More Than You Ever Wanted to Know About Electrical Engineering: More About Inductance
We’ve been talking about three-phase circuits of the kind you might see in residential systems, generally at 120 or 208 VAC. The voltage you actually see on a utility line is much higher than this, though, as it is more efficient (and consequently cheaper) to transmit over long distances at very high voltages. So how do you go from the very high voltage circuits on a utility line to the much lower voltages in a commercial or residential electrical system?
The device to handle this problem is a transformer. To understand how it works, we’re going to need to take a closer look at inductors and a little bit of electromagnetic theory.
At this point, we know that an inductor is basically a coiled bit of wire that stores and releases energy in a magnetic field. Let’s examine how that works a bit more closely.
There are two physical laws that will be relevant for us here. The first is Ampere’s Law, which simply says that any time you have an electric current, you get a magnetic field. So if we pass a current through a coil of wire, we’ll produce a magnetic flux,
The geometry of the coils actually amplifies this effect - the coils in close proximity to each other “catch” more of the overall magnetic flux. You’ll see a term called flux linkage,
λ, get thrown around. This is just a measure of how much magnetic flux is caught up in the coil, and it’s directly proportional to both the number of turns of the coil, N, and the overall flux.
We’ve already said that the presence of the magnetic flux is related to the current flowing through the coil, so we should also expect that the flux linkage is proportional to current. The constant of proportionality between the two is the coil’s inductance. This is all inductance really is: a measure of the relationship between the current flowing through a coil and the magnetic flux it generates.
The other physical law of interest to us here is Faraday’s Law, which states that anytime we have a changing magnetic flux, it creates a voltage.
We can substitute in our equation linking flux linkage, inductance, and current here. Applying the chain rule, we get something that starts to look a little familiar.
In most circumstances, inductance is a constant. We don’t have to worry about it changing over time, so for our purposes, this equation reduces to the equation relating voltage, current, and inductance which we’ve used before.
It’s a mono box with big knobs, tubes and transformers. It was made in a little shop in New Jersey between the 1950s and 1970s. The company was called “Pulse Techniques” aka Pultec! The design they pioneered is called the “passive inductor” style of EQ, using passive filters to peak or dip the tones, and then making up the resulting gain-loss with a tube-amplifier on the output. Pultec program EQs are universally considered the the sweetest most musical eqs in history, and are a big fat deal in pro audio. Vintage units are hard to get and demand big bucks. That’s why so many modern companies make Pultec-type equalizers. Here are just a few….
More Than You Ever Wanted to Know About Electrical Engineering: Variable Frequency Networks
We’ve spent a lot of time talking about the impedance of resistors, capacitors, and inductors. We know that the impedance of inductors and capacitors is dependent on frequency, but we haven’t really explored what that means.
A resistor presents the same amount of resistance regardless of frequency.
For an inductor, the impedance increases linearly as frequency increases.
For a capacitor, the impedance decreases rapidly as frequency increases.
So what about a circuit which includes all three elements? Its combined impedance will be the sum of the individual impedances. You’ll get an overall impedance that is high at very low frequencies, becomes low at a slightly higher frequency, and then gradually increases again.
In other words, this thing is basically a filter that blocks very high and low frequencies and lets signals of lower-midrange frequencies through with relatively little difficulty.
If we rearrange equation a little, we get something that’s kind of ugly, but fairly compact. We’ll substitute s for jω
- we’ll talk about why later on, but for now, just know that s=jω. We’ll be seeing a lot more of this equation in future articles.
Just in case people haven’t heard, they’ve found another tumour in Stefan’s liver. Here’s the google translated Icelandic post from his Facebook.
If anyone can offer a clean-up, as it is Google translate after all and some of it is a little mistranslated…
“What is the worst thing that can happen? Everyone keeps that fear inside.
This week we got to know that there are two new metastases in Stefán’s liver. Gallbladder cancer is a scapegoat. Tomorrow we will take the couple to Copenhagen and will enjoy being together for a couple of days, but Stephen goes to the jailbreak outside on Tuesday.
