# Basics

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) $$\Large V_1=h_{11}I_1+h_{12}V_2$$
$$\Large I_2=h_{21}I_1+h_{22}V_2$$

$$\Large z_{11}=\frac{V_1}{I_1}$$ input impedance
$$\Large z_{12}=\frac{V_1}{I_2}$$ 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:

1. Replace power supplies and measuring devices with their internal resistance
2. Simplify as much as possilbe
3. 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: $$\Large V_C=V_S(1-e^{-\frac{t}{RC}})$$

Discharging voltage: $$\Large V_C=V_S*e^{-\frac{t}{RC}}$$

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

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