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Basic electronics theory.

Physics

Some formulas that are fundamental:

Ohm's Law: $$ V=IR $$
Power (watts): $$ P=VI $$

With these two formulas, you can build other calculations. Eg: $P=VI=V(V/R)=V^{2}/R$

Fundamentals

$V_{cc}$ is the power supply voltage. It is the voltage supplied at the collector.

Diodes

   Anode (+)         Cathode (-)
   ----------[   |]----------

   Electronic symbol:
             | \  | 
   ----------|   &gt;|---------
             | /  |

Forward bias = on, lets current pass through
Reverse bias = off, restricts current completely

The I-V curve shows relationship between voltage and current. The ideal diode will allow all current through at any forward voltage and no current at any reverse voltage. A real diode will have some limitations:

Forward voltage ( $V_{f}$ ) - voltage at which the diode turns on and allows forward current to flow. This is the voltage that is required for the diode to be in forward bias
Breakdown voltage ( $V_{br}$ ) - the negative voltage which the diode fails to stop current from flowing backwards. You can expect the diode to withstand this voltage in the reverse bias before reverse current flows freely. A diode in breakdown is not necessarily broken. What breaks it is the amount of current that goes through it in this state because the diode does not limit the current.
Forward voltage drop - the voltage that is 'lost' by going across the diode

Diodes will have a maximum forward current with the limitation typically because of heat dissipation. This means there will be two maximums: One that is constant (maximum forward continuous current, $I_{F}$ ) and one that is peak.

Determining the forward voltage with a multimeter can be done by using the test option across the diode. Test by connecting the black probe to cathode (the side of the diode with the black stripe) and the red probe to anode.

Example Components:

1N4148 Signal Diode
1N4001 Rectifier Diode (for rectifying power)

Schottky diode

Similar to a normal diode but:

Has a lower forward voltage drop
Faster switch action

In general, a shottky diode has better characteristics than a typical diode but is more expensive.

Zener Diode

Has a specific zener breakdown voltage which allows current to flow in reverse bias
Zener breakdown voltage is typically labeled with the device. Eg. 5V1 = 5.1 volts

Can be used to create a constant voltage reference by exploiting the breakdown voltage. Any excess voltage will be 'spilled' over via the zener diode.

The resistor is required in order to limit current that can pass through the diode. Because of this design, attempting to use a zener diode as a voltage regulator for a load is inefficient since a lot of power is wasted with the resistor. For high load or a large voltage difference, the resistor will generate a lot of heat (P=IV).

Transient Voltage Suppression (TVS) Diode

A TVS diode is similar to two zener diodes that are connected together in opposite direction. Connecting this to a circuit will prevent voltage from spiking past a certain voltage. It does not conduct in either direction until the breakdown voltage is reached.

Transistors

There are two types: Bipolar Junction Transistor (BJT) and Field-Effect Transistor (FET). BJT controls current by the current through in the base by the gain. FET controls current by the voltage in the gate.

Bipolar Junction Transistor

BJT transistors consists of 2 transitions between the positively doped (P) and negatively doped (N) silicon. The two combinations of these layers result in NPN and PNP types each exhibiting different behavior. In summary, NPN transistors turn on when the base has a higher voltage than the emitter while PNP transistors 'turns on' when the base has a lower voltage than the emitter. The simplified construction and diagram for each type can be seen in the figure below. A simple mnemonic for the symbol is NPN's arrow is it does not point in. When reading data sheets or schematics, PNP transistors may sometimes drawn upside down (flipped vertically).

In a nutshell, a transistor turns on when current flows through the diode (the arrow in the transistor diagram). This only happens if the voltage is sufficient (the minimum V_BE(SAT) value), which in the case for most general purpose transistors starts at around 0.6V. The current that is allowed to flow through the transistor is the current through the base multiplied by the transistor's gain (h_FE). Applying this principle, we can see NPN transistors turn on when the base has a voltage higher than the emitter and PNP transistors turn on when the base is lower than the collector. Consequently, when driving loads with BJT, loads must be placed on 'high' side for NPN and on the 'low' side for PNP in order to drive the transistor.

