Electronics

Basic electronics theory.

Formulas

Some important formulas:

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

With these two formulas, you can build other calculations. Eg:

$P=VI=V(V/R)=V^{2}/R$

Diodes

Diodes restrict the direction of current flow. A diode is forward bias is when the anode has a higher voltage which for most diodes allow current to flow. On the other hand, a reverse bias occurs when the cathode has a higher voltage and most diodes restrict current.

An ideal diode would allow all current flow at any forward bias and none in the reverse bias. However, real-world behavior is bound by the following limitations which are found in the datasheet:

• Non-zero Forward voltage ($V_{f}$). A diode typically requires some forward voltage before it becomes forward bias and allows current to flow.
• A non-infinite breakdown voltage ($V_{br}$). A diode when in reverse bias may allow current to flow in the reverse direction when a certain reverse voltage is reached. This is sometimes useful behavior and is a feature of Zener diodes.
• A non-zero forward voltage drop. If voltage drop is important, find diodes with a low voltage drop such as Schottky diodes.
• A delay in switch action. High frequencies may be an issue as a result. Schottky diodes have faster switching.
• A limit on the maximum current flow
• A limit on heat dissipation. Both in terms of continuous current and peak current.

Note that 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.

The forward bias and reverse bias behavior is charted in a current-voltage (I-V) curve that graphs current flow relative to the forward or reverse voltage. These graphs are found in the datasheet.

Regular p-n junction Diodes

The most common diode are the 1N4001 through 1N4007 rectifier diodes and are used to rectify power. For lower voltage applications, use a signal diode such as the 1N4148.

A light emitting diode (LED) emits light when forward biased.

Schottky diode

Schottky diodes have better characteristics than a normal diode and is more expensive. Better characteristics include:

• Has a lower forward voltage drop
• Faster recovery and switch action

Zener Diode

Zener diodes have a specific breakdown voltage that allows current to flow while in reverse bias, known as the Zener breakdown. This breakdown voltage is useful when creating a constant voltage reference, where excess voltage is 'spilled' over through the Zener diode.

When using a Zener as a voltage reference, a resistor is required in order to limit current that can pass through the diode. As a result, using a Zener as a a voltage regulator with a load is inefficient since a lot of power is wasted through the resistor.

Strictly speaking, Zener diodes have a breakdown voltage of under 5 volts. Anything higher are usually Avalanche diodes. A related diode used to suppress voltage spikes is the Transient Voltage Suppression (TVS) Diode which clamps a voltage from spiking past a certain voltage.

Transistors

There are three types of transistors:

1. Bipolar Junction Transistor (BJT)
2. Field-Effect Transistor (FET)
3. IGBT (BJT with MOSFET gate)

In short, the differences between the types are outlined in the following table.

	BJT	MOSFET	IGBT
Cost	Cheap	Medium	Expensive
Voltage Capabilities	Wide: 40-1000V	Medium: 20-400V	Very high voltages, up to 4000V
ESD Damage	Robust against static discharge	Can be easily damaged	Can be easily damaged
Noise	Linear behavior results in low noise	Non-linear behavior results in high noise	Not intended as an amplifier
Switching Speed	<2MHz when used as a saturating switch. Slow turn-off	<20MHz with high power loads	<50kHz
Efficiency	High efficiency at high current when in saturation mode	low-medium currents acts as a low-valued resistor	Efficient for very large currents, similar but less than BJT
Ease of Use		Easy to drive because of open circuit gate
Current Direction	collector to emitter	Bi-directional when on	collector to emitter
Important Characteristics	Abs. Max $I_{C}$: Maximum current through collector Abs. Max $V_{CEO}$: Maximum voltage through collector and emitter Abs. Max $V_{CBO}$: Maximum voltage through collector and emitter $V_{CE}$: Voltage required to turn on $H_{fe}$: current gain	Abs. Max $I_{D}$: Maximum current through drain $V_{DSS}$: Breakdown voltage $R_{DS}$: Resistance when on Threshold $V_{GS}$: Minimum voltage to start turning on. Use a $V_{GS}$ with an acceptable $R_{DS}$ value.

