diff --git a/01_Devices/Actives/BJT.tex b/01_Devices/Actives/BJT.tex index fc39876..20098d9 100644 --- a/01_Devices/Actives/BJT.tex +++ b/01_Devices/Actives/BJT.tex @@ -1,13 +1,11 @@ \subsection{Bipolar Junction Transistor (BJT)} -A BJT is three-port (has three terminals), active, non-linear (the -relationship between the voltage and current is not a straight line) -and time-variant (behaviour changes as their parameters drift due -to temperature, age, etc.) device. It is physically built from two -PN junctions that share a single region, with the two junctions -oriented oppositely. This shows up in its governing model. It is -called a \emph{bipolar} device because both electrons and holes -are involved in the conduction process. +A BJT is three-port, active, non-linear and time-variant device. +It is physically built from two PN junctions that share a single +region, with the two junctions oriented oppositely. This shows +up in its governing model. It is called a \emph{bipolar} device +because both electrons and holes are involved in the conduction +process. The three terminals are the base (B), the collector (C) and the emitter (E). It is often called a \emph{current controlled device} diff --git a/01_Devices/Passives/Capacitor.tex b/01_Devices/Passives/Capacitor.tex index c89ea6e..60b9f43 100644 --- a/01_Devices/Passives/Capacitor.tex +++ b/01_Devices/Passives/Capacitor.tex @@ -1,56 +1,94 @@ \subsection{Capacitor} -A capacitor is a two-port passive device that stores energy in the form of -an electric field. The property of a capacitor is called capacitance and is -measured in Farads (F). The core relationship between charge, capacitance -and voltage is given by: -\begin{align*} - Q = C \cdot V \\ - \frac{dQ}{dt} &= C \cdot \frac{dV}{dt} \hspace{1cm} \text{(assuming \(C\) is constant)} \\ - I &= C \cdot \frac{dV}{dt} \hspace{1cm} [I = \frac{dQ}{dt}] -\end{align*} -This is the fundamental relationship between current and voltage in a -capacitor or if you may call this the capacitor's version of Ohm's law. -The inverse of capacitance is called elastance (\(S\)) and is measured in Farads -inverse (F\(^{-1}\)). +An ideal capacitor is a two-port, passive, linear, time-invariant, +non-dissipative device that stores energy (\& thus charge) in the +form of an electric field. -The impedance of a capacitor is given by: -\[ - Z_C = \frac{1}{j\omega C} = \frac{1}{j 2 \pi f C} = \frac{1}{s C} -\] -The inverse of impedance is called admittance (\(Y\)) and is measured in -Siemens (S). The relationship between impedance and admittance is: -\[ - Y = \frac{1}{Z} = \frac{1}{\frac{1}{sC}} = sC -\] -You'll notice when we apply KCL to circuits within this book, we'll mostly -use admittance \(Y\) to express the impedance, we do this as it simplifies -the analysis a lot. The admittance version of Ohm's law is: -\[ - I = V \cdot Y -\] -The impedance of a capacitor is inversely proportional to frequency. This -means that at low frequencies, the impedance of a capacitor is very high and -at frequencies, the impedance of a capacitor is very low. This is why -capacitor effects are more pronounced at high frequencies as their -impedance drops enough to load the circuit. This is also why capacitors are -used for decoupling (they act as a short circuit at high frequencies). +\begin{itemize} + \item \textbf{Capacitance:} + The relationship between charge and + voltage is expressed by a proportionality factor called capacitance + (\(C\)) and is measured in Farads (F). It also gives us the + capacitor's version of Ohm's law: + \begin{align*} + Q = C \cdot V \\ + \frac{dQ}{dt} &= C \cdot \frac{dV}{dt} \hspace{1cm} \text{(assuming \(C\) is constant)} \\ + I &= C \cdot \frac{dV}{dt} \hspace{1cm} [I = \frac{dQ}{dt}] + \end{align*} + The inverse of capacitance is called elastance (\(S\)) and is measured in Farads + inverse (F\(^{-1}\)). + \item \textbf{Impedance:} + Unlike resistor where a proportionality factor directly relates + voltage and current, a capacitor is different, the relationship + between voltage and current is related instead by a differential + equation. We thus can not describe resistance of a capacitor in the + same way we do for a resistor. We