NPN transistors are easier to use especially with digital devices such as microcontrollers as the input voltage to the base need not match the collector voltage. PNP transistors are less intuitive to use because loads must be placed on the low side in order to ensure that the collector remains at a higher voltage than the base even when the transistor is turned on. Extra care is also required to ensure that the voltage on the collector side isn't so high that unintended current flows through the base. For example, if the base is controlled by a 5V microcontroller, attempting to drive loads higher than 5.6V (5V + 0.6 V_BE) will result in current flowing through the base uncontrollable by the microcontroller.

When choosing a BJT, the important factors to consider are:

Maximum collector current (I_C)
Maximum voltage between collector and emitter (V_CEO)
The gain (h_FE)

NPN transistors will have a complementary counterpart with similar characteristics.

NPN	PNP	V_CE	I_C	P_D
BC547	BC557	45V	100mA	500mW
BC337	BC327	45V	800mA	625mW
TIP 29	TIP 30	40V	1A	2W
TIP3055	TIP2955	60V	15A	90W
2n3904	2n3906	40V	200mA	625mW

Transistors come in a few different packages:

TO-90 - signal transistors; dissipates a few hundred milliwatts of heat
TO-220 - power transistors (looks like fets); dissipates few watts or more with a heatsink

Modes

Cutoff Mode

Fully off; blocks all current.

Cutoff happens when:

NPN transistor: Voltage between base and emitter is less than some voltage threshold ( $V_{BE}<V_{TH}$ ), where $V_{TH}$ is some positive value such as 0.7V.
PNP transistor: Voltage between base and emitter is greater than some voltage threshold ( $V_{BE}>V_{TH}$ ), where $V_{TH}$ is some negative value such as -0.7V.

NPN: $V_{E}>V_{B}<V_{C}$
PNP: $V_{E}<V_{B}>V_{C}$

There is a specific forward voltage required before semiconductors conduct (like a diode); until that happens, the current flowing through the transistor is 0.

When the forward voltage is met, the base and the emitter acts as a short circuit and no current is limited. This means it is important to limit the amount of current that can flow from the base to the emitter (with a resistor).

Active Mode

Partially on. Also known as the linear region because there is a relationship between the current flowing through the transistor and the current flowing through the base.

$I_{C}=h_{FE}*I_{B}$ , where $h_{FE}$ is the current gain, also sometimes written as a uppercase beta.

$h_{FE}$ may change from operating conditions.

NPN: $V_{E}<V_{B}<V_{C}$
PNP: $V_{E}>V_{B}>V_{C}$

Example: A typical transistor has a $h_{FE}$ of 100. If a transistor has 1mA flowing through the base ( $I_{B}$ ), then 100mA can flow through the collector (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): I_C ). The current flowing through the emitter will be equal to the sum of the base and collector (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): I_E = I_C + I_B )

Saturation Mode

Fully on; Acts like a short circuit between the collector and emitter.

Changing the current flowing through the base will not affect the current through the collector.

NPN: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): V_E < V_B > V_C
PNP: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): V_E > V_B < V_C

Ideally, the voltage drop between collector and emitter (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): V_{CE} ) is 0. In practice, it is typically something small at around 0.2V. This voltage drop is also known as the saturated emitter-collector voltage or Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): V_{CE(Sat)} .

On a PNP transistor, the voltage drop is negative since the collector has a higher voltage than the emitter and base.

It is important to limit the amount of current that can flow from the collector to emitter because the transistor acts as a short circuit.

Important characteristics

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): V_{CEO} is the maximum voltage between the collector and emitter in an open circuit.
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): V_{CBO} is the maximum voltage between the collector and base in an open circuit.
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): V_{EBO} is the maximum voltage between the emitter to the base base in an open circuit.
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): I_C is the continuous collector current. This is the amount of power that can be dissipated by the transistor while operating in saturation mode (ie. smallest voltage drop Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): V_{CE(Sat)} * I_C ). If operating in any other mode, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): V_{CE} could be higher and the power generated could be higher!
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): I_{CP} is the pulse collector current
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): h_{FE} is the current gain and may be different at different voltages and collector currents.

Power dissipation is the total energy that can be dissipated by the component. For every degrees above 25 degrees Celsius, subtract 5 milliwatts from the maximum rating. Silicon will degrade past 150 degrees celsius.

Field-Effect Transistor

Most commonly fabricated by the controlled oxidation of silicon (ie. metal-oxide semiconductor, the MOS in MOSFET).