Transistors come in a few different packages:

TO-90	TO-220
Signal transistors; dissipates a few hundred milliwatts of heat	Typically used for power transistors; dissipates few watts or more with a heatsink

Different packages have different amounts of power dissipation. As a rule of thumb, for every degrees above 25 degrees Celsius, subtract 5 milliwatts from the maximum rating. Silicon will degrade past 150 degrees Celsius.

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. Fundamentally, the two types are identical with the polarities reversed. This results in NPN transistors turning on when current flows through the base while the PNP version turns off. 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 internal diode (the arrow in the transistor diagram). Current only begins flowing when the forward voltage is sufficient for the diode (the minimum V_BE(SAT) value), which in most general purpose transistors starts at around 0.6V. Current flowing through the base is directly proportional to the current through the collector and emitter (the gain or h_FE). The flavor of NPN and PNP flips the direction of this diode. NPN transistors 'turn on' when the base has a voltage higher than the emitter while PNP exhibit the opposite behavior where it turns on when the base has a lower voltage than the collector.

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. It is also more intuitive to use as we can turn something on by setting something high.

PNP with its reversed polarities sometimes result in awkward circuit configurations since in order to allow the base to be lower than the collector, loads must be placed on the emitter ('low') side. Furthermore, extra care is also required to ensure that the maximum voltage on the collector 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 typically have a complementary PNP version with similar characteristics. For example:

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

Modes

There are 4 modes a BJT can be in:

• Cutoff - when the transistor acts like an open circuit and allows no current flow between collector and emitter. Cutoff only occurs when the voltage between the base and emitter is below the threshold voltage of the diode (ie. the arrow, between the collector and emitter).
• Active - When the voltage exceeds the threshold voltage of the diode, current from collector to emitter is proportional to the current flowing into the base, amplified by the transistor's gain.
• Reverse-Active - Similar to Active but current flow is reversed, where current flows from emitter to collector.
• Saturation - Once the voltage between the collector and base exceeds the saturation threshold voltage, the transistor acts like a short circuit and current flows freely from collector to emitter. The current flowing into the base no longer governs the current flowing through collector and emitter.

In summary, the voltage relation to the different modes are:

Voltage Relations	NPN	PNP
$V_{E}<V_{B}<V_{C}$	Active	Reverse
$V_{E}<V_{B}>V_{C}$	Saturation	Cutoff
$V_{E}>V_{B}<V_{C}$	Cutoff	Saturation
$V_{E}>V_{B}>V_{C}$	Reverse	Active

Field-Effect Transistor

Field-Effect Transistors are transistors that use a field-effect the control current flow. A field effect can be demonstrated by a glowing fluorescent tube placed near a high voltage source. Rather than having current control the electron flow through the silicon, a FET instead uses a electric field. Since FETs is a different technology, it also has slightly different terminology: Base is replaced by a gate, collector is the source, and emitter is the drain. The electrical isolation between the gate and the source is demonstrated by the various symbols representing a FET (gate never touches the source). As a result, only the voltage potential between the gate and source rather than current controls current flow. Similar to BJT, there are also two types of FETs: N-Channel and P-Channel.

N-Channel	P-Channel

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 or a voltage lower than source.

When choosing a FET for a project, the most important characteristics to keep in mind are:

• $R_{DS(on)}$ - Resistance between the drain and the source while ON and OFF.
• $V_{GS(th)}$ - Threshold voltage required to turn the FET on or off.

As a side note, some FETs are fabricated by the controlled oxidation of silicon, also known as metal-oxide semiconductor (MOS) and are called MOSFETs. For TO-220 packages, the metallic backs used to attach a heat sink to are connected to the drain. Care must be taken if multiple MOSFETs are connected to one heat sink in the event they require electrically separate sinks.

FETs that are used for logical level typically have an 'L' in the name. For example, the IRLZ44N.

Some useful FETs include:

N-Channel	P-Channel
Logic capable (3.3V or 5V): IRF3708, Rds = 0.0095Ohm at Vgs=4.5V IRLZ44N, Rds = 0.025ohm at Vgs=5.0v General Purpose: 2N700 FQP30N06 IRF540	Logic capable (3.3V or 5V): NDP6020P General Purpose: 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. $Cparallel=C1+C2+C3...$ $Cseries=1/(1/C1+1/C2+...)$

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:

1. Bipolar
   • Structured as either PNP or NPN
2. Metal Oxide Semiconductor
   • Classified under PMOS, NMOS, and CMOS
3. 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

Operational Amplifiers (op amp for short) are versatile components which can be used in many applications.