Stefán’s doctors believe that as the corpse is in the uterus, it is possible to cut it up and remove it. The Yese Scanner will provide further information on the status of the inductor and also whether there is anything else on the go. If anything else becomes apparent, the status will be re-evaluated.
It’s hard to wait for their answers.
We are naturally angry and welcome this new news, but we are also confident that Stephen is in good hands and everything will be done to improve his health.
I want to say something cool and constructive, but your mouth is full of salt.
One thing, though, I know that life is not yesterday, not tomorrow or sometime later. Life is now”
It was a chilly Friday evening when Dylan’s car slowly rolled by a large white van that had been sitting on the side of the road a few blocks away from Dylan’s house. It’s been there for almost three weeks and to the best of their knowledge no one they knew owned it, or had moved it since then.
Eric leaned forward in his seat, to try and get a glimpse of what was inside. All he could make out were large objects and electrical wires.
“I wonder what’s inside it.” Eric said aloud, as he turned his neck & the van grew smaller and smaller as Dylan’s car continued to drive by.
“You wanna take a look?” Dylan asked.
Eric turned to face him fully and gave him a quizzical look. “You want to just waltz up to a van in the middle of no where and see what’s in it?”
Dylan shrugged, “I don’t see why not.”
Eric grinned massively making Dylan chuckle, “I’ll take that as a yes.”
Soon Dylan’s car was pulling into an unfamiliar driveway before pulling out & turning around. Then they were well on their way to cause some mischief.
Dylan pulled his car to a stop ten feet away from the van, before turning to Eric.
“What’s the plan baby?”
“I think I saw some electrical wires in the front seat. So if there are wires, then there must be more electrical equipment. We need wires for the propane bombs, and timers. I could make use of the other stuff if it’s worth anything.”
A few moments passed before Eric waved his index finger in an up & downward motion at Dylan as he spoke. “The trick to stealing is to just take it like you own it, so we just gotta walk up to the van like we own it, open it, & take the stuff out like its our damn job.” Eric ended his full proof plan with a snap of his fingers. Satisfied with the quality of what he had concocted in a short amount of time.
Dylan playfully snapped his fingers back at Eric and said, “Except, we don’t have the keys.”
Eric chuckled while waving his hands dismissively, “Oh Dylan, you sweet boy. We don’t need keys.” Drawling out the last sentence as if it was obvious.
“In the year 2072, the world’s energy
problems seem solved by a network of cross-dimensional electric-field
inductors—"coils"—that extract energy from a seemingly infinite source.
That source is the W dimension, a fourth plane that exists beyond the X,
Y, and Z dimensions.
In this world, unofficial “illegal” coils harness powers that the police
can’t hope to counter. Dealing with these coils is the job of
coil-hating repo man Kyoma, whose run-in with the unique coil android
Mira leads the two to form a reluctant partnership.” Aired:
Jan 10, 2016 to Mar 27, 2016
More Than You Ever Wanted to Know About Electrical Engineering: Amplifiers, Gain, and Frequency
We’ve met amplifiers before in the form of op-amps. We’re going to see a lot more of them. In general terms, an amplifier makes a small signal bigger. But there’s some subtlety to this: not all signals are created equal. We’ve been looking at the effects of frequency on impedance, so we know that a signal of the same frequency will behave differently going through a capacitor than it will going through an inductor or a resistor. With what we know now, we have the power to create amplifiers that selectively boost some frequencies and attenuate others.
Let’s think a little bit about what this kind of amplification looks like. The kind of amp we’re all familiar with is an audio amp. If you’re amplifying an audio signal, you want all the stuff within human audible range (about 50 Hz - 15000 Hz) to be amplified equally. So the frequency response for your amplifier might look something like this:
A couple of things to notice about this graph. Gain is a unitless
number describing the ratio of the output to the input. So a gain of 100
means the strength of the output is 100 times the strength of the
input. The equation below shows a voltage gain, but you can also talk
about other kinds of gain.