must somehow trick the above + capacitor relationship into giving us a proportionality factor + between voltage and current. Lapalace Transform can be used to + achieve this, + \begin{align*} + I &= C \cdot \frac{dV}{dt} \\ + I(s) &= C \cdot s V(s) \\ + V(s) &= \frac{1}{sC} I(s) + \end{align*} + We can now define the impedance of a capacitor as the ratio + of voltage to current in the Laplace domain: + \[ + Z_C = \frac{1}{s C} = \frac{1}{j\omega C} = \frac{1}{j 2 \pi f C} + \] + \item \textbf{Admittance:} + The inverse of impedance is called admittance (\(Y\)) and + is measured in Siemens (S). The relationship between impedance + and admittance is: + \[ + Y = \frac{1}{Z} = \frac{1}{\frac{1}{sC}} = sC + \] -An ideal capacitor is a linear (that is, the relationship between voltage and -current is a straight line) and time-invariant (that is, the relationship -between voltage and current does not change with time) of the three passive -components. It is also the only device that in its ideal form does not -dissipate energy. - -A capacitor can be formed anywhere two conductors are separated by an -insulator. The charges are stored on the surface of the conductors and the -energy is stored in the electric field between the conductors. The energy -stored in a capacitor is given by: -\begin{align*} - I &= C \cdot \frac{dV}{dt} \\ - P &= V \cdot I \\ - P &= V \cdot C \cdot \frac{dV}{dt} \\ - P &= C \cdot V \cdot \frac{dV}{dt} \\ - P &= C \cdot \frac{1}{2} \cdot \frac{d(V^2)}{dt} \hspace{1cm} [\frac{d(V^2)}{dt} = 2V \cdot \frac{dV}{dt}] \\ - \int P dt &= \int C \cdot \frac{1}{2} \cdot \frac{d(V^2)}{dt} dt \\ - E &= \frac{1}{2} C V^2 -\end{align*} + You'll notice when we apply KCL to circuits within this book, + we'll mostly use admittance \(Y\) to express the impedance, we + do this as it simplifies the analysis a lot. The admittance + version of Ohm's law is: + \[ + I = V \cdot Y + \] + \item \textbf{Frequency Response:} + The impedance of a capacitor is inversely proportional to + frequency. This means that at low frequencies, the impedance + of a capacitor is very high and at frequencies, the impedance + of a capacitor is very low. This is why at high frequencies, + the capacitor starts to load the circuit which is often a + very desirable effect in many applications. This is also why + capacitors are used for decoupling (they act as a short + circuit at high frequencies). + \item \textbf{Energy and Power:} + The energy and power stored in a capacitor is given by: + \begin{align*} + I &= C \cdot \frac{dV}{dt} \\ + P &= V \cdot I \\ + P &= V \cdot C \cdot \frac{dV}{dt} \\ + P &= C \cdot V \cdot \frac{dV}{dt} \\ + P &= C \cdot \frac{1}{2} \cdot \frac{d(V^2)}{dt} \hspace{1cm} [\frac{d(V^2)}{dt} = 2V \cdot \frac{dV}{dt}] \\ + \int P dt &= \int C \cdot \frac{1}{2} \cdot \frac{d(V^2)}{dt} dt \\ + E &= \frac{1}{2} C V^2 + \end{align*} + \item \textbf{Types of Capacitors}: + There are many types of capacitors, some of the most common are: + \begin{itemize} + \item \textbf{Ceramic Capacitor}: Used for decoupling and filtering. + They are very useful in power supply circuits. Examples include + 0805, 0603, 0402, etc. + \item \textbf{Electrolytic Capacitor}: Used for bulk capacitance. + They are very useful in power supply circuits. Examples include + 10uF, 100uF, 1000uF, etc. + \item \textbf{Tantalum Capacitor}: Used for bulk capacitance. + They are very useful in power supply circuits. Examples include + 10uF, 100uF, 1000uF, etc. + \item \textbf{Film Capacitor}: Used for decoupling and filtering. + They are very useful in power supply circuits. Examples include + 10nF, 100nF, 1uF, etc. + \end{itemize} + \item \textbf{They're everywhere in the real world}: + A capacitor exists anywhere where you have two conductors + separated by an insulator. The charges are stored on the + surface of the conductors and the energy is stored in the + electric field between the conductors. +\end{itemize} diff --git a/01_Devices/Passives/Diode.tex b/01_Devices/Passives/Diode.tex index 30b5c16..37ec214 100644 --- a/01_Devices/Passives/Diode.tex +++ b/01_Devices/Passives/Diode.tex @@ -2,8 +2,169 @@ \subsection{Diode} A diode is a two-terminal, active, non-linear