At its basic form, op-amps have 5 terminals: two inputs, one output, a positive and negative supply voltage. Its operation is to sense the difference between the two input terminals and multiply this by a differential/open-loop gain of A which ideally is infinite, but in reality is in the order of 10⁵ - 10⁶. An ideal op-amps have inputs that draw no current (infinite impedance, it only senses voltage) while the output maintains its voltage regardless of any load (zero impedance) by acting as a current source when positive and current sink when negative. When both inputs are equal, an ideal op-amp should have an output voltage of 0V, a property known as common-mode rejection.

Amplifier gains represents a ratio of an output to an input (100,000:1). Datasheets may write the gain as 100V/mV or 100,000mV/mV. Alternatively, the gain can be written using a logarithmic measure known as a decibel. $Gain_{dB}=20log|A|$. Typical values in decibels are 120dB (1,000,000 gain), 100dB (100,000 gain). Negative gains means there will be a 180° phase difference.

Real life op-amps are very close to the ideal nowadays though there are a few limitations to keep in mind:

• Output voltage cannot be greater than positive rail or less than negative rail. Op-amps that have output voltages come very close to its positive and negative input voltages are sometimes called rail-to-rail op-amps.
• 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.
• Some op-amps offer an offset null terminal which 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. Ideally this should be 0A. A LM358 has 20 nanoamps.

Additional example uses here: https://www.arrow.com/en/research-and-events/articles/fundamentals-of-op-amp-circuits

Inverting Op-Amp Circuit

The inverting op-amp circuit is the most commonly used configuration. As the name implies, this circuit inverts the signal. A negative feedback loop is created by connecting the output to the negative input.

Since op-amps with feedback loops such as the one above are governed by the formula $v_{O}/A=v_{2}-v_{1}$ where A is ideally infinite, the op-amp will try to satisfy $0=v_{2}-v_{1}$. In other words, an op-amp in an inverting circuit will try to make both inputs be at same voltage. The behavior between these two pins is referred to as a virtual ground and can be used ease the calculation of $v_{O}$ by using it as a reference point. While it is called a virtual 'ground', it isn't actually ground. It is just a quasi-concept to say that both input pins have roughly the same voltage. In fact, $v_{2}$ could be offset to some positive or negative voltage to bias the output.

Using the concept of a virtual ground, we can save a lot of extra work by safely assuming that both input pins have about equal voltage.

If we do not use the virtual ground idea to make this assumption, the calculation requires a bit more work. Since we know that the current flowing through both resistors must be equal (because no current can flow into the input of an op-amp), calculating the current through R1 and solving for V=IR after R2 will give us our answer. The work to do this can be seen on the right hand image.

It turns out that a inverting op-amp's output ends up being $v_{O}=-{\frac {R_{2}}{R_{1}}}v_{i}$. Despite having an infinite bias, this circuit's use of negative feedback allows us to precisely control its output gain.

Basic Op-Amp Circuit

The inverting op-amp where the output is inverted and adjusted by the two resistors.

Summation Op-Amp Circuit

The output is the sum of the input voltages, weighted by their resistor values.

Non-Inverting Op-Amp

A non-inverting op-amp circuit is identical to the inverting op-amp circuit with the difference being the input is now applied to the positive input.

The input in a non-inverting op-amp circuit is not inverted. The bias is also different because our input is no longer directly going into the feedback loop. Other example configurations are given below.

Voltage Follower / Buffer

The output follows the input and is also known as a buffer or unity gain.

Summation Op-Amp Circuit

The summer adds all voltages. Inputs can be weighed based on the input resistor.

Example Components

An example op-amp is the LM741 which contains only one op-amp in the 8-pin PDIP package.

A LM358 is a 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

Comparator

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

• $V_{+}>V_{-}$, then $V_{out}=+V_{CC}$
• $V_{+}<V_{-}$, then $V_{out}=-V_{CC}$

Typically, $V_{-}$ is connected to a voltage reference (typically ground, or using a zener diode).

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

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