Electronics and Electrical Engineering Formulas Flashcards

These flashcards cover general electronics, AC/DC circuit analysis, electromagnetism, Maxwell's equations, Op-Amps, transistors (BJT/FET), and control system theory based on the provided lecture notes.

How is the Duty Cycle ($D.C.$) calculated based on the signal timing?

$$D.C. = \frac{T_{ON}}{T_{PERIOD}}$$

What is the relationship between Frequency ($f$) and Period ($T$)?

$$f = \frac{1}{T}$$

What is the formula for Electric Field Intensity ($E_F$)?

$E_F = \frac{F}{Q}$, where $F$ is Force in Newtons and $Q$ is Charge in Coulombs.

What is the formula for Gravitational Force between two masses?

$F = G \frac{M_1 M_2}{r^2}$ where $G \approx 6.674 \times 10^{-11}\,N$

What is Plank's Constant formula for energy?

$$E = h \times f$$

What do the mnemonics ICE and ELI signify regarding capacitors and inductors?

ICE: In a Capacitor, Current ($I$) leads Voltage ($E$); ELI: In an Inductor, Voltage ($E$) leads Current ($I$).

What is the time constant ($\tau$) for a Capacitor and an Inductor?

Capacitor: $\tau = R \times C$; Inductor: $\tau = \frac{L}{R}$

How is the energy stored calculated for a capacitor and an inductor?

Capacitor: $E = \frac{1}{2} C V^2$; Inductor: $E = \frac{1}{2} L I^2$

What are the relationships defined by the turns ratio ($a$) in a transformer?

$$a = \frac{N_p}{N_s} = \frac{V_p}{V_s} = \frac{I_s}{I_p} = \sqrt{\frac{Z_p}{Z_s}}$$

How is Total Capacitance ($C_{TOTAL}$) calculated for capacitors in series?

$$C_{TOTAL} = (C_1^{-1} + C_2^{-1} + C_3^{-1} + ...)^{-1}$$

What are the formulas for Inductive Reactance ($X_L$) and Capacitive Reactance ($X_C$)?

$X_L = 2\pi fL$ and $X_C = \frac{1}{2\pi fC}$

What is the resonance formula for an RLC circuit?

$$f_r = \frac{1}{2\pi \sqrt{LC}}$$

What is the formula for Bandwidth ($B.W.$) in an RLC circuit?

$$B.W. = \frac{R}{2\pi L}$$

How is Quality Factor ($Q.F.$) calculated from the resonant frequency and bandwidth?

$Q.F. = \frac{f_r}{B.W.}$ or $Q.F. = \frac{X_L}{R}$

What is the formula for Resistance at a specific temperature ($R$)?

$R = R_0 (1 + \alpha [T - T_0])$ where $\alpha$ is the temperature coefficient.

According to Ohm's Law, how is Terminal Voltage ($V_T$) expressed considering internal resistance ($r$)?

$$V_T = E - Ir$$

What is the formula for Coulomb's Law (Electric Force $F_e$)?

$$F_e = \frac{1}{4\pi \epsilon_0} \frac{q_1 q_2}{r^2}$$

How is Electric Flux ($\Phi$) calculated?

$$\Phi = E \cdot A \cos(\theta)$$

What is Magnetic Force ($F_B$) on a charge moving through a magnetic field?

$$F_B = |e| v B \sin(\theta)$$

What is the relationship between Magnetic Flux Density ($B$) and Magnetic Field Intensity ($H$)?

$$B = \mu H$$

What does the 1st Maxwell Equation ($\nabla \cdot D = \rho_v$) signify?

Volume charge density is the same as the divergence of electric flux density.

What are the characteristics of an Ideal Operational Amplifier (Op-Amp)?

Infinite voltage gain ($A_v = \infty$), Infinite input resistance ($R_{IN} = \infty$), and Zero output resistance ($R_{OUT} = 0$).

What is the Voltage Gain ($A_v$) for an Inverting and a Non-Inverting Op-Amp?

Inverting: $A_v = -\frac{R_f}{R_{in}}$; Non-Inverting: $A_v = 1 + \frac{R_f}{R_{in}}$

In which BJT region does the transistor act as an amplifier?

Active Region (Base-Emitter is forward-biased, Base-Collector is reverse-biased).

How is the JFET Drain Current ($I_D$) calculated?

$$I_D = I_{DSS} (1 - \frac{V_{GS}}{V_P})^2$$

What is the transfer function for a Negative Feedback system?

$$T(s) = \frac{G}{1 + GH}$$

What are the Settling Time ($T_s$) and Rise Time ($T_r$) for a 2% criteria in a 1st order system?

$T_s = 4\tau$ and $T_r = 2.2\tau$

What is the condition for a stable system using the Routh-Hurwitz Condition (for a 3rd order system)?

Inner Product ($i.p.$) must be greater than Outer Product ($o.p.$).