessarily indicate the shape of the waveform or the combined amplitude of all the input components at any specific time. A typical frequency-domain plot of the square wave is shown in Figure below. Sine Wave in Frequency Domain | Engineer's Knowledge (engineersknowledge.blogspot.com) Frequency Spectrum The frequency spectrum of a waveform consists of all the frequencies contained in the waveform and their respective amplitudes plotted in the frequency domain. The figure below shows an example of frequency spectrum. shows the time-domain representation of a signal while the shows a frequency-domain plot of electronic signals. It is the key test instrument in designing, analyzing, and troubleshooting communication equipment. Most electronic circuits in communication are used to process signals, such as to manipulate signals to produce a desired result. All signal processing circuits involve either gain or attenuation. Gain means amplification If a signal is applied to a circuit such as the amplifier shown in Figure, and the output of the circuit has a greater amplitude than the input signal, the circuit has gain. Gain is simply the ratio of the output to the input. What is the voltage gain of an amplifier that produces an output of 750 mV for a 30-μV input? Since most amplifiers are also power amplifiers, the same procedure can be used to calculate power gain 𝑨𝑷 . 𝑨𝑷 = 𝑷𝒐𝒖𝒕 𝑷𝒊𝒏 where 𝑃𝑖𝑛 is the power input and 𝑃𝑜𝑢𝑡 is the power output. The power output of an amplifier is 6 watts (W). The power gain is 80. What is the input power? When two or more stages of amplification or other forms of signal processing are cascaded, the overall gain of the combination is the product of the individual circuit gains. The figure below shows three amplifiers connected one after the other so that the output of one is the input to the next. The voltage gains of the individual circuits are marked. To find the total gain of this circuit, simply multiply the individual circuit gains: If an input signal of 1 mV is applied to the first amplifier, the output of the third amplifier will be 60 mV. The outputs of the individual amplifiers depend upon their individual gains. Three cascaded amplifiers have power gains of 5, 2, and 17. The input power is 40 mW. What is the output power? A two-stage amplifier has an input power of 25 μW and an output power of 1.5 mW. One stage has a gain of 3. What is the gain of the second stage? Attenuation refers to a loss introduced by a circuit or component. Many electronic circuits, sometimes called stages, reduce the amplitude of a signal rather than increase it. If the output signal is lower in amplitude than the input, the circuit has loss, or attenuation. Like gain, attenuation is simply the ratio of the output to the input. Circuits that introduce attenuation have a gain that is less than 1. The letter A is used to represent attenuation as well as gain: When several circuits with attenuation are cascaded, the total attenuation is, again, the product of the individual attenuations. The figure below is an example. The overall attenuation is Decibel The decibel is a unit of logarithmic gain measurement and is commonly used to express amplifier response. The term decibel has its origin in the fact that power and audio levels are related on a logarithmic basis. The term bel is derived from the surname of Alexander Graham Bell. For standardization, the bel (B) is defined by the following equation relating two power levels, 𝑷𝟏 𝒂𝒏𝒅 𝑷𝟐 . It was found, however, that the bel was too large a unit of measurement for practical purposes, so the 𝐝𝐞𝐜𝐢𝐛𝐞𝐥 (𝐝𝐁) is defined such that 𝟏𝟎 𝒅𝒆𝒄𝒊𝒃𝒆𝒍𝒔 = 𝟏 𝒃𝒆𝒍 The terminal rating of electronic communication equipment (amplifiers, microphones, etc.) is commonly in decibels The Equation above indicates clearly that the decibel rating is a measure of the difference in magnitude between two power levels. For a specified terminal (output) power (𝑷𝟐 ) there must be a reference power level (𝑷𝟏 ). The reference level is generally accepted to be 1 mW. When the 1-mW level is employed as the reference level, the decibel symbol frequently appears as 𝑑𝐵𝑚. In equation form Because the decibel (dB) can be used to represent only power ratios, not actual power, the dBm provides a convenient way to express actual power output of an amplifier or other device. Typical sound levels and their decibel levels. (Boylestad, Electronics Circuits Cascaded Stages One of the advantages of the logarithmic relationship is the manner in which it can be applied to cascaded stages. The equation states that the decibel gain of a cascaded system is simply the sum of the decibel gains of each stage, that is, Find the magnitude gain corresponding to a voltage gain of 100 dB. A power amplifier with a 40-dB gain has an output power of 100 W. What is the input power? An amplifier has a gain of 60 dB. If the input voltage is 50 μV, what is the output voltage? A power amplifier has an input of 90 mV across 10 kΩ. The output is 7.8 V across an 8-Ω speaker. What is the power gain, in decibels? You must compute the input and output power levels first The input power to a device is 10,000 W at a voltage of 1000 V. The output power is 500 W and the output impedance is 20 Ω. a. Find the power gain in decibels. b. Find the voltage gain in decibels An amplifier rated at 40-W output is connected to a 10-Ω speaker. a. Calculate the input power required for full power output if the power gain is 25 dB. b. Calculate the input voltage for rated output if the amplifier voltage gain is 40 dB THANK YOU! Questions?
