Basic Electronics on the Go - Types of Resistors

From www.electronicshub.org/types-of-resistors/

Types of Resistors

Like all electronic components, resistors are also available in different sizes, shapes and types. These variations in resistors bring advantages in some types and limitations in other types. This in turn makes some resistors suitable for some applications rather than others. 

Resistors Types Based on Composition

Carbon Composition Resistors

Carbon Composition Resistors are commonly used resistors which are manufactured at low cost. This is because of the simpler construction process. They are generally called carbon resistors. The main composition is finely ground carbon along with ceramic clay acting as a binding agent

This is covered in a plastic case and the leads are made of tinned copper. The proportions of carbon and clay are the factor in determining the resistive value. Resistance is higher when the quantity of carbon is lesser.

Carbon resistors can be manufactured in wide range of values ranging from 1Ω to a high value as 22 MΩ. Due to its low cost, they are used in circuits where cost is a criterion rather than the performance.

The advantages of carbon resistors are its ability to remain undamaged from high energy pulses, available at very low cost and at all local vendors and good durability. The disadvantages are high sensitivity to temperature, unstable noise properties and stability issues when hot.

Carbon composition resistors are suitable for high frequency applications as they have low inductance. They are easily affected by humidity and hence the tolerance is only 5%. They also have a low-medium range power rating i.e. < 5W.

Metal Film type resistors have much higher tolerance and better temperature stability when compared to carbon resistors. Hence they are used in applications like active filters where low temperature coefficient and tight tolerance are required.

Metal oxide resistors have much better temperature stability and better surge current capacity.

Thin Film Resistors

Thin film resistors are manufactured by depositing a resistive layer on an insulating base like ceramic. The thickness of the resistive film is equal to or smaller than 0.1 micro meters.

Vacuum deposition is the technique used to deposit the resistive film on the ceramic. The resistive material which is often an alloy of nickel and chromium called Nichrome is sputtered on an insulator base which is ceramic. This process will create a uniform film of 0.1 micrometer thick.

The thickness of the metallic film can be controlled by controlling the time of sputtering. Patterns are created by laser trimming process on the dense and uniform layer to create and calibrate the resistive path and resistance value.

Thin film resistors can be produced as SMD resistors or axial leaded resistors. Because of their high tolerance and low temperature coefficient, thin film resistors are used in precision applications.

Thick Film Resistors

In thick film resistors, the thickness of resistive film is nearly 1000 times thicker than that in thin film resistors. The main difference between thick film and thin film resistors is the procedure for applying the resistive film. The resistive film in thick film resistors is made from a mixture of a binder, carrier and metal oxide.

Glass frit bonding is used to bind the mixture. Carrier is the extract of organic solvent and oxides of iridium or ruthenium are used. This mixture is made as a paste and the resistive film is produced by applying this paste on to a ceramic base using stencil and screen printing process.

Thick film resistors can be used in applications where less cost is important, high power  and high stability is important.

Wire Wound Type Resistors

Wire wound resistors are the most precise and high power rated resistors. The construction of wire wound resistors involves a winding of thin metal or metal alloy wire around an insulating substrate.

Generally the metals used are manganin or constantan and a nickel chromium alloy which is also called as nichrome is used in case of metal alloy. The resistive value can be varied by varying wrap pattern, diameter, length and type of alloy.


The resistance tolerance of wire wound resistors is as tight as .005% and the power ratings are in the range of 50W-300W. These are precision wire wound resistors. In case of power resistors, the tolerance is 5% and the power rating is in the range of kilo watts.

They are limited to low frequency applications because of the nature of their construction. Since there is a metal wire wound as a coil around an insulator, they act as inductors. This results in reactance and inductance and when used in A.C circuits there is a chance of phase shift when operated at higher frequencies.

There is a possibility to overcome this limitation by winding each half of wire in different directions. This will cancel each other’s inductive effect. These resistors are called as Non-Inductive Wire Wound Resistors. Normally the cost of wire wound resistors is higher when compared to carbon composition resistors. In high frequency applications Non-Inductive Wire Wound Resistors can be used but their cost is more than normal wire wound resistors.

Wire wound resistors are used in many applications. Some of them are circuit breakers, transducers, temperature sensors and current sensors.