and time-variant device that allows current to flow in one direction while blocking -it in the opposite direction. The most common type of diode is the -semiconductor diode, which is made from a piece of semiconductor -material (usually silicon) that has been doped with impurities to create -a p-n junction. Other types of diodes include Schottky diodes, Zener -diodes, light-emitting diodes (LEDs) and photodiodes. +it in the opposite direction. + +It is constructed from a semiconductor material where one side is doped +with a material that has an excess of electrons and the other side +is doped with a material that has a slightly less electrons that +the first side. The region where the two side meet is called the +PN junction \& due to recombinations there are no free charge +carriers. For a voltage to cross the depletion region, it must be +of greater than a known magnitude called the threshold voltage +(determined by the material, doping and the depletion width) and +is typically around 0.7V for silicon diodes and 0.3V for germanium +diodes. + +\begin{enumerate} + \item \textbf{Types of Diodes}: + There are many types of diodes, some of the most common are: + \begin{itemize} + \item \textbf{Rectifier Diode}: Used to convert AC to DC.\ They + are very useful in power supply circuits. Examples include 1N4001, + 1N4007, 1N5408, etc. + \item \textbf{Zener Diode}: Used to regulate voltage. They exploit + the reverse breakdown region of the diode to maintain a + constant voltage across the diode. Examples include the + 1N4733A (5.1\,V), 1N4742A (12\,V), and the BZX79 series. + \item \textbf{Light Emitting Diode (LED)}: Used to emit + light when current flows through it. Under the photovoltaic + effect, they can also be used to convert light into electrical + current. Although they aren't as efficient as photodiodes. + Examples include the 5\,mm red T-1 3/4 (e.g.\ Kingbright L-53LID), + and high-power types such as the Cree XLamp XP-G3 and Lumileds + Luxeon Rebel. + \item \textbf{Schottky Diode}: Used for fast switching + applications. The Schottky diode has a lower forward voltage + drop than a regular diode, which allows it to switch on and + off faster. Examples include the 1N5817, 1N5819, and the + SS14 (surface-mount). + \item \textbf{Photodiode}: Used to convert light into + electrical current. Examples include the BPW34, BPW21, and + the SFH 203 series. + \item \textbf{Varactor Diode}: Used to vary capacitance in + a circuit. The varactor diode is a reverse-biased diode that + has a variable capacitance that changes with the applied voltage. + Examples include the BB135 and the 1SV149, commonly used in + RF tuning circuits and voltage-controlled oscillators (VCOs). + \item \textbf{TVS Diode}: Used to protect circuits from voltage + spikes. The TVS diode is a bidirectional diode that can clamp + voltage spikes to a safe level. These are often used to protect + sensitive electronics from electrostatic discharge (ESD) and + other transient voltage events. Examples include the P6KE + series (unidirectional/bidirectional, 600\,W) and the + SMBJ series (surface-mount). + \end{itemize} + \item \textbf{Diode Parameters}: + The parameters of a diode are: + \begin{itemize} + \item \textbf{Forward Voltage Drop (\(V_F\))}: The voltage drop + across the diode when it is forward biased. + \item \textbf{Reverse Breakdown Voltage (\(V_{BR}\))}: The voltage + at which the diode will conduct in reverse bias. + \item \textbf{Reverse Saturation Current (\(I_S\))}: The current + that flows through the diode when it is reverse biased. + \item \textbf{Maximum Forward Current (\(I_F\))}: The maximum + current that can flow through the diode when it is forward biased. + \item \textbf{Maximum Reverse Current (\(I_R\))}: The maximum + current that can flow through the diode when it is reverse biased. + \end{itemize} + \item \textbf{Diode Models}: + The models of a diode are: + \begin{itemize} + \item \textbf{Ideal Diode Model}: The ideal diode model assumes + that the diode has zero forward voltage drop and infinite reverse + resistance. It is a good approximation for low current applications. + It is given by the following equation: + \[ + I = \begin{cases} + 0 & \text{if } V_D < 0 \\ + \infty & \text{if } V_D > 0 + \end{cases} + \] + \item \textbf{Shockley Diode Model}: The Shockley diode model + is a more accurate model that takes into account the forward voltage + drop and the reverse saturation current. It is a good approximation + for high current applications. + \[ + I = I_S \left( e^{\frac{V_D}{n V_T}} - 1 \right) + \] + where: + \begin{itemize} + \item \(I\) is the current through the diode. + \item \(I_S\) is the reverse saturation current. + \item \(V_D\) is the voltage across the diode. + \item \(n\) is the ideality factor (typically between 1 + and 2). + \item \(V_T\) is the thermal voltage, given by \(V_T = \frac{kT}{q}\). + \end{itemize} + This model does not account for the reverse breakdown conduction of + the diode, nor does it account for the series or breakdown resistance + of the diode. + \item \textbf{Piecewise Linear Model}: The piecewise linear model + is a more accurate model that approximates the current-voltage + relationship as a series of linear segments. It is obtained by + asymptotically solving the Shockley Diode Model in two separate + voltage regimes: forward, cutoff. The breakdown regime is added as + an independent term to account for reverse breakdown conduction. + The model also includes the effects of series resistance and breakdown + resistance. + \begin{enumerate} + \item \textbf{Series Resistance:} + The Shockley Diode Model treats the entire applied voltage \(V_D\) + as appearing across the ideal exponential junction. In a real diode, + part of \(V_D\) drops across the bulk and contact series resistance + \(R_S\), so only the remainder, the junction voltage + \(V_j = V_D - I R_S\), drives the exponential term: + \[ + I = I_S \left( e^{\frac{V_D - I R_S}{n V_T}} - 1 \right) + \] + This equation is transcendental in \(I\) and has no closed-form + solution. The piecewise linear model is obtained by solving it + asymptotically in three separate voltage regimes. + \item \textbf{Forward Regime:} + For \(I \gg I_S\), the \(-1\) term is negligible and + \(I \approx I_S e^{V_j / (nV_T)}\), so + \[ + V_j \approx n V_T \ln\!\left(\frac{I}{I_S}\right) + \] + Because the logarithm varies slowly, \(V_j\) changes by only + \(n V_T \ln(10) \approx 60\,\text{mV}\) per decade of current, so + across a diode's typical operating range \(V_j\) is well + approximated as constant. Fixing \(V_j \approx V_{TH}\), the + junction voltage at some nominal operating current \(I_0\), and + substituting into \(V_j = V_D - I R_S\) gives + \[ + I \approx \frac{V_D - V_{TH}}{R_S} \hspace{1cm} \text{if } V_D \geq V_{TH} + \] + \item \textbf{Cutoff Regime:} + For \(-V_{BR} \leq V_D < V_{TH}\), the current is small enough that + \(I R_S\) is negligible, so \(V_j \approx V_D\), and \(V_D\) is not + large enough for the exponential term to matter. The Shockley model + then reduces directly to + \[ + I = I_S \left( e^{V_D / (nV_T)} - 1 \right) \approx -I_S \approx 0 + \] + since \(I_S\) is typically \(10^{-9}\) to \(10^{-15}\,\text{A}\). + \item \textbf{Breakdown Regime:} + Reverse breakdown arises from avalanche multiplication or Zener + tunneling, mechanisms entirely absent from the minority-carrier + diffusion current that the Shockley equation models. No asymptotic + limit of the exponential term can reproduce this behavior, so it + must be introduced as an independent term. Modeled with the same + linear structure as the forward regime, using breakdown resistance + \(R_{ZK}\): + \[ + I \approx \frac{V_D + V_{BR}}{R_{ZK}} \hspace{1cm} \text{if } V_D < -V_{BR} + \] + \item \textbf{Assembled Model} + \[ + I \approx + \begin{cases} + \dfrac{V_D + V_{BR}}{R_{ZK}} & \text{if } V_D < -V_{BR} \\[2mm] + 0 & \text{if } -V_{BR} \leq V_D < V_{TH} \\[2mm] + \dfrac{V_D - V_{TH}}{R_S} & \text{if } V_D \geq V_{TH} + \end{cases} + \] + \end{enumerate} + \end{itemize} +\end{enumerate} diff --git a/01_Devices/Passives/Inductor.tex b/01_Devices/Passives/Inductor.tex index 7e37631..be96e73 100644 --- a/01_Devices/Passives/Inductor.tex +++ b/01_Devices/Passives/Inductor.tex @@ -1,53 +1,108 @@ \subsection{Inductor:} -An inductor is a two-port passive device that stores energy in