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Study Notes
The Development of Electronics
- The field of electronics has been a great success story of the 20th century, evolving from crude spark-gap transmitters and "cat's-whisker" detectors to sophisticated vacuum-tube electronics and eventually solid-state electronics.
- The first half of the 20th century saw the development of vacuum-tube electronics, which found applications in communications, navigation, instrumentation, control, and computation.
- The latter half of the 20th century brought significant advances in solid-state electronics, first with discrete transistors and later with integrated circuits (ICs), leading to compact and inexpensive consumer products.
Advances in Electronics
- Modern electronics have enabled the creation of compact and inexpensive consumer products that contain millions of transistors in VLSI (very large-scale integration) chips.
- These products can process sounds, images, and data, and permit wireless networking and access to the Internet.
- The cost of an electronic microcircuit decreases significantly as the manufacturing process is perfected, often to a fraction of its initial cost.
The Focus of this Book
- This book aims to convey the excitement and know-how of electronics, starting with the basics of voltage, current, power, and electronic components.
- The book will cover the laws, rules of thumb, and tricks that constitute the art of electronics.
- The first chapter will focus on the foundations of electronics, which may require some abstraction and dependence on visualizing instruments like oscilloscopes and voltmeters.
Voltage and Current
- Voltage (V) is the energy required to move a unit of positive charge from a more negative point to a more positive point in a circuit.
- Voltage is also known as potential difference or electromotive force (EMF).
- The unit of voltage is the volt (V), with common expressions in volts (V), kilovolts (kV), millivolts (mV), or microvolts (μV).
- A joule (J) of work is done in moving a coulomb (C) of charge through a potential difference of 1 V.
- Current (I) is the rate of flow of electric charge past a point.
- The unit of current is the ampere (A), with common expressions in amperes (A), milliamperes (mA), microamperes (μA), nanoamperes (nA), or picoamperes (pA).
- A current of 1 A equals a flow of 1 C of charge per second.
- By convention, current flows from a more positive point to a more negative point in a circuit.
- Important: voltage is applied across two points in a circuit, and current flows through a device or connection in a circuit.
Voltage and Current Relationships
- Voltages are generated by doing work on charges in devices such as batteries, generators, and solar cells.
- Currents are obtained by placing voltages across things.
- The oscilloscope is a useful tool for visualizing voltage and current in a circuit as a function of time.
Rules for Voltage and Current
- The sum of the currents into a point in a circuit equals the sum of the currents out (conservation of charge), also known as Kirchhoff's current law (KCL).
- In a series circuit, the current is the same everywhere.
- Things connected in parallel have the same voltage across them, and the sum of the "voltage drops" from one point to another via any path is equal to the sum via any other route.
- The power (energy per unit time) consumed by a circuit device is P = V I, where P is in watts (W), V is in volts, and I is in amps.
Resistor Types
- Various types of resistors are available, including wirewound ceramic power resistors, wirewound power resistors, carbon composition resistors, surface-mount thick-film resistors, and surface-mount resistor arrays.
Relationship between Voltage and Current: Resistors
- The current through a metallic conductor (or other partially conducting material) is proportional to the voltage across it.
- This is an interesting fact, but not a universal law for all objects, e.g., the current through a neon bulb is a highly nonlinear function of the applied voltage.
Resistors
- A resistor is made out of some conducting stuff (carbon, metal, or carbon film) with a wire or contacts at each end.
- It is characterized by its resistance (R = V/I), measured in ohms (Ω) for V in volts and I in amps.
- Ohm's law states that R is constant for a given resistor, but it can vary with temperature, voltage, time, and humidity.
- Resistors are used to convert a voltage to a current, and vice versa.
Types of Resistors
- Metal-oxide film, metal film, or carbon film resistors are the most frequently used type.
- They come in values from 1 ohm (1 Ω) to about 10 megohms (10 MΩ).
- They are also characterized by power rating, physical size, tolerance, temperature coefficient, noise, and voltage coefficient.
Resistors in Series and Parallel
- The resistance of two resistors in series (R1 and R2) is R = R1 + R2.
- The resistance of two resistors in parallel (R1 and R2) is R = R1R2 / (R1 + R2) or R = 1 / (1/R1 + 1/R2).
Power in Resistors
- The power dissipated by a resistor (or any other device) is P = IV.
- Using Ohm's law, P can be expressed as P = I²R or P = V² / R.
Voltage Dividers
- A voltage divider is a circuit fragment that accepts an input voltage and produces a corresponding output voltage.
