# Basics

Current flows from positivle lead to negative lead.

Kirchoff's current law: the sum of the currents into a node equals the sum of the current flowing out of the node.

Kirchoff's voltage law: the sum of the voltages around any closed circuit is zero.

# Power

\( \Large P=V*I \) measured in Watts (W) (Joules per second ( \( \Large \frac{J}{s} \) )

Resistor power
\( \Large P=I^2*R \) and \( \Large P=\frac{V^2}{R} \)

# Resistance

## Calculating material resistance

\( \Large R=\frac{\rho L}{A} \)

\( \rho - resistivity \)

\( L - length \)

\( A - cross sectional area \)

Common \( \rho \) values: silver 1.6, copper 1.7, nichrome 100, carbon 3500

## Color codes

Band closest to one end is first digit. Second color is second digit and thrid digit is multiplier. Last band is tolerance.

## Resistors in cicuit

Resistors in series: \( R=R_1+R_2+R_3 + ... \)

Resistors in parallel: \( \Large \frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} + ...\)

Two resistors in parallel: \( \Large R=\frac{R_1*R_2)}{R_1+R_2} \)

## Internal resistance

\( \Large R_{int}=(\frac{V_{NL}}{V_{FL}}-1)R_L \)

\( V_{NL} - no\: load\: voltage \)

\( V_{FL} - load\: voltage \)

\( R_L - load\: resistance \)

# RMS (Root mean square)

RMS value for sine wave:

\( \Large V_{RMS}=V_{pk}\frac{1}{\sqrt{2}}=V_pk*0.7071 \)

RMS combined

\( \Large V_{RMS}=\sqrt{\frac{V_1^2}{2}+\frac{V_2^2}{2}+...} \)

# Twoport

Twoport is described by a matrix of 4 values: 2 currents and 2 voltages.

z-parameters (ohm)

\(\Large V_1=z_{11}I_1+z_{12}I_2 \)

\(\Large V_2=z_{21}I_1+z_{22}I_2 \)

y-parameters (siemens)
\(\Large I_1=y_{11}V_1+y_{12}V_2 \)

\(\Large I_2=y_{21}V_1+y_{22}V_2 \)

h-parameters (h11 ohm, h12 h21 none, h22 siemens)
\(\Large V_1=h_{11}I_1+h_{12}V_2 \)

\(\Large I_2=h_{21}I_1+h_{22}V_2 \)

\(\Large z_{12}=\frac{V_1}{I_2} \) transfer impedance

\(\Large z_{21}=\frac{V_2}{I_1} \) transfer impedance

\(\Large z_{22}=\frac{V_2}{I_2} \) output impedance

\(\Large y_{11}=\frac{I_1}{V_1} \) input admittance

\(\Large y_{12}=\frac{I_1}{V_2} \) transfer admittance

\(\Large y_{21}=\frac{I_2}{V_1} \) tranfer admittance

\(\Large y_{22}=\frac{I_2}{V_2} \) output admittance

h11 and h12

\(\Large h_{11}=\frac{V_1}{I_1} \) input impedance

\(\Large h_{12}=\frac{V_1}{V_2} \) voltage transmittance

h21 and h22

\(\Large h_{21}=\frac{I_2}{I_1} \) current transmittance

\(\Large h_{22}=\frac{I_2}{V_2} \) output admittance

# Capacitor

## Capacitor energy

\[\Large W=\frac{IVt}{2}=\frac{qV}{2}=\frac{CV^2}{2}\]

## RC circuit

RC - low pass filter

CR - high pass filter

### Time constant

Time constant: \(\Large \tau=RC \)

Finding time constant:

- Replace power supplies and measuring devices with their internal resistance
- Simplify as much as possilbe
- Calculate

# Inductor

## Inductor energy

\[\Large W=L*i^2 \]

## RL circuit

RL - step response r(0)=1

LR - step response r(0)=0

Time constant: \(\Large \tau=\frac{L}{R} \)

Cutoff frequency: \( \Large f_{co}=\frac{R}{2\pi L} \)

### Carging and discharging voltage

Charging voltage: \(\Large V_C=V_S(1-e^{-\frac{t}{RC}})\)

### Cutoff frequency

\(\Large f_c=\frac{1}{2\pi RC} \)

i

# LED

## Forward voltage

\( V_{forward}=1.7V \)

\( V_{forward}=2.0V \)

\( V_{forward}=2.1V \)

\( V_{forward}=2.2V \)

\( V_{forward}=3.0V \)

## Calculating current

\[ \Large I=\frac{V_{supply}-V_{forward}}{R} \]

# Logic

## NAND latch

S | R | Action |

0 | 0 | Not allowed |

0 | 1 | Q=1 |

1 | 0 | Q=0 |

1 | 1 | No change |

## NOR latch

S | R | Action |

0 | 0 | No change |

1 | 0 | Q=1 |

0 | 1 | Q=0 |

1 | 1 | Invalid state |

# Ohm's law

\[ \Large V=IR \]

\[ \Large I=\frac{V}{R} \]

\[ \Large R=\frac{V}{I} \]

# Transmittance

Ratio between input and output

\(\Large T=\frac{V_{out}}{V_{in}} \)

\(\Large T=\frac{I_{out}}{I_{in}}\)

## Decibel (dB)

The decibel(dB) is a unit of measurment used to express the ratio of one value of a power or field quantity to another on logarithmic scale.

\(\Large L_p=10\log({\frac{P}{P_0}})dB \)

For field quantities it is usual to consider the ratio of the squares of measured field

\(\Large L_F=\ln(\frac{F}{F_0})N_p=10\log({\frac{F^2}{F_0^2}})dB=20\log({\frac{F}{F_0}})dB \)

Same applies for voltages:

\(\Large L_G=10\log{(\frac{V_{out}}{V_{in}})}dB \)