The best way to learn Electronics is by refurbishing an Analog Reel To Reel Tape Deck before 1965 so there are no ICs, just very cleverly coiled, routed, and foiled copper.

I have been thinking about Electronics constantly since 2016. I had a box where I would keep all the nice I suctors and Transformers I salvaged. I literally had a box dedicated to them BECAUSE I had no idea how to use them but I knew they were prohibitively expensive to purchase new. So whenever I found one in an old sidewalk come up from a 1980s beta max or from a Cathode Ray Tube I would throw it in the box assuming I would figure them out one day.

But that day never came. I knew Faradays law, Lenz Law, Maxwell’s Equations, Ampere’s Force Law, Gauss’s law…I knew that motors required flyback Diodes to dissapate the back EMF generated upon suddenly stopping. I knew that magnetism was involved somehow with the performance of Transformers, I even eventually figured out that the Laminated Iron Core of non continuous interwoven Layers prevented losses from occuring due to the formation if Circular Eddy Currents.

What I did not know was that the wave propogation of EM waves (or for simplicity let’s just say light) that lights waves were propegating through a vacuum because when at zero volts AC (when the rate of change in current is largest as it crosses zero) the magnetic flux, of change n agnetic force, was at it’s largest. I did not know that like back EMF resisting changes in current through self-indutance, that there is a demagnetizing field within the ferromagnetic material that causes the magnetism to decrease in the medium. I did not know that the magnetic field was due to the changing force due to magnetism at the poles of the magnet, that is to say, Maxwell’s Equation for the Divergence if the Magnetic field is zero because the field is the magnets way of demagnetizing itself outside of the material because within the material their is a net magnetism that generates a North and South Pole.

I did not know that this results in Magnetic Hysteresis which contributes perhaps the most considerable effect to wave propegation as magnetism is not the aggregate flow of charged particles with very low mass, magnetism is not bound by mass or gravity.

I did not know that recorded magnetic data is not stored as discretely sampled values like computer memory is but is stored via it’s rate of change, hence why hard drives are rotating disks while RAM has no moving parts, yet must be always supplied with a voltage to retain data.

I did not know how to use an inductor, I did not know what calculations are necessary, I did not know how reactive inductance and reactive capacitance related to impedance, I did not know that magnetism is a result of iron having a 3D valence shell with 6 electrons, two are paired in opposing spin while the other four are not paired and naturally tend to form a Body Centered Cubic Crystal Lattice that aligns the unpaired electrons along the cubes four edges (if viewed as a cube these are the four edges that are vertical. Only iron has this ferromagnetic property because the cubic Crystal having one atom at it’s core is the only electron formation that creates the phenomena of filling higher energy layers before filling the valence shell.

There is so much more, so much more, but a tape deck will require you to spend maybe $20 to buy two broken ones you can Frankenstein into one working unit. It will be the inly time you will have the opportunity to work with inductors and magnetism in a non academic way (that is, I had only knew about magnetism through research, and we all know that doing it with your hands provides 1000x better information). Your only opportunity these days would be EMI concerns when designing PCB, but even the guys doing that started out just winging it and didn’t know the reason why the two large inductors in an audio speaker passive crossover system are orthogonal with regards to each other, the voice coil, and the large torroidal impedance Transformer for driving the speaker.

Here, Maxwell’s Equations are the reason electricity is even a thing.

Equation one states that an electric field will form when there is a difference in voltage between two points. Even though they are not connected. This can only be due to the chang magnetic Field of Faraday’s law but there is no conductor, so the demagnetizing force within the charge is creating an equal magnetizing force outside the charge, but the magnetizing force never changes because the force demagnetizing nit is the same force creating it, the energy is conserved because the Divergence of. Magnetic Field is Zero which is Equation Two of Maxwell’s Equations.

Number three is Faraday’s law with Lenz law, perhaps the most important Equation ever created in regards to it’s effect on society as it allowed us to produce electricity, and it remains the inly way we can do it (spinning a coil within a perpendicular magnetic field.) An electric field with a magnitude proportional to the rate of change in magnetic flux is generated in opposition to the current thag is generating the magnetic field lines surrounding the coil itself yet perpendicular to one another in each case.