- The transfer function H is the ratio of output voltage to input voltage.
- With only resistors, we can already look at a voltage divider, which can be used as a "de-amplifier".
Voltage Dividers
- A voltage divider is a circuit that produces a predictable fraction of the input voltage as the output voltage.
- The simplest voltage divider consists of two resistors (R1 and R2) connected in series, with the input voltage (Vin) applied across them.
- The output voltage (Vout) is the voltage across R2, which is smaller than the input voltage.
How Voltage Dividers Work
- The current (I) through the circuit is the same everywhere, assuming no load on the output.
- The current is calculated by: I = Vin / (R1 + R2)
- The output voltage is calculated by: Vout = IR2 = (R2 / (R1 + R2)) * Vin
Characteristics of Voltage Dividers
- The output voltage is always less than or equal to the input voltage.
- Voltage dividers can be used to generate a particular voltage from a larger fixed or varying voltage.
Adjustable Voltage Dividers
- An adjustable voltage divider can be made using a fixed and variable resistor, or a potentiometer.
- The output voltage can be adjusted by changing the value of the variable resistor.
Applications of Voltage Dividers
- Voltage dividers are often used in circuits to generate a particular voltage from a larger fixed or varying voltage.
- They can be used as "volume controls" to adjust the voltage level of a signal.
- They can also be used to represent the output of an amplifier and the input of a following stage.
Other Types of Voltage Dividers
- Some contemporary circuits use a long series chain of equal-value resistors with electronic switches to choose the output voltage.
- This design allows for electrical adjustment of the voltage ratio.
Voltage Sources
- A perfect voltage source is a two-terminal device that maintains a fixed voltage drop across its terminals, regardless of load resistance.
- A real voltage source has a limited maximum current it can supply and behaves like a perfect voltage source with a small resistance in series.
- A voltage source "likes" an open-circuit load and "hates" a short-circuit load.
- The symbols used to indicate a voltage source are shown in Figure 1.9.
- A real-life approximation to a voltage source is a battery.
- A standard 9-volt alkaline battery behaves approximately like a perfect 9-volt voltage source in series with a 3 Ω resistor.
- A battery can provide a maximum current when shorted, but this will drain the battery quickly.
Current Sources
- A perfect current source is a two-terminal device that maintains a constant current through the external circuit, regardless of load resistance or applied voltage.
- A real current source has a limit to the voltage it can provide, called the output-voltage compliance, and does not provide absolutely constant output current.
- A current source "likes" a short-circuit load and "hates" an open-circuit load.
- The symbols used to indicate a current source are shown in Figure 1.10.
Characteristics of Batteries
- A standard D-size flashlight cell has a terminal voltage of 1.5 V, an equivalent series resistance of about 0.25 Ω, and a total energy capacity of about 10,000 watt-seconds.
- The characteristics of a battery gradually deteriorate with use, affecting its voltage and internal series resistance.
Thevenin Equivalent Circuit
- The Thevenin equivalent circuit is represented in Figure 1.11.
- It is a major topic of Chapter 9.
Thevenin Equivalent Circuit
- Thevenin's theorem states that any two-terminal network of resistors and voltage sources can be equivalent to a single resistor R in series with a single voltage source V.
- This means that a complex circuit can be simplified into a single resistor and voltage source.
- To find the Thevenin equivalent circuit, you need to calculate the open-circuit voltage (VTh) and the short-circuit current (RTh).
- The formula to calculate RTh is RTh = V (open circuit) / I (short circuit).
Example of Thevenin Equivalent Circuit
- The voltage divider circuit can be simplified into a Thevenin equivalent circuit.
- The open-circuit voltage is V = Vin * R2 / (R1 + R2).
- The short-circuit current is Vin / R1.
- The Thevenin equivalent circuit is a voltage source VTh = Vin * R2 / (R1 + R2) in series with a resistor RTh = R1 * R2 / (R1 + R2).
Multimeters
- Multimeters are instruments used to measure voltage, current, and resistance.
- There are two types of multimeters: analog multimeters (VOM) and digital multimeters (DMM).
- Analog multimeters use a meter movement that measures current, and they respond slowly to changing voltages.
- Digital multimeters use electronic amplification and have a high input resistance, making them ideal for measuring voltage, current, and resistance.
- Multimeters can have several voltage and current ranges, and they can also measure resistance.
Loading Effects
- Loading effects occur when a load resistor is attached to a circuit, causing the output voltage to drop.
- The Thevenin equivalent circuit can be used to calculate the output voltage and current with a load resistor.