A MOSFET can be thought of as a variable resistor where the resistance is a function of the voltage difference between the gate and source.

Like BJT transistors, there are two types of FETs. In a nutshell:

N Channel - Source is connected to ground. To let current flow, gate is connected to a higher voltage.

P Channel - Source is connected to power. To let current flow, gate is connected to ground.

The back of MOSFETS (for heat sinks) are connected to the drain. Multiple mosfets connected to one heat sink must be electrically isolated.

Important datasheet values to keep in mind are:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): R_{DS(on)} - Resistance between the drain and the source while ON and OFF.
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): V_{GS(th)} - Threshold voltage required to turn the FET on or off.

Examples:

N-Channel: IRF540, IRLZ44N
P-Channel: IRF9540

Capacitors

Capacitors can be used to smooth out voltage, as reservoirs for electrical energy storage, or to block DC current.

Capacitors allow DC to pass for a very short period of time until the capacitor is charged. On the contrary, AC passes freely through them, but with a changed, rectified, shape.

Capacitor's capacitance is measured in Farads (F). Typically, capacitors have smaller units and are typically written as micro-farads (µF) or pico-farads (pF).

1000 µF = 1F
1000 pF = 1 µF

Multiple capacitor's capacitance can be added when connected in parallel. It is reduced when connected in series. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): Cparallel = C1 + C2 + C3 ... Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): Cseries = 1 / (1/C1 + 1/C2 + ...)

A perfect capacitor should have zero resistance, also known as the equivalent series resistance (ESR). A good capacitor should have a low ESR. Failing capacitors might still have a proper capacitance, but a very high ESR.

When using a capacitor, ensure that you do not exceed the rated voltage. For electrolytic capacitors, ensure you have connect the polarities correctly.

Capacitor Tiers

The list here was gathered from https://www.tomshardware.com/reviews/power-supplies-101,4193-5.html.

Japanese capacitors are typically higher quality. These include:

Rubycon
United Chemi-Con (or Nippon Chemi-Con)
Nichicon
Sanyo/Suncon
Panasonic
Hitachi
FPCAP or Functional Polymer Capacitor (ex-Fujitsu caps segment, which was bought by Nichicon)
ELNA

Other high quality brands include:

Cornell Dubilier (USA)
Illinois Capacitor (Currently owned my Cornell Dubilier)
Kemet Corporation (USA)
Vishay (USA)
EPCOS (TDK company, Germany)
Würth Elektronik (Germany)

Taiwanese manufacturers with factories in China perform well and are cheaper.

Taicon (belongs to Nichicon)
Teapo
SamXon (except GF series which belongs to a lower Tier)
OST
Toshin Kogyo
Elite

Above grade:

Jamicon
CapXon

Bottom of the barrel:

G-Luxon
Su'scon
Lelon
Ltec
Jun Fu
Fuhjyyu
Evercon

IC Technology

Silicon IC technology can be classified into:

Bipolar
- Structured as either PNP or NPN
Metal Oxide Semiconductor
- Classified under PMOS, NMOS, and CMOS
BiCMOS
- Employs both CMOS and Bipolar transistors in the same semiconductor chip

Bipolar Junction Transistors (BJT) are manufactured in either NPN or PNP. Transistor-Transitor Logic (TTL) is a logic family that is built on BJT.

Complementary metal oxide semiconductor (CMOS) technology is used to construct digital logic as well as some analog circuits using a combination of PMOS and NMOS transistors. Negative Channel Metal Oxide Semiconductor (NMOS) is a type of semiconductor that is built with n-type source and drain and a p-type substrate. Carriers are electrons and when a voltage is applied to the gate, NMOS will conduct. NMOS are faster than PMOS since carriers bare electrons and travels twice as fast as holes. In contrast, Positive Channel MOS (PMOS) which works by moving electron vacancies or holes. A a voltage is applied to the gate, PMOS will not conduct.

Benefits of CMOS technology are low static power consumption and high noise immunity.

Operational Amplifiers

Symbolized as a sideways pointing triangle with 5 inputs. The inputs are:

Differential inputs:

Non-inverting (positive) input
Inverting (negative) input

Output, with its voltage referenced to common ground:

Output

Outer rails, which provides power to the op-amp:

$V_{S+}$
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): V_{S-}

The input to an op-amp is the difference in voltage between the two input terminals. The golden rule for op-amps:

The input draws no current; Treat the input with an infinitely high input impedance.
The output attempts to make the voltage difference between the inputs zero (for closed-loop?)