Note also that the
frequency axis on the graph above is one a log scale. At the range of
frequencies we’ll commonly be dealing with, this is a necessity just due
to space constraints, but we’ll see later on that logarithmic graphs
can give us some interesting insight into amplifier behavior.
the amplifier in the graph above boosts signals within a range of about
50 Hz to 15 kHz more or less equally. It’s not perfect - you lose a
little at the extreme high and low ranges, but there’s a solid midband
letting most of the frequencies of interest come through. Suppose you
wanted to boost the bass of your audio. Bass frequencies run about 40 Hz
- 400 Hz. Your amplifier frequency response in this case might look
You might do this by chaining two
amplifiers one after the other - one for the bass, one for the rest of
the signal range. We’ll look more closely at the specifics of how to
make and analyze these in the coming weeks.
Just a little ficlet to go with the pic, my first attempt, nothing special:
An idle afterschool Thursday in springtime Hill Valley; rain batters the roof and walls and ill-fitting doors of the garage at 1646 JFK. A soaked denim jacket is hanging off of the bedpost across the room, the best place they could find to dry it in this nest of clutter, and Marty figures his parents will take one look at the downpour and know why he’s not home. No big deal, he’d insisted a few storms ago, and they’re not really interested enough to push.
Thought you might be interested in this: When Mycroft opens his notebook, one of the things there is the number 611174. This is the case number for Hamamy syndrome, which is a rare genetic disorder that affected two brothers in 2007 which causes, among other things, defects in the heart and “borderline intelligence. Oh and they’re unable to produce tears. Symbolic? Another is the name Vernet, an 18th century painter who is renowned for making the human figure an integral part of his landscape design. More importantly, in the ACD original “The Greek Interpreter” Sherlock say that his grandmother was Vernet’s step-sister. This could also refer to Vernet’s son or grand-son, who were also painters. Perhaps a comment on like-minded families, or maybe we’ll learn more about the Holmes family
Scarlet Roll, with what looks like an m after. The closest I could find is “The Ancient and Masonic Order of the Scarlet Cord”, which is a sector of freemasonry, and they have a Roll of honour scheme. Maybe a hint for season 4.
And this one took some real working out but
is Maxwell-Faraday equation or Faraday’s Law of Induction. This is a basic law of electromagnetism which predicts how a magnetic field will interact with an electric circuit to produce an electromotive force. Its fundamental to transformers, inductors and many electric motors, ut I have no idea where any of this fits in.
There was also a vector, but I can’t get anything on it.
I have no idea why any of this would be under the heading Redbeard. I’m assuming Redbeard is Mycroft’s code for “Sherlock is fucked up but why”, or just for Sherlock himself. Maybe all the mistakes he’s made with Sherlock? Or some brand new mystery?
Anyway, let me know what you think of this theory, maybe someone smarter than I can piece it all together.
so for an assignment working w contact mics and inductors i made this fun thing i had a good time and used a bong some kids toys an alarm clock radio and a wind-up music box if u play this be careful it gets loud in some parts
More Than You Ever Wanted to Know About Electrical Engineering, Part 29: Power Triangle and Power Factor Correction
We’ve spent some time talking about power factor as basically a measure of efficiency for a circuit - the amount of power we put into a circuit that we can get to do actually do work for us. We’ve shown that a power factor closer to 1 results in fewer losses and a more efficient system. Knowing this, it makes sense that there are circumstances where it may be necessary or desirable to alter a circuit’s power factor.
Let’s visualize this in a slightly different way. We know that in an AC circuit, we’re generally dealing with complex power, S, comprised of real power, P, and reactive power, Q, and that the power factor is the ratio of the real to the complex power.
We can represent this graphically as a right triangle with S as the hypotenuse, P as the base, and Q as the height. Since the power factor is the ratio of P to S, it will be the cosine of the angle between them.