- To minimize loading effects, the load resistance should be much greater than the source resistance.
- The concept of equivalent internal resistance applies to all sources, not just batteries and voltage dividers.
Power Transfer
- The maximum power is transferred to the load when the load resistance is equal to the source resistance.
- If the load resistance is too low or too high, the power transferred to the load is zero.
Important Notes
- Circuits are usually designed so that the load resistance is much greater than the source resistance.
- Anthropomorphizing, or attributing human-like qualities to circuits, is a common pitfall in engineering and science.
Small-signal Resistance
- Small-signal resistance (incremental resistance or dynamic resistance) is the ratio of a small change in applied voltage to the resulting change in current, ΔV/ΔI (or dV/dI).
- It has the units of resistance (ohms) and is used in many calculations.
- Small-signal resistance substitutes for resistance in devices where I is not proportional to V.
Zener Diodes
- Zener diodes are used to create a constant voltage inside a circuit.
- They are provided with a roughly constant current derived from a higher voltage within the circuit.
- The I–V curve of a zener diode shows a narrow range of voltages corresponding to a range of applied currents.
- Dynamic resistance is specified for a zener diode at a certain current, e.g., 10 Ω at 10 mA and 5 V.
- A 10% change in applied current results in a change in voltage of ΔV = RdynΔI.
- Zener diodes have good voltage-regulating ability, e.g., a 10% change in current results in a 0.2% change in voltage.
Zener Regulator Circuit
- The zener current is typically obtained through a resistor from a higher voltage available in the circuit.
- The circuit behaves like a voltage divider, with the zener replaced by a resistor equal to its dynamic resistance at the operating current.
- The output-voltage regulation can be estimated using the dynamic resistance of the zener diode.
Characteristics of Zener Diodes
- Dynamic resistance of a zener diode varies roughly in inverse proportion to current.
- Low-voltage zener diodes (e.g., 3.3 V) behave poorly in terms of constancy of voltage versus current.
- Two-terminal voltage references (ICs) are designed to substitute for zener diodes, with superior performance (e.g., much lower dynamic resistance and excellent temperature stability).
Temperature-Sensing Circuit
- A temperature-sensing circuit can be created using a voltage divider, a comparator, and an LED to indicate when the room temperature exceeds 30°C (86°F).
Components and Their Functions
- R4: temperature-sensing device that decreases in resistance by about 4%/°C, with a resistance of 10kΩ at 25°C.
- Comparator: a device that switches its output according to the relative voltages at its two input terminals.
- LED: behaves electrically like a 1.6 V zener diode, and lights up when current is flowing.
Voltage Divider and Comparator
- The voltage divider (R3R4) has an output that is compared with the temperature-insensitive divider (R1R2).
- When the temperature is above 30°C, the comparator output is pulled to ground.
LED and Resistor
- The LED is connected to the output of the comparator, with a series resistor (R5) sized to allow 5 mA of current when the comparator output is at ground.
- R5 is calculated as 3.4 V/5 mA, or 680 Ω.
Adjustable Setpoint and Hysteresis
- The setpoint can be made adjustable by replacing R2 with a 5k pot in series with a 5k fixed resistor.
- Adding hysteresis to the comparator is recommended to encourage decisive switching.
Ratiometric Techniques
- The circuit is insensitive to the exact power supply voltage because it compares ratios, making it a good design technique.
- Ratiometric techniques will be seen again in later applications.
Signals
- Signals are voltages that change in time in a particular way, and are essential for understanding alternating-current (ac) circuits.
Sinusoidal Signals
- Sinusoidal signals are the most common type of signal, and are what you get out of a wall plug.
- They are described by the equation: V = Asin(2πft) or V = Asin(2πft + φ), where A is the amplitude, f is the frequency in hertz, and φ is the phase.
- The angular frequency ω is measured in radians per second, and is related to the frequency f by the equation: ω = 2πf.
- Sinewaves are the solutions to certain linear differential equations that describe many phenomena in nature and the properties of linear circuits.
- Linear circuits have the property that their output, when driven by the sum of two input signals, equals the sum of its individual outputs when driven by each input signal in turn.
Properties of Sinewaves
- A linear circuit driven by a sinewave always responds with a sinewave, although the phase and amplitude may be changed.
- No other periodic signal can make this statement.
- The frequency response of a circuit describes how it alters the amplitude of an applied sinewave as a function of frequency.
- Sinewave frequencies can range from a few hertz to a few tens of megahertz, and higher frequencies can be generated with special techniques.