Resistors Types Based on Termination and Mounting

SMD Resistors

Surface Mount Devices (SMD) are produced as a result of a technique called Surface-mount Technology (SMT). In this technique the components are placed directly on the printed circuit board.

SMD Resistors are also developed similarly. The development of Surface-Mount Technology and Surface Mount Devices is a result of requirement of smaller, faster, cheaper and more efficient components by PCB manufacturers.

SMD resistors consist of an insulator substrate which is generally ceramic and a layer of metal oxide film is deposited on this substrate. The value of resistance is determined by the thickness of the film.

Because of their small size they are suitable for circuit boards. They have very little inductance and capacitance and can perform well at radio frequencies.

Through-hole Resistors

Through-hole is a mounting technique where the components are inserted into holes that are drilled on a PCB. For this purpose, the electronic component consists of small metallic leads. All the resistors with leads coming out of them for contact purpose come under Through-hole resistors.

Through-hole resistors are available in carbon composition resistors, carbon film resistors, metal film resistors, metal oxide resistors, wire wound resistors and many others.

Apart from discrete components, through-hole resistors can be found as pack of resistors with the usage of Dual in-line package and Single in-line package techniques.

These SIP and DIP resistors are generally used in resistor ladder networks, pull-up and pull-down networks, bus terminators etc.

Resistors Types Based on Shape

Resistors are classified based on their physical shape. They are Square chip, leadless, open and sealed type in the category of Surface–mount technology. Radial and axial type resistors come under leaded type category.

Square chip type includes SMD resistors

Leadless type resistors are round chip resistors and metal electrode lead less face or MELF resistors.

Open type are general wire wound resistors

Radial lead type resistors are vertical taping compatible. Axial lead type resistors are those in which the leads come out of the body axially.

Resistors Types Based on Power Ratings

Resistors can be classified based on their power ratings. The power rating of a resistor is a benchmark used to indicate the maximum permissible power through a resistor for uninterrupted operation at a specified temperature. Beyond this power, the resistor gets hot and may burn up. If a resistor is rated as 0.25W, then a maximum power of 0.25W can be fed to it.Hence it is important to find the power in a circuit.

Power is rate of doing work. In electrical terminology, power is the rate at which energy is transferred by a circuit. Here the energy is electrical energy.

Power P = VI = V2/R = I2R watts.

When a resistor with known resistance and a fixed supply voltage is present then the power is calculated with this resistance along with supply voltage.

For example a resistor of resistance 400Ω and voltage of 12V is used to power up an LED. The power is calculated as

P = V2/R = (12)2 / 400 = 0.36W

Then a resistor of a power rating of 0.50W should be used.

he standard available power ratings are 0.25W, 0.5W, 1W, 2W, 5W, and 25W.Generally resistorsare available with power ratings up to 500W.

Other Types of Resistors

Fixed Resistors

As the name indicates fixed resistors are those which have a predefined or fixed value of resistance. When the term resistor is used, it generally refers to fixed resistor. Ideally fixed resistors should work independent to changes in temperature, voltage and frequency.

However, this is not possible practically as all resistor materials have temperature coefficient which leads to temperature dependency. The stray capacitance which is present in all resistors will result in impedance and hence the actual resistance will be different from expected.

Fixed resistors are available in different sizes, shapes, leaded, leadless, etc. They can be manufactured based on carbon composition type, carbon film type, metal film type, metal oxide film type, wire wound type, SMD, etc.

Variable Resistors

When there are fixed resistors, there is a scope for resistors with resistance value that is not fixed. Variable resistors are those in which the value of resistance can be varied or adjusted.

The resistance path is provided by the  track and the terminals of the device are connected to the track. The wiper is used to increase or decrease resistance through its motion.

Potentiometer

A potentiometer or pot is an electro mechanical resistor with three terminals and is the most commonly used variable resistor.

The two terminals on the either end will deliver a constant resistance which is the formal resistance. The terminal in the center is movable and is called the wiper. This movable wiper maintains contact with the resistive surface.

The resistance between first terminal and the wiper plus the resistance between the wiper and the second terminal is equal to the formal resistance of the device. The name potentiometer is given to this device as it adjusts the  voltage using voltage divider principle.

The best application is their use in tuning circuits  in radio receivers.