the form of -a magnetic field. The property of an inductor is called inductance and is -measured in Henrys (H). The core relationship between flux, inductance -and current is given by: -\begin{align*} - \Phi &= L \cdot I \\ - \frac{d\Phi}{dt} &= L \cdot \frac{dI}{dt} \hspace{1cm} \text{(assuming \(L\) is constant)} \\ - V &= L \cdot \frac{dI}{dt} \hspace{1cm} [V = \frac{d\Phi}{dt}] -\end{align*} -This is the fundamental relationship between voltage and current in an -inductor or if you may call this the inductor's version of Ohm's law. -The inverse of inductance is called reluctance (\(R\)) and is measured in -Henrys inverse (H\(^{-1}\)). -\[ - R = \frac{1}{L} -\] -The impedance of an inductor is given by: -\[ - Z_L = j\omega L = j 2 \pi f L = s L -\] -The inverse of impedance is called admittance (\(Y\)) and is measured in -Siemens (S). The relationship between impedance and admittance is: -\[ - Y = \frac{1}{Z} = \frac{1}{sL} -\] -You'll notice when we apply KCL to circuits within this book, we'll mostly -use admittance \(Y\) to express the impedance, we do this as it simplifies -the analysis a lot. The admittance version of Ohm's law is: -\[ - I = V \cdot Y -\] -The impedance of an inductor is directly proportional to frequency. At low -frequencies, the impedance of an inductor is very low and at high frequencies, -the impedance of an inductor is very high. This is why inductor effects are -more pronounced at low frequencies as their impedance rises enough to load -the circuit. This is also why inductors are used for filtering (they act as -a short circuit at low frequencies). +An ideal inductor is a two-port, passive, linear, time-invariant +and dissipative device that stores energy in the form of a +magnetic field. -An ideal inductor is a linear (that is, the relationship between voltage and -current is a straight line) and time-invariant (that is, the relationship -between voltage and current does not change with time) of the three passive -components. It is also the only device that in its ideal form does not -dissipate energy. The energy stored in an inductor is given by: -\begin{align*} - V &= L \cdot \frac{dI}{dt} \\ - P &= V \cdot I \\ - P &= L \cdot \frac{dI}{dt} \cdot I \\ - P &= L \cdot I \cdot \frac{dI}{dt} \\ - P &= L \cdot \frac{1}{2} \cdot \frac{d(I^2)}{dt} \hspace{1cm} [\frac{d(I^2)}{dt} = 2I \cdot \frac{dI}{dt}] \\ - \int P dt &= \int L \cdot \frac{1}{2} \cdot \frac{d(I^2)}{dt} dt \\ - E &= \frac{1}{2} L I^2 -\end{align*} +\begin{itemize} + \item \textbf{Inductance:} + The relationship between flux and current is + expressed by a proportionality factor called inductance (\(L\)) + and is measured in Henrys (H). It also gives us the inductor's + version of Ohm's law: + \begin{align*} + \Phi &= L \cdot I \\ + \frac{d\Phi}{dt} &= L \cdot \frac{dI}{dt} \hspace{1cm} \text{(assuming \(L\) is constant)} \\ + V &= L \cdot \frac{dI}{dt} \hspace{1cm} [V = \frac{d\Phi}{dt}] + \end{align*} + The inverse of inductance is called reluctance (\(R\)) and is + measured in Henrys inverse (H\(^{-1}\)). + \[ + R = \frac{1}{L} + \] + \item \textbf{Impedance:} + In the same way we did for capacitors, we can use Laplace + Transform to define the impedance of an inductor as the ratio + of voltage to current in the Laplace domain: + \begin{align*} + V &= L \cdot \frac{dI}{dt} \\ + V(s) &= L \cdot s I(s) \\ + \end{align*} + We can now define the impedance of an inductor as: + \[ + Z_L = s L = j\omega L = j 2 \pi f L + \] + \item \textbf{Admittance:} + The inverse of impedance is called admittance (\(Y\)) and is + measured in Siemens (S). The relationship between impedance + and admittance is: + \[ + Y = \frac{1}{Z} = \frac{1}{sL} + \] + You'll notice when we apply KCL to circuits within this book, + we'll mostly use admittance \(Y\) to express the impedance, we + do this as it simplifies the analysis a lot. The admittance + version of Ohm's law is: + \[ + I = V \cdot Y + \] + \item \textbf{Frequency Response:} + The impedance of an inductor is directly proportional to + frequency. At low frequencies, the impedance of an inductor is + very low and at high frequencies, the impedance of an inductor + is very high. This means that at low