Real-World Applications
- A stereo amplifier, for instance, should be characterized by a "flat" frequency response over the range 20 Hz to 20 kHz.
- Lower frequencies, down to 0.0001 Hz or lower, can be generated with carefully built circuits, if needed.
- Higher frequencies, up to say 2000 MHz (2 GHz) and above, can be generated, but they require special transmission-line techniques.
Signal Amplitudes and Decibels
- Signal amplitude can be characterized by peak-to-peak amplitude (pp amplitude) and root-mean-square amplitude (rms amplitude)
- For sinewaves, rms amplitude (Vrms) is related to amplitude (A) by Vrms = (1/√2)A = 0.707A
- The nominal voltage across a wall socket in the US is 120 volts rms, 60 Hz, with an amplitude of 170 volts and a peak-to-peak amplitude of 339 volts
Decibels
- Decibels (dB) are used to compare the relative amplitudes of two signals
- The ratio of two signals in decibels is defined as dB = 10log10(P2/P1), where P1 and P2 are the power in the two signals
- For signals with the same waveform, dB = 20log10(A2/A1), where A1 and A2 are the signal amplitudes
- Examples of decibel ratios:
- +6 dB: a signal with twice the amplitude of another signal
- +20 dB: a signal 10 times as large as another signal
- -20 dB: a signal one-tenth as large as another signal
- Decibels can be used as an absolute measure of amplitude by assuming a reference signal level and expressing other levels in decibels relative to it
Other Signals
Ramp
- A ramp is a signal that rises (or falls) at a constant rate
- It can be approximated by a finite ramp or a periodic ramp (sawtooth)
Triangle
- A triangle wave is a symmetrical ramp
Noise
- Noise is a catch-all phrase that usually applies to random noise of thermal origin
- Noise voltages can be specified by their frequency spectrum (power per hertz) or by their amplitude distribution
- Band-limited white Gaussian noise is a type of noise that has equal power per hertz in some band of frequencies and exhibits a Gaussian distribution of amplitudes
Square Wave
- A square wave is a signal that varies in time with a constant amplitude and frequency
- It is characterized by amplitude and frequency (and perhaps phase)
- The peak amplitude and the rms amplitude of a square wave are the same
Pulses
- A pulse is a signal that has a defined amplitude and pulse width
- Pulses can have positive or negative polarity and can be positive-going or negative-going
- The pulse repetition rate and duty cycle can be defined for a train of periodic pulses
Steps and Spikes
- Steps and spikes are signals that are used to describe what happens in a circuit
- They can be used to describe a square wave or a sudden jump in voltage
Logic Levels
- Pulses and square waves are used in digital electronics to represent two possible states (HIGH and LOW)
- Each digital logic family specifies legal HIGH and LOW states and an input decision threshold
Signal Sources
- Signal sources are essential for testing circuits and come in three types: signal generators, pulse generators, and function generators.
- Signal generators:
- Are sinewave oscillators with a wide range of frequency coverage.
- Can modulate (vary) output amplitude or frequency.
- Can be sweep generators, which repeatedly sweep output frequency over a range.
- Often have digital frequency synthesizers as the signal source.
- Pulse generators:
- Make only pulses, but with adjustable parameters such as pulse width, repetition rate, amplitude, polarity, and rise time.
- Can generate pulse pairs with settable spacing and repetition rate.
- Often have logic-level outputs for easy connection to digital circuitry.
- Function generators:
- Are the most flexible signal sources.
- Can generate sine, triangle, and square waves over a wide frequency range.
- Can control amplitude and dc offset.
- Often have provision for frequency sweeping, modulation, and pulse outputs.
Capacitors and AC Circuits
- Capacitors are essential components in AC circuits, used for waveform generation, filtering, and blocking and bypass applications.
- Capacitors have two wires and the property Q = CV, where Q is the stored charge and C is the capacitance.
- The capacitance of a parallel-plate capacitor is proportional to the area and inversely proportional to the spacing.
Capacitors
- A capacitor is a device that stores energy in its internal electric fields.
- The energy stored in a capacitor is UC = 1/2 CV^2, where UC is the energy in joules, C is the capacitance in farads, and V is the voltage in volts.
- Capacitors come in various shapes and sizes, including parallel-plate, cylindrical, and film capacitors.
- Different types of capacitors have unique properties, such as ceramic, polyester, polycarbonate, polystyrene, polypropylene, Teflon, and glass dielectric.
- Capacitors are used in various applications, including filtering, energy storage, and resonant circuits.