Preset

Preset is a variable resistor which is used in occasional adjustment conditions.

Generally presets are mounted on printed circuit board and are adjusted using the rotary control present on top of it with the help of a screw driver. In contrast to potentiometers where the resistance varies linearly, the resistance in preset varies exponentially. 

Presets are made available in single turn and multi turn operations. Presets are used in designs where the value of the resistance is set in the circuit during the time of production. Due to their sensitivity, presets are often used in sensing circuits like temperature or light sensing.

Rheostat

A rheostat is a two terminal variable resistor. In the rheostat, one end of the resistive track of a variable resistor and its wiper terminal are connected to the circuit. This connection will limit the current in the circuit according to the position of the wiper.

Rheostats are used to control the resistance without interrupting the flow of current. Because of this significant flow of current, rheostats are made as wire wound resistors.

Rheostats are used in applications where current is more important than power rating. They are generally used in tuning circuits and power control applications.

Light Dependent Resistor (LDR)

Light Dependent Resistors or Photo resistors are light sensitive resistors whose resistance varies according to the intensity of the light incident on them. 

Light dependent resistors are made of semiconductors with high resistance. In the absence of light or in the dark, the resistance of light dependent resistors is very high usually in the range of Mega Ohms (MΩ).

When light is incident on the surface of light dependent resistors, photons fall on the semiconductor material and the valence electrons of the semiconductor are excited to conduction band.

For the valence electrons to jump to conduction band there should be enough energy in the photons. Therefore the light incident should exceed a certain frequency and the number of free electrons depends on frequency of light. The free electrons will conduct current and hence lowers the resistance.

Based on the semiconductor material used,light dependent resistors are divided into intrinsic and extrinsic. Intrinsic Light dependent resistors use undoped or pure semiconductors like silicon.

There should be enough energy in the photons to excite the entire band gap. Therefore intrinsic light dependent resistors are used for shorter wavelength or higher frequency photons.

On the other hand, extrinsic light dependent resistors use semiconductor materials with impurities in them. These impurities are called dopants and generally boron or phosphorous are used. These impurities create an intermediate energy band which is closer to the conduction band.

Hence the energy required to excite these electrons is less. Lower energy photons i.e. longer wavelength or lesser frequency like Infra-red are suitable for extrinsic light dependent resistors.

Network Resistors

Network resistors are single package resistors with two or more resistors. They generally come in Single in-line package or Dual in-line package.

Resistor networks are used to reduce the board space, improve reliability, reduce solder connections and improve tolerance matching. Generally resistor networks are used in resistor ladders, bus terminators and small computer system interface terminators.

They are available as both surface mount devices and through-hole devices.

Varistor

Varistor is the portmanteau of the  variable resistor. It is an electronic component with non-linear current voltage characteristics like the diode. The resistance in the varistor is changed according to the change in voltage across it. This makes it a voltage sensitive device hence it is also called Voltage Dependent Resistor. Generally varistors are made from semiconductor materials.

The resistance of  the varistor is very high under normal operating conditions. But the resistance decreases dramatically when the voltage increases beyond the rated value of the varistor.

Metal oxide Varistors are the  most common type of varistors. Grains of Zinc oxide are used because it provides P-N diode characteristics. Hence it is used to protect electronic and electrical circuits from over voltage surges.

Basic Electronics on the Go - Resistors

http://www.electronicshub.org/introduction-to-resistors/

What is a Resistor?

A resistor is a device in which electricity cannot pass through it easily. When certain amount electricity is allowed to pass through a resistor, the electrical energy is changed into another form, usually light or heat. The working principle of a bulb is that electricity is passed through the filament usually tungsten, which is a resistor. The energy is converted to and released as light and heat.

The resistor is an electrical component which creates a resistance in the flow of electric current. It is a passive component as it consumes energy from a source (active component).

Although resistors are generally used to reduce the flow of current or lower the levels of voltage in a circuit, they are used in many electronic circuits for many purposes. Some of them are the basic current flow limitation ability, to provide a biasing condition to some of the active elements like transistors or to act as a terminating device in transmission lines.

Practically resistors are discrete components of various forms but are also implemented on integrated circuits.

ResistorSymbols

Generally there are two standards that are used to denote the symbol of a resistor viz.Institute of Electrical and Electronics Engineers (IEEE) and International Electro Technical Commissions (IEC).