Equation 4 is Ampere’s law relating how magnetic field forms from the current through a conductor and the electric field between two charges separated by some permiable dielectric are diffuse only because they have a continuous magnetic force.

H is Magnetic Force around a straight wire and us equal to 0.1*I/the radius of the field lines at that distance the wire. When coiled the equation is H=..4πNIA/L as the 1d wire forms a 3d Cylinder made of concentric 2D coils which is integrated into that form as L is length, A is 2D Area and π provides the 4th order need when integrating a 3D Volume. Imagine those distance variables we’re all represented by x, you would have H=.4*x^4*I, the derivative would be H=.4/4x^3 which is represented by radius for two directions and the 3rd direction is the direction of current flow. In the 4th order integral N is a function of how tightly wound a coil if length L is, which is related to the Area A, resulting in the inner magnetic force having a near uniform linearity.

Capacitors…my first nemesis…but now my dearest friend

When I first hear of a Capacitor it was my buddy telling me I could kill myself if I touched one in my Tube Amplifier for my guitar. I didn’t know what they looked like or what they did but the note was stored safely in my brains Grey matter as I have been grabbing my goggles and wearing rubber gloves when going “Deep Capacitoring” ever sense.

So far I have not zapped myself but I’m well aware of their shocking potential *Pun Intended*. I always get a kick out of discharging a cap with my screwdriver by shorting the leads and enjoy the sometimes SIZABLE spark. Only twice have I jettisoned a Polarized Electrolytic off my breadboard and into my face…once drawing blood. and don’t get me started on Tantalum Caps….I have never used one that hasn’t catastrophically failed. I know Tantalum is a conflict mineral so I probably purchased fakes as I can’t imagine they have the terrible design flaw of always exploding even when oriented correctly and within it’s Voltage limit.

My first experience with the real power of Capacitors was when I did my first real electronics repair: my 1985 Fender Telecaster got new pickups (two humbuckers: one that fit my Tele’s single coil Neck Mount and a unique hum-bucking Lipstick Pick-up; going from Single Coil to Humbuckers – Dual, 180 Degree Out of Phase Coils- as a guitar with only two single coil pick-ups and a three way switch is virtually unplayable on stage dsue to interference), Shielded Cloth Wire -it’s very cozy under he control plate and the cloth allows tidy wiring plus Shielded wires that don’t have any grounding issues, Three Way Switch (modified due to going from two single coils to two humbuckers means more wires to the switch), Linear Tapered Pots, new input jack, and new capacitors on the tone pot and the treble bleed circuit on the Volume knob. Now I had no idea what a Low Pass Filter was until that project but once I discovered it could take my $450 Fender Telecaster sound better than my $6,000 Gibson Les Paul I started looking into DIY Electronics to see what other musical devices I could Fix/Mod/DIY/or just learn about. (Here is a link to the Video I made of the Tele’s Overhaul: https://www.youtube.com/watch?v=EBZ6NtohRbk)

That repair got me interested in Elkectronics but I had no Idea how that Capacitor worked. I remember it was a Green Mylar at 47 picoFarads (Single Coils usually use 47 pF, Humbuckers use 22pF and Soapbar style pickups use 15pF traditionally). Unfortunately, at the time I didn’t know that the “Orange Drop” caps sold for $7 each at guitar center would do the exact same thing as any 1 cent capacitor I now currently own thousands of. But what I knew was that it went between ground and the Tone potentiometers Wiper. I read it was an LP Filter and the tone response had to do with the Cutoff Frequency dictated by the Potentiometer and Capacitor’s combined product. So I understood the first elementary thing about Capacitors through that learning experience:

First: the Definition, the Math, the Physical process by which a capacitor can easily be visualized.

Visualizing what goes on inside a Capacitor was an extremely difficult thing for me to do because I visualized it multiple wrong ways until I came across new circuits that didn’t fit within my visualization and then became confused.

First: A Capacitor stores a Charge and Charge is Measured in Coulombs and is equal to a Quantity of Electrons. However, all atoms have electrons and no electrons enter or leave the Capacitor because that would result in the creation of a bunch of ions in the Capacitor which wouldn’t be very stable. So how does it “Store” charge? It more accurately stores an Electric Field. A

What is “inside’ that metal can? What magic is going on in there that can sustain a magnetic field?