Math and Capacitors
- The derivative of the defining equation Q = CV is I = CdV/dt, which shows that the current is proportional to the rate of change of voltage.
- The capacitance of a capacitor can be calculated using the formula C = 8.85 x 10^-14 εA/d, where ε is the dielectric constant, A is the plate area, and d is the spacing.
Capacitors in Parallel and Series
- The capacitance of several capacitors in parallel is the sum of their individual capacitances.
- The formula for capacitance in parallel is: Ctotal = C1 + C2 + C3 + …
Capacitors in Series
- The formula for capacitance in series is: Ctotal = 1 / (1/C1 + 1/C2 + 1/C3 + …)
- For two capacitors in series, the formula is: Ctotal = (C1C2) / (C1 + C2)
Capacitors Charging and Discharging
- The current that flows in a capacitor during charging is not proportional to voltage, but rather to the rate of change of voltage.
- The power associated with capacitive current is not turned into heat, but is stored as energy in the capacitor's internal electric field.
- The energy stored in a capacitor is returned when it is discharged.
RC Circuits: V and I versus Time
- When dealing with AC circuits, there are two approaches: talking about V and I versus time, or amplitude versus signal frequency.
- The simplest RC circuit is described by the equation: CdV/dt = I = -V/R
- The solution to this equation is: V = Ae^(-t/RC)
- The product RC is called the time constant of the circuit.
Time Constant
- The time constant is in seconds, for R in ohms and C in farads.
- A microfarad across 1.0k has a time constant of 1 ms.
RC Charging Circuit
- The equation for the RC charging circuit is: I = CdV/dt = Vf - Vout / R
- The solution to this equation is: Vout = Vf + Ae^(-t/RC)
- The constant A is determined by initial conditions, such as V = 0 at t = 0.
- The final equation is: Vout = Vf(1 - e^(-t/RC))
Decay to Equilibrium
- Eventually, V reaches Vf, which is the final voltage.
- The "5RC rule of thumb" states that a capacitor charges or decays to within 1% of its final value in five time constants.
Simplification by Thevenin Equivalents
- Thevenin equivalents can be used to simplify more complicated circuits.
- By using the Thevenin equivalent of a voltage divider, the output V(t) can be found.
Circuit Example: Time-Delay Circuit
- The circuit uses an RC and a pair of CMOS buffers to produce a delayed digital waveform.
- The first buffer provides a replica of the input signal, with low source resistance, to prevent input loading by the RC.
- The RC output has the characteristic decays and causes the output buffer to switch 10 μs after the input transitions.
One Minute of Power Circuit
- The circuit uses a comparator, powered from a positive dc voltage, to drive its output either to V+ or to ground.
- The comparator has three important properties: it doesn't draw current from its inputs, it drives loads up to 20mA, and its output is either HIGH (at V+) or LOW (ground).
- The circuit uses a voltage divider (R3R4) to set a reference voltage, which is 37% of the supply voltage.
- When the START button is pushed, the capacitor C1 charges quickly, causing the comparator's output to switch to +5V.
- After the button is released, the capacitor discharges exponentially, with a time constant of τ = R2C1, which is set to 1 minute.
Applications of the One Minute of Power Circuit
- The output can be used to drive an LED, a piezo beeper, or an electromechanical relay to control a load.
- The relay provides electrical isolation between the timing circuit and the load.
- The circuit can be used to make a self-stopping flashlight key fob, a noise-making device, or an electromechanical relay to control a load.
Details of the Circuit
- The addition of R1 limits the peak current to 5mA when charging the capacitor.
- The comparator output may bounce around due to electrical noise, which can be fixed by adding hysteresis (positive feedback) to the circuit.
- It's a good idea to bypass the dc supply with a capacitor to prevent noise and voltage droop.
Differentiators
- A differentiator circuit produces an output proportional to the rate of change of the input waveform (dVin/dt).
- The ideal differentiator circuit is impractical, but a simple RC circuit can approximate the function.
- The output of the differentiator is proportional to the input waveform's rate of change, but with a small error due to the resistor's presence.
Applications of Differentiators
- Differentiators can detect leading edges and trailing edges in pulse signals.
- They can be used in digital circuitry to generate short pulses in response to input transitions.
Unintentional Differentiators
- Capacitive coupling between signals can cause unintentional differentiators, which can be recognized by their output waveforms.
- Broken connections can also cause unintentional differentiators, which can be diagnosed by recognizing the characteristic output waveforms.
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This quiz covers the introduction to the field of electronics, its history, and development from vacuum-tube to solid-state electronics.