The IEEE symbol of resistor is a zigzag line .

Resistance

The definition of resistance can be derived from the Ohm’s law in its Electromagnetic theory form or Continuum form

J = σ E —-1

Here σ is the conductivity of the material i.e. conductor.

E is the electric field developed along the length of conductor due to flow of electrical energy through the conductor.

If ‘V’ is the voltage drop across the conductor and ‘L’ is the physical length of conductor then

E = V/L —-2

The current density J is resulted within the conductor due to the flow of electrical energy through the conductor.

If ‘I’ is the current flowing through the conductor and ‘A’ is the cross sectional area of conductor, then by the definition of current density

J = I/A —-3

Now combining equations 1, 2 and 3

I/A = σ V/L

V = (L/Aσ) I —-4

The term in parenthesis is constant and let us denotes it by ‘R’.

∴V = R I

Resistance Measurement

Resistors are main components in electric and electronic circuits as they determine the amount of current that flows in a circuit and also the potential at different points in a circuit. Therefore it is important to make sure that the value of resistance is known for a given resistor which is placed in a circuit.

From Ohm’s law, it is easy to calculate the resistance. Ohm’s law relates the Voltage V, Current in the circuit I and the Resistance of the resistor R.

R = V/I

∴In terms of units, 1 Ohm (Ω) = 1 Volt (V) / 1 Ampere (A).

In other terms, a resistor is said to be having a resistance of 1Ω when 1A of current is passed through it for a supply voltage of 1V.

Ohmmeter is a device designed specifically for this purpose. A resistor is connected across the terminals of ohmmeter and the reading of the ohmmeter is the value of the resistance of that resistor along with the resistance offered by the wires used to connect the resistor to ohmmeter.

Even though the resistance of wire is very small, it can’t be neglected. Hence the values measured using an ohmmeter is not accurate.

The next best way to determine the resistance is to make use of both voltmeter and an ammeter in the circuit.

Resistivity

Electrical Conductivity of a material is the measure of its ability to conduct current.

Resistivity is the reciprocal of conductivity. Resistivity is the measure of a conductors’ ability to resist the flow of electric current.

Resistance Units

Resistance R = V/I

This results in the units of resistance as volts per ampere. This combination is given a special name called Ohm named after the physicist  Georg Simon Ohm.

Carbon Resistors

Carbon Composition Resistors are commonly used resistors which are manufactured at low cost. This is because of the simpler construction process. They are generally called carbon resistors. The main composition is carbon clay which is covered in a plastic case and the leads are made of tinned copper. The main advantage of carbon resistors is that they are easily available at very low cost at all local vendors and the durability is good. The only disadvantage is that they are very sensitive to temperature.

Carbon resistors can be manufactured in wide range of values as low as 1 Ω value to a high value as 22 MΩ. Due to its low cost, they are used in circuits where cost is a criterion rather than the performance.

Variation of Resistance with Temperature

The effect of changes in temperature is a change in the value of resistance of the material. The reason for this change is not because of the variations in the dimensions of the material but rather the change in the resistivity of the material.

The flow of current in materials like conductors is the movement of electrons between atoms in the presence of an electric field. This is achieved by applying a potential difference across the conductor. This potential difference will cause the negatively charged electrons to move towards the positive terminal from atom to atom. These electrons which move freely between atoms are called free electrons. The conductivity of a material is dependent on the number of these free electrons in the atom of the material.

An increase in temperature on a conductor will result in an increase in its resistance as the atoms will vibrate more. These vibrating atoms will impede the path of the electrons flowing through.

In mathematical terms, a fractional change in resistance is directly proportional to the change in the temperature.

∆R/R0∝∆T

Where ∆R is the small change in resistance

∆R = R – R0

R is resistance at temperature T

R0 is resistance at temperature T0

∆T is change in temperature

∆T = T – T0

If we denote the proportionality constant in the above equation as alpha (α)

Then ∆R/R0 = α∆T

Where α is the temperature coefficient of the resistance.

The temperature coefficient of resistance is used to describe the relative change in resistance in association with change in temperature.

The above equation can be written as

R = R0 [1+α (T-T0)]

If the resistance increases with increase in temperature, then the material is said to be having a positive temperature coefficient. These materials are conductors.

