1250

CTools

 

Algebra

Simultaneous equations

Example (pdf)

Circuits

Basic DC circuits

Sources: v, i independ, depend

Example 1 (pdf)

Passive sign convention

Example 1 | (pdf)

Example 2 | (pdf)

Kirchhoff's laws

Current sums at nodes | (pdf)

Voltage loops | (pdf)

Writing v and i eqns

Example 1 | (pdf)

Example 2 | (pdf)

Solving circuits

Example 2 (pdf)

Ohm's law

Statement

Series resistors

Parallel resistors

Resistor networks

Example 1 (pdf)

v and i dividers

Voltage divider

Current divider

Example (pdf)

Thevenin equivalent

Thevenin equivalent circuit

Norton equivalent circuit

Thevenin<->Norton xform

Example (pdf)

Deriving Thevenin equivalent

vThev = vout open circuit

RThev derivation

R seen from output

vThev/ishort circuit

1V/iinto circuit

Example (pdf)

Max power xfer

Example (pdf)

Fourier Series

Definition | (pdf)

Orthogonality of sinusoids | (pdf)

Completeness

Coefficients (pdf)

Inner products

Determining scaling factors

Example series

Example 1 (pdf)

Example 2 (pdf)

Example 3 (pdf)

Square wave (pdf)

Triangle wave (pdf)

†Gaussian wave

Applications

Speech recognition (pdf)

Fft Matlab® plot code: FourierSerAppSpeechRec.m

Circuit response

Example (pdf)

A/D and D/A Converters

A/D (Analog-to-Digital)

Sampling and aliasing

Sample and hold

Counting A/D

Successive approximation A/D

Dual-slope A/D

Flash A/D

Sample and hold waveforms

Aliasing and Nyquist theorem

Dual-slope converter

Flash converter

Successive approximation

D/A (Digital-to-Analog)

Weighted R D/A

R-2R ladder D/A

PWM (Pulse Width Modulated) D/A

Conversion spectrum

RLC circuits

C (capacitor) equations

i = C dv/dt

Series capacitors

Parallel capacitors

Initial conditions

C = open circuit

Charge sharing

V src model

Final conditions open circuit

Energy stored

Example 1 (pdf)

Example 2 (pdf)

General RC/RL solution

General solution

Time const Thev equiv

Solution procedure

Example 1 (pdf)

Example 2 (pdf)

Example 3 (pdf)

Example 4 (pdf)

Example 5 | (pdf)

Example 6 (pdf)

Example 7 (pdf)

Op-Amps

Golden rules

V+ = V-

Zero input current

Example 1 (pdf)

Example 2 (pdf)

Superposition

Circuits

VDC + VDC

Example 1 (pdf)

Example 2 (pdf)

Circuits

VAC + VAC

Example (pdf)

Complex Analysis

explanations of j

Convenient examples

Basic math

Addition and subtraction

Example | (pdf)

Multiplication

Rationalization

Example 1 | (pdf)

Example 2 | (pdf)

Conjugate

Definition | (pdf)

Example 1 | (pdf)

Example 2 | (pdf)

Example 3 | (pdf)

Magnitude

Example 1 | (pdf)

Phase

Re[]

Example 1 | (pdf)

Example 2 | (pdf)

Im[]

Roots and Powers

Nth roots

example | (pdf)

Nth roots of unity

Powers

example | (pdf)

Rect and Polar Forms

Euler's formula (complex exp)

Polar form

Rect<->polar xform triangle

Example 1 | (pdf)

Example 2 | (pdf)

Example | (pdf)

Phasors

Tutorial | (pdf)

Rotating stick shadow

Identities

Phasor math

Phasor<->inv-phasor xform

Example 1 | (pdf)

Example 1 (cont) (pdf)

Example 2 | (pdf)

Example 2 (cont) (pdf)

Phasor diagrams

Example (pdf)

Impedance circuits

Ohm's law

Statement

Series impedances

Parallel impedances

Impedance networks

Example 1 (pdf)

Example 2 (pdf)

Kirchhoff's laws

Example (pdf)

Node-voltage method

Example (pdf)

Thevenin equivalent

Deriving Thevenin equivalent

Example 1 (pdf)

Example 2 (pdf)