Output voltage cannot be greater than positive rail or less than negative rail.

An example op-amp is the 741 which contains only one op-amp in the 8-pin PDIP package. A 358 has 2 op-amps.

An op-amp functions as a differential amplifier with the output voltage equal to the difference of the non-inverting input and the inverting input voltage, multiplied by the open-loop gain (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): A_{OL} ). Op-amps are designed to have a large open-loop gain, typically over 100,000.

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): V_{OUT} = A_{OL}(V_+-V_-)

When an op-amp is used like a comparator, it is in the open-loop configuration. Using an op-amp in an open-loop configuration makes it very easy to saturate the op-amp because a tiny voltage difference between the input pins will yield a very large change in the output.

To reduce the sensitivity, a closed-loop configuration can be used where the op-amp's output is feed back to one of the input in order to stabilize itself.

Negative Feedback: When the feedback is routed to the inverting input (negative). Output counteracts changes to input, and lets the circuit achieve equilibrium.

Positive Feedback: Feedback is routed to the non-inverting input (positive). The output quickly goes into one of two states: Saturating at the positive or negative supply rail value. Less common.

LM358: Low cost, low power, a dual op-amp.

Characteristics

Power supply: Can be either single or dual supply.

Single: Voltage given to positive supply rail, with the negative supply rail connected to ground
Dual: Voltage is given to the positive and negative supply rail. Negative supply rail does not need to be ground and can be some negative voltage.

Open-loop differential voltage gain. Typically 100dB, or 100,000 gain.

1dB = 1000x voltage gain.

The voltage gain decreases as input frequency increases.

Wide unity gain bandwidth is the highest frequency the op-amp can operate with a gain of 1 before distorting the signal

Input offset voltage is the voltage difference between the two input pins when shorted together. ie. Shorting the inputs will still yield a value of 'input-offset-voltage*Gain' in the output. A LM358 has 3mV.

On some op-amps, an offset null terminal can be used to compensate for the offset voltage.

Input offset current is the amount of current flowing into each of the input terminals in order to bias the internal transistors. A LM358 has 20 nanoamps.

The output current has two conditions based on the differential output voltage.

Positive: Output acts as a current source (current is pushed out of the output terminal to raise output voltage) and
Negative: Output acts as a current sink (current is drawn into the output terminal, lowering the output voltage).

Comparator

An op-amp can be used as a comparator to compare two input signals.

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): V_+ > V_- , then Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): V_{out} = +V_{CC}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): V_+ < V_- , then Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): V_{out} = -V_{CC}

Typically, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): V_- is connected to a voltage reference (typically ground, or using a zener diode).

This acts as a 1-bit analog to digital converter.

Buffer Signal

Simplest closed-loop op-amp circuit, where the output is tied to the negative inverting input terminal. This creates a voltage follower and effectively makes the op-amp have a gain of 1, also known as a unity gain. Signals passed through this circuit are neither amplified or attenuated.

The use for this is to buffer the signal between to different circuits. This is done because the impedance between the input and output are different. The input impedance is low, but the impedance in the output is high.

Dual Voltage Supply

A dual voltage is required if a AC signal is desired.

When using a DC input source, you can create a negative voltage using a DC-to-DC voltage converter, such as the TC7660H.

Alternatively, use a 'virtual ground' by dividing the input voltage. This requires the impedance on both sides of the virtual ground to be equal. An op-amp can be used to

Inverting Amplifier

Connect the op-amp's output through a resistor $R_{f}$ and the input signal through another resistor Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): R_{in} to the negative inverting input terminal with.

The non-inverting input is connected to ground.

By doing so, the gain can be controlled using this formula: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): \text{Voltage Gain} = \frac{V_{out}}{V_{in}} = -\frac{R_f}{R_{in}}

Non-Inverting Amplifier

Connect the op-amp's output through a resistor Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): R_f and ground through another resistor Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): R_2 to the negative inverting input terminal with.

The non-inverting input terminal is connected to Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): V_{in} .

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): \text{Voltage Gain} = 1 + \frac{R_f}{R_2}

It is not possible to build a non-inverting amplifier circuit with a gain less than 1.