If the resistance decreases with increase in temperature, then the material is said to be having a negative temperature coefficient. These materials are insulators.

The units of temperature coefficient are /0K or K-1.

Resistor Packages

Surface Mount Technology is a technique where the components are directly placed on the surface of the circuit board. These components are called Surface Mount Devices. Resistors are also manufactured as SMDs. SMD Resistors are generally smaller with small leads or no leads. 

Basic Electronics on the Go - The Atom

From  http://www.livescience.com/37206-atom-definition.html


Atoms are the basic units of matter and the defining structure of elements. Atoms are made up of three particles: protons, neutrons and electrons.

 
 Structure of a beryllium atom: four protons, four neutrons and four electrons.


Protons and neutrons are heavier than electrons and reside in the center of the atom, which is called the nucleus. Electrons are extremely lightweight and exist in a cloud orbiting the nucleus. However, the radius of the electron itself is approximately 2.5 times of the  radius of the proton.

Protons and neutrons have approximately the same mass. Atoms always have an equal number of protons and electrons, and the number of protons and neutrons is usually the same as well. Adding a proton to an atom makes a new element, while adding a neutron makes an isotope, or heavier version, of that atom.

The Nucleus


The nucleus was discovered in 1911, but its parts were not identified until 1932. Virtually all the mass of the atom resides in the nucleus. The nucleus is held together by a strong force - the nuclear force,  one of the four basic forces in nature. This force between the protons and neutrons overcomes the repulsive electrical force that would, according to the rules of electricity, push the protons apart otherwise.


Protons

Protons are positively charged particles found within atomic nuclei. They were discovered by Ernest Rutherford in experiments conducted between 1911 and 1919.

The number of protons in an atom defines what element it is. For example, carbon atoms have six protons, hydrogen atoms have one and oxygen atoms have eight. The number of protons in an atom is referred to as the atomic number of that element. The number of protons in an atom also determines the chemical behavior of the element. The Periodic Table of the Elements arranges elements in order of increasing atomic number.

Protons are made of particles called quarks. There are three quarks in each proton — two "up" quarks and one "down" quark — and they are held together by other particles called gluons.

Electrons

Electrons have a negative charge and are electrically attracted to the positively charged protons. Electrons surround the atomic nucleus in pathways called orbitals. The inner orbitals surrounding the atom are spherical but the outer orbitals are much more complicated.

An atom's electron configuration is the orbital description of the locations of the electrons in an unexcited atom. Using the electron configuration and principles of physics, chemists can predict an atom's properties, such as stability, boiling point and conductivity.

Typically, only the outermost electron shells matter in chemistry. The inner electron shell notation is often truncated by replacing the long-hand orbital description with the symbol for a noble gas in brackets. This method of notation vastly simplifies the description for large molecules.

For example, the electron configuration for beryllium (Be) is 1s22s2, but it's is written [He]2s2. [He] is equivalent to all the electron orbitals in a heliumatom. The Letters, s, p, d, and f designate the shape of the orbitals and the superscript gives the number of electrons in that orbital.

Neutrons

Neutrons are uncharged particles found within atomic nuclei. A neutron's mass is slightly larger than that of a proton. Like protons, neutrons are also made of quarks — one "up" quark and two "down" quarks. Neutrons were discovered by James Chadwick in 1932.

Isotopes

The number of neutrons in a nucleus determines the isotope of that element. For example, hydrogen has three known isotopes: protium, deuterium and tritium. Protium, symbolized as 1H, is just ordinary hydrogen; it has one proton and one electron and no neutrons. Deuterium (D or 2H) has one proton, one electron and one neutron. Tritium (T or 3H) has one proton, one electron and two neutrons.

Circuits and Electronics - Breaking the Abstraction Barrier (Lecture 28)

Video Lectures: -  https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-002-circuits-and-electronics-spring-2007/video-lectures/lecture-25/

Lecture Notes: - https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-002-circuits-and-electronics-spring-2007/lecture-notes/

This is our final sequence. So in this sequence, we will violate just about everything that we have learned in this course just to show you that rules and abstractions only take you this far.
At the end of the day, we made a set of assumptions. But as long as you work within those assumptions, you are OK. However, in practical life, many of these assumptions are
violated and things do not quite behave as we expect them to. So you have to be very careful here and understand where the abstractions are violated. And in many cases, you really have to go back to
fundamentals and do things again.