frequencies, the inductor + does not load the circuit which is often a very desirable + effect in many applications. This is also why inductors are + used for filtering/chokes (they act as a short circuit at low + frequencies but as an open circuit at high frequencies). + \item \textbf{Energy Stored in an Inductor:} + The energy and power stored in an inductor can be derived + from the voltage-current relationship of an inductor: + \begin{align*} + V &= L \cdot \frac{dI}{dt} \\ + P &= V \cdot I \\ + P &= L \cdot \frac{dI}{dt} \cdot I \\ + P &= L \cdot I \cdot \frac{dI}{dt} \\ + P &= L \cdot \frac{1}{2} \cdot \frac{d(I^2)}{dt} \hspace{1cm} [\frac{d(I^2)}{dt} = 2I \cdot \frac{dI}{dt}] \\ + \int P dt &= \int L \cdot \frac{1}{2} \cdot \frac{d(I^2)}{dt} dt \\ + E &= \frac{1}{2} L I^2 + \end{align*} + \item \textbf{Types of Inductors}: + There are many types of inductors. Some common types include: + \begin{itemize} + \item Air Core Inductors: These inductors have no magnetic core and are + typically used in high-frequency applications. + \item Iron Core Inductors: These inductors have a magnetic core made of + iron or ferrite, which increases the inductance and allows for + higher current handling. + \item Toroidal Inductors: These inductors have a doughnut-shaped core, + which helps to reduce electromagnetic interference (EMI) and improve + efficiency. + \item Variable Inductors: These inductors allow for the adjustment of + inductance by changing the position of a movable core or by using a + variable capacitor in series with the inductor. + \end{itemize} + Some special inductors also exist to perform a unique function, such as: + \begin{itemize} + \item Chokes: These inductors are designed to block high-frequency + signals while allowing low-frequency signals to pass through. + \item Transformers: Two or more inductors that are magnetically coupled + to transfer energy between circuits. They are very important in power + (to step up or step down voltage) and signal (to isolate circuits) + applications. + \end{itemize} + \item \textbf{Advise:} These are some important things to keep in mind when + working with inductors. + \begin{itemize} + \item \textbf{Kickback Voltage:} When an inductor is suddenly disconnected + from a circuit, it can generate a high voltage spike (called a transient) + due to the collapsing magnetic field. This phenomenon is known as + \'kickback\' and can damage other components in the circuit. To prevent this, + a flyback diode is often placed across the inductor to safely dissipate + the energy. + \item \textbf{Saturation:} Inductors have a maximum current rating, beyond + which the core material can become saturated. When saturation occurs, + the inductance decreases significantly, and the inductor may not function + as intended. It is important to choose an inductor with an appropriate + current rating for the application. + \end{itemize} +\end{itemize} diff --git a/01_Devices/Passives/Resistor.tex b/01_Devices/Passives/Resistor.tex index f8b5ac9..64f97f3 100644 --- a/01_Devices/Passives/Resistor.tex +++ b/01_Devices/Passives/Resistor.tex @@ -1,27 +1,40 @@ \subsection{Resistor} -A resistor is a two-port passive device that opposes the flow of current, -we call this property resistance. The unit of resistance is Ohm (\(\Omega\)). -Everything has resistance. A good way to imagine resistance is to -think about its value as a constant of proportionality between voltage -and current. The relationship is given by Ohm's law: -\[ - V = I_ \cdot R -\] -The inverse of resistance is called conductance (\(G\)) and is measured -in Siemens (S). The relationship between resistance and conductance is: -\[ - G = \frac{1}{R} -\] +An ideal resistor is a two-port, passive, linear and time-invariant +device that opposes the flow of current. -You'll notice when we apply KCL to circuits within this book, we'll mostly -use conductance \(G\) to express the resistance, we do this as it -simplifies the analysis a lot. The conductance version of Ohm's law is: -\[ - I = V \cdot G -\] -An ideal resistor is a linear (that is, the relationship between voltage and -current is a straight line) and time-invariant (that is, the relationship -between voltage and current does not change with time) of the three passive -components. It is also the only device that in its ideal form does not -store energy. This is why at low frequencies, if a resistor can be used -in place of a capacitor or inductor, use it. +\begin{itemize} + \item \textbf{Resistance:} + This act of opposition is called resistance and is measured in + Ohms (\(\Omega\)). A good way to imagine resistance is to think + about its value as a proportionality factor between voltage and + current. In fact, This is precisely the relationship that gives + us Ohm's law: + \[ + V = I_ \cdot R + \] + \item \textbf{Conductance:} + The inverse of resistance is called conductance (\(G\)) and is + measured in Siemens (S). The relationship between resistance and + conductance is: + \[ + G = \frac{1}{R} + \] + You'll notice when we apply KCL to circuits within this book + that contain resistors, we'll mostly use conductance \(G\) to + express the resistance. This simplifies the analysis a lot. The + ohms law can be rearranged for conductance: + \[ + I = V \cdot G + \] + \item \textbf{Power Dissipation:} + A resistor dissipates energy in the form of heat. The power + dissipated by a resistor is given by: + \[ + P = I^2 \cdot R = V^2 \cdot G + \] + \item \textbf{Non-Ideal Resistor:} + In practise, resistor's are not ideal and thus most of our + assumptions above (linear, time-invariant, dissipative) fall + apart at very high frequencies but for the most part, we can + treat resistors as ideal devices. +\end{itemize} diff --git a/01_Devices/Passives/main.tex b/01_Devices/Passives/main.tex index fe72828..306369b 100644 --- a/01_Devices/Passives/main.tex +++ b/01_Devices/Passives/main.tex @@ -1,8 +1,11 @@ \section{Passives} -These are mostly two-port devices (with two terminals) that can simply -be placed in a circuit and they will work. They can store energy, -dissipate energy, or both but they can never amplify the existing energy. +It is not necessary but it is common to find many two port devices are +passive in nature. Once placed in a circuit, they will start working +automatically as they do not require any external power source to operate. +These devices are ideally linear and time-invariant although in practice, +they are not (for example, a device property can change with temperature, +age, and even the voltage or current interacting with it). \input{01_Devices/Passives/Resistor} \input{01_Devices/Passives/Capacitor} diff --git a/01_Devices/main.tex b/01_Devices/main.tex index 80edae4..6051bd5 100644 --- a/01_Devices/main.tex +++ b/01_Devices/main.tex @@ -5,18 +5,21 @@ \chapter{Devices \& Basic Blocks} and behavior. In the context of analog circuits, devices are primarily classified into two categories: passive and active devices. \begin{itemize} - \item Passive Devices: These devices do not require an external - power source to operate. They can store or dissipate energy - but cannot generate it. Examples of passive devices include - resistors, capacitors, inductors, and transformers. + \item Passive Devices: These do not require an external power + source to operate. They can only attenuate, store or dissipate + energy. \item Active Devices: These devices require an external power - source to operate. They can amplify signals, control current - flow, and perform other functions that passive devices cannot. - Examples of active devices include transistors, and - operational amplifiers. + source to operate. Alongside attenuating, storing, or dissipating + energy, they can also amplify signals and provide gain to the + circuit. \end{itemize} -We'll take a closer look at each device and its characteristics in the -following sections. + +We'll often use the term \'one-port\', \'two-port\', or \'three-port\' to +describe the number of terminals (pins/contacts) a device has. We'll +also use terms like \'linear\' (the relationship between voltage and +current is proportional by a factor), \'time-invariant\' (the relationship +between voltage and current does not drift with time), dissipative +(the device dissipates energy usually in the form of heat). \input{01_Devices/Passives/main} \input{01_Devices/Actives/main}