This visualization is called a power triangle. It can be a helpful way of quickly getting an intuitive handle on the situation you’re dealing with.
Anyway, we’ve established that in an ideal world, we want the power factor of our circuit to be close to 1. Since the power factor is the cosine of φ_z, that means we want the angle φ_z to be as small as possible.
There’s two ways we could do that. We could make P larger. That would make for a long, skinny triangle and decrease our φ_z. But remember, P is the real power we’re consuming. If we’re after efficiency, increasing P is the last thing we want to do.
The other thing we could do is reduce Q, our reactive power. This doesn’t change the amount of real power being consumed at all, so this looks like what we want.
How do we accomplish this?
Remember that reactive power is power that’s tied up in energy storage elements - that is, inductors and capacitors. Remember also that inductors and capacitors sort of work in opposite directions - conditions that will charge a capacitor will discharge an inductor and vice versa. A positive impedance means a lagging power factor, which means an inductive load, and a negative impedance means a leading power factor, which means a capacitative load. As with impedance, a capacitor will have negative reactive power (or it will supply reactive power, if you prefer to think of it that way) and an inductor will have positive reactive power (or it will consume reactive power). What this means is that you can change the value of Q, and consequently,
the power factor, by introducing additional capacitance or inductance
into your circuit.
More Than You Ever Wanted to Know About Electrical Engineering, Part 22: Resistance, Reactance, and Impedance
We’re starting to look at circuits with time-varying sources. For a lot of the stuff we want to do, this means a sinusoidal source whose voltage and current will look something like this:
What exactly does a time-varying source like this mean for circuit elements?
For resistors, it doesn’t really matter. A resistor just dams up the pipes a little, makes it harder for current to get through. It’ll present the same resistance to any source you throw at it.
Capacitors and inductors are another story.
Remember, these are elements where time is important - they require time to charge and time to discharge. So think about what happens when you expose a capacitor to the time-varying voltage above.
Let’s say the capacitor starts out fully charged to Vpk at t0. When it’s fully charged, remember that it acts like an open circuit - no current can flow through it. That’s going to change, though - the source voltage starts falling as soon as it passes t0. Now the capacitor is holding onto the highest voltage in the circuit and it starts to discharge. It’ll discharge increasingly rapidly as the source voltage drops, allowing more and more current to flow, and then once the source voltage starts climbing again, it’ll start recharging and letting less current flow as it gets closer to a full charge.
So in a circuit with a time-varying voltage like this, you are forcing capacitors and inductors to constantly charge and discharge. As a capacitor charges (or an inductor discharges), it lets less and less current through. When it starts discharging (or charging in the inductor’s case), more and more current can flow. Since the changing source forces the element to rubberband between these two states, there’s going to be some average impediment to the flow of current caused by a capacitor or inductor. This average quantity is called reactance, usually written as X. Its exact value will depend on the frequency of the source - that is, how long the element is allowed to charge or discharge - and the capacitance or inductance of the element - that is, how much of a charge it can hold. Here’s what the reactance looks like for a capacitor and an inductor:
Note that at higher frequencies, a capacitor has less reactance, but an inductor has more reactance.
The combined resistance and reactance of a circuit is called the impedance, Z. Z is written like this:
Note the imaginary number cropping up again and the similarity to the way we described sinusoids. You can convert this to polar form if you like, same as with sinusoids, and it will make dealing with circuits with time-varying sources and capacitance or inductance a thousand times easier to deal with mathematically. You’ll sometimes see resistance called the real component of impedance and reactance called the imaginary component. It’s a misleading way of talking about it - reactance is very much a real phenomenon and has a definite impact on circuit behavior. The “imaginary” indicates that what’s impeding the flow of current doesn’t really have to do with a “blockage” per se - it’s just a consequence of the way capacitors and inductors store energy. A resistor dissipates energy - a capacitor or inductor holds some of it back so that it’s not available for immediate use.