And we got into that playground by making the assumptions of the lumped matter discipline. There were three key assumptions. One assumption was that you are not going to have any net charge build up inside our elements. Notice that even for capacitors, the net charge build up on both the positive and negative plates is 0, so they satisfy our discipline. The second was dPhi by dt was going to be
zero outside our elements. The third assumption of the lumped matter discipline was that our signal speeds of interest would be substantially lower than the speed of light.

So we will start with what I call the double take. So consider the following little scenario. So suppose I have a voltage source, v_I. And that voltage source connects through some resistor, R. And I can measure and observe the voltage v_0 at this point. Let's further assume that from this point, I have a bunch of other wires - three wires- going to different parts of the circuit.

And then one of them  may connect to some other pieces of circuitry, an inverter, in this case.
And then from the inverter, I may have a connection going to something else. Now, let me assume that my input voltage takes a 0 to 1 transition.

What I expect at v_0, given that I'm not connecting my circuit anywhere, in that I have an open circuit here-- so this input connects to an open circuit here. So given such a scenario, my input step that goes from 0 to 1, or 0 to 5 volts, I should see the same thing reflected at v_0.

But I want to show you a demonstration where you are going to see something totally strange.
There would be a break in the signal - a forbidden region.

We then see the different scenarios that take place when voltage is measured at V_O and V_E.

Let's look at what is going on, OK? It turns out that that wire is more properly modeled as a
distributed LC circuit. This is actually the model for a transmission line.

For a step rise in the voltage, it actually turns out that you can look upon the effect of this inductance
capacitance distributed sequence on that step as if it behaved like a resistor. And that resistance is called the characteristic impedance of this wire. For coaxial cable is on the order of 50 ohms. OK.

So what happens now? So here is my 5 volt step. And the 5 volt step at this point, at V0, suddenly thinks it's seeing it as resistance R looking in.

It's an instantaneous voltage divider, and so the voltage divider divides this into 2.5 volts. So what I end up with is 2.5 volts.
That pulse comes all the way down to VE. So that 0 to 2.5 volt pulse then shows up all the way at
the very end. OK, notice that it takes some time to get there. So I get the 2.5 volts at VE. And now this is an open circuit. So the energy has to go someplace. So the pulse comes to the end, and then it
starts to run back. So notice what will happen at VE here. At VE, because the pulse has started to head back, what ends up happening is that there are two wave forms. There is the forward going wave, 0 to 2.5, and then there's the backward going wave, 0 to 2.5 volts as well. And the net is that the effective voltage at VE is gonna look like  a 0 to 5 volt pulse.

And how come anything worked?  The first reason is the following. The first reason is, by and large, when I have connection-- so let's say I have a gate driving another gate. Notice that there's a wire connecting the two pairs of gates, and I'm observing the signal at the end of the wire. I may have a second wire driving another gate. And again, I'm observing the signal at the end of the wire.
I'm not looking at the signal at the middle of the wire. If I look at the signal at the middle, I have the danger that I saw with v0 here. So in many cases, I look at the signal at the end off our wires.
And recall at the end of the wire here, my output had a nice clean 0 to 5 volt transition. This would be at vE. That would be quite nice. So this thing worked.

So do not try to take connections from the middle of wires.

One idea is called source termination. So in this idea, when you have a long wire, so in this case,
I have a long wire here, what you do is you have-- and this long wire has a characteristic impedance of R, say, 50 ohms. So then what you do is you connect a resistance of 50 ohms at the source.
And then at the end of that, do not connect any other resistances. Just leave it as an open circuit or connect it to circuits that offer infinite or virtually infinite input resistance. And then at that endpoint, you will see a nice little 0 to 5 volt waveform.

So there's no trouble there. And what the source resistor is really doing for you is that when the waveform comes shuttling back, the energy in the return wave is then absorbed in the source resistor.
So that energy comes back and gets cleanly absorbed in the source resistor, and you don't see some other funky shuttling back and forth. So that energy is dissipated, and things are completely fine.
So this idea is called source termination. You have a resistor here that terminates the wave of energy
that is coming back at you.