Schematics! The visual description of a circuit by using standardized symbols of the different electrical components. Thus far, we’ve gone through resistors, capacitors, inductors, diodes, transistors, fuses, circuit breakers, switches, and relays.
Quite a few. I’ll show the basic symbols for the following, but for more detailed/specific ones, google is a fantastic resource :p.
The arrows always point towards the N-type material.
As you can tell, these are pretty similar to the switches.
I think I’ll come up with a more interesting way to demonstrate these schematic symbols.
An Attempt to Change the Current in an Inductor Instantaneously.
Inductors do not react well when current is changed suddenly on them and will kick up their voltage in response. The high voltage in this case ionized the air between the seperating ends and the electricity was able to travel through the air to keep the connection and not drop current.
More Than You Ever Wanted to Know About Electrical Engineering: Transformers
We’ve been talking about mutual inductance and magnetically coupled circuits. If you have a couple of coils of wire adjacent to each other such that they can get caught up in each other’s magnetic fields when a current is run through one or both of them, one coil can induce a voltage in the other, even though the circuits are not physically connected.
This setup is the basic construction for a transformer, one of the most ubiquitous pieces of equipment in power transmission. Just as in the examples we’ve been looking at, a transformer consists of two coils of wire next to each other. In a transformer, they’re both usually wrapped around a magnetic core of some kind. The purpose of this is to channel the magnetic flux so that more of it is caught by the coils and increase the strength of the magnetic coupling between them.
Let’s assume for the moment that this core is perfectly ideal - that it channels ALL the magnetic flux perfectly efficiently, such that the same magnetic flux is experienced by both coils.
If this is the case, then the ratio of the coil voltages is equal to the ratio of coil turns. In other words, you can convert from one voltage to another by adjusting the number of coils in the transformer.
There’s a similar relationship going on with the currents.
If we manipulate these equations a little, we find that the total power of the transformer is zero. (For an ideal transformer, at least.)
More Than You Ever Wanted to Know About Electrical Engineering, Part 24: AC Power
We know that power is energy per unit time. When we were talking about purely resistive circuits, we said that we could characterize the power dissipated as the product of the voltage across an element and the current through it.
This picture gets a little more complicated now that we’re bringing AC sources into the picture. Now, instead of having a constant voltage and current, we get a voltage and current that look something like this:
Both the voltage and current vary moment-to-moment. Moreover, depending on what kind of impedance we have in the circuit, they may not vary in sync- if we have energy-storage elements like capacitors or inductors, they’ll hold on to some of their energy for part of the cycle, so we’ll get a situation where the voltage and current are out of phase.
So what does this mean for our definition of power as the product of voltage and current?
Well, it doesn’t totally break it. Power is still the voltage across an element multiplied by the current through it. But we do have to get a little careful to specify whether we’re talking about instantaneous power or average power. Generally speaking, from now on, when we’re talking about instantaneous or time-varying quantities, they’ll be in lower case, and when we’re talking about average quantities, they’ll be in upper case. So instantaneous power will be p(t), but average power will be P.
If we’re talking about instantaneous power, we’re talking about a quantity that will change moment-to-moment like the voltage and current will. It’ll have a similar sinusoidal waveform, and we can get it by applying the power formula we already know to the trigonometric expressions we now have for voltage and current. We’ll need to use a trig identity to get it into something helpful, but overall it’s pretty straightforward.
Let’s examine this a little more closely. We can tell just looking at it that it’s some kind of sinusoid, just like we’d expected. It looks kind of ugly, but don’t let the presence of two cosines throw you off - since the phase angle of the voltage and the current won’t change, that first cosine is really just a constant term that the sinusoid will center around. In other words, that first term is the average power.
You can also get the average power by integrating the voltage and current over a full period and dividing by a full period. This boils down to the same thing we got by inspection, but if you’re dealing with a non-sinusoidal waveform, this is the way to do it analytically.