The second idea is-- what I'm going to do is recall the problem that I had. I had a waveform that was showing up at the end at vE, and that was giving  2.5 volts. And I said, look, it was an open circuit at vE. vE was initially open, and this energy had nowhere to go and so it bounced back. So what I'm going to do instead is the following. I'm not going to put an open circuit. Rather, I am going to connect a resistance here. Let's say this was 50 ohms. I want to connect a 50-ohm resistance here, so R.  So here what it's going to do, It's going to see a 50-ohm resistor, and the energy is going to be
absorbed in the resistor. We are  going to see a 2.5-volt waveform there. Notice that there's no waveform going back. There is no wave going back because it's been absorbed in the resistor.

So oftentimes in circuits, we can put a resistance here at vE, and that will cause the waveform to be cleanly absorbed, and I don't see this funky little step.

 There's a third reason why our circuits worked so far. And the reason is  the wires were short.
When you have long wires, signals take time to propagate down those long wires, and it was that propagation time that was much longer than my signal speed of interest.

With the 2.5 jump at vE, notice that I'm going to get a reflection as before, so we end up with 5 volts, zero to 5 volts, at V, which is not surprising. It's the same as before. But notice that my wave reaches back it really, really quickly and this will then transition up to the full 5 volts. So really what is going on is that my T and 2T are very, very close together. So in the past, where my T and 2T were very long, here I take a quick little blip and then my wave form goes up to 5 volts right away.


let's look at another scenario that I'm going to call the double dip. Before I dive into the double dip, let me mention-- it just occurred to me-- mention one more idea that would make the double take not as significant. And the idea there is, notice that I had a circuit where they got this funky little wave form at 2.5 volts. One way around that is to use a clock. So the point number four would be use a clock. So here, if I had a clock that we said, look at the signal only on the rising edge of the clock,
I would not have any trouble. This is because by arranging the clock carefully, according to the
lengths of wire in the circuit, I could make sure that whenever I expected the signal to be funky because of wire length and the speed of signals, I could just make sure that I did not sample the
signal at that time.


Now, let's look at a second situation  called  the double dip where there are two inverters.  The  power supply connects to a long wire to a big inverter. And the same power supply also connects to another inverter. This works okay.


I need to do some impedance matching, create a parallel termination of a 50 ohm, 50 ohm is a pretty low resistance. And the moment I add that resistance, I'm telling you that  we will see something really strange.  At the output of the second inverter, we see something really, really funky. Wires are not perfect wires, and that is what is happening. A wire abstraction is being violated.


And let us say that inverter is being modeled here,  using a PFET and an NFET.
So what is going on? I was getting these funky spikes at the output. It turns out that  it has some reasonable inductance. So modeling its inductance and sticking that inductance of this little circuit.
Corresponding to that long length of wire. So let me draw some signals here.
When the current steps up and down, there is a change in current. Now recall that inductors do not like to change the current that flows through them instantaneously. They like to hold their current.
And that sudden burst in the current is going to cause a spike, a voltage across the inductor.
The voltage across inductors is given by Ldi dt, so plus minus Ldi dt.

Why did our circuits work before?

Keep wires short. If I keep my wires short, the inductance associated with the wires is going to be short.  If L is small, than Ldi dt is also going to be very small.  So you try be clever well how you build the wires for power supplies, and so on, and try to build low inductance wires.
Third point-  the other thing you can do is notice here that the problem occurred because I had the same power circuit. I had Vs with the same power circuit for both my high powered MOSFET--
so this was a big FET, and the same circuit going to the power rail for a small inverter. So I shared the same power circuit for something that was very sensitive and something that was a current hog.
So one solution is keep separate power grids.

Do not connect these two things together. So for example, what we could do is take a connection directly from the power supply, or even have a separate power supply and connect it to the other inverter. So this way, since we were taking the connection directly from the power supply, there is a separate circuit which had a big current draw was going to be isolated from this other circuit.

 The next idea, avoid big current swings. Try not to swing large amounts of current in one final swoop. And I fully understand that sometimes you just can't do that. You have to charge up a big capacitor for whatever reason. So another way to do that is if you do really want to have big current swings, then avoid sharp transitions. Try to make your transitions slightly smoother. Have more of a slope to them.