  1. A Capacitor Consists of two plates that are parallel to eachother but separated by a dielectric, like a sandwich.
  2. Each plate is connected to some part of the circuit by a single lead
  3. The key property is its ability to form an Electric Field that is spanned across the Dielectric that will store This field as Voltage to the extent that the dielectric has the permittivity necessary for the E field to form Permittivity is like conductivity or susceptibility but Current is not the fluid being exchanged here. It is Electric Field lines.
  4. Imagine The left input plate being connected to V+. There is one lead in and out and electrons do not flow from the positive lead, they are negatively charged, yet they are our charge carriers
  5. However due to Voltage being the potential difference between two points, and the dielectric being non conductive yet permeable the difference in voltage will hold the charge even after the voltage source is disconnected BECAUSE, the Dielectric is an OPEN CIRCUIT so that charge can’t flow through the capacitor, and if the positive lead is disconnected then where can that positive charge escape to, same with the negatively charged side.
  6. Itwill, however discharge through any conductive path connecting the plates that has a smaller voltage drop because the charge will always seek the lowest entropy state and the Electric-Field stored when given a path will take it.
  7. Imagine lightning. It’s not certain the exact workings but you can think of the clouds acting like a Dielectric between the Ground (where our Negative Charges are their most abundant, and therefore the polarized nature of water will transfer this charge through the cloud into the largely inert sky. Normally Light ( a form of electromagnetic radiation) energizes electrons passing straight through the atmosphere. But with thunderstorms the charge inthe sky collects and will start charge storage due to the clouds now being a dielectric. Eventually the Negative charge above the clouds will find a path where it can find a way to a portion of the ground that has less negative charge, thus discharging.

Why would anyone need this? Electricity measured in Amps is and Average of many multiples of trillions of discrete electron movements with charges of 1.392^(-23) and so at any moment the actual value of charge in Coulombs being conducted to the load will never exactly be the Average value. It actually has a Gaussian distribution and so there will be Noise in ever conductor and at ever interconnect. if the noise exceeds the voltage allowable by the Integrated Circuit then a local Ceramic Capacitor will soak up the noise charge for the pivo second it exists, and since that ekectron has become stable its contribution to the current falls so there will be a drop in current of 1.602^(-23) coulombs, which may require The extra charge on the Capacitor to be released and used to supply your OP AMP with the input Bias Voltage it needs to keep it’s inputs equal.

So first and foremost the Capacitor exists to provide Stability voltage levels throughout a circuit where the ever changing current creates ever changing Magnetic fields, creating ever changing Voltage Potential creating ever changing Electric Fields. By storing those incredibly small charges over incredibly short periods of time the circuit can function smoothly as it’s Voltage References are all stable.

Not only does it stabilize the positive voltages but those voltage references have to be referred to Ground and the Capacitor, by form an electric field that retains the Voltage Potential instead of conducting it to ground, it isolates each circuit component (usually only active components or circuit blocks). With a Ground that is constantly fluctuating slightly around 0 volts the entire circuit will be a mess.

SECONDLY, THEY PROVIDE THE MOST COMPLICATED EQUATIONS IN ELECTRONICS THROUGH THEIR ATTENUATION OF TIME VARYING SIGNALS. Capacitors have a Frequency Response dependent on the RC Filter’s Time Constant “Tau” which was simply the product of the Resistance & Capacitance.

Three years later I now finally understand why and how RC Filters works ( I can also do the necessary Complex Analysis to derive it’s properties as well. But at first the Capacitor always had me stumped as I had no idea what it did, how it did it, why they were everywhere, and what were they doing in all those spots. I was going to list “why they are a specific value” but have learned Capacitors have a very large Tolerance Range for Value and also do not have to be precisely calculated outside Complex Active Filtering or Timing Circuitry.

The hard part about learning about capacitors is that in todays world you see them performing one of just a few functions:

  1. Power Supply Filtering to remove Ripple from a Sinusoidal Signal when Rectifying AC mains to DC (these are the large in size, large in capacitance, and Large in voltage rating Electrolytics you see on circuit boards near where the power cord meets the PCB.
  2. Decoupling Digital/Analog Integrated Circuits – like the above purpose the function here is to provide a stabilized voltage to the Chip lest the fluctuating Digital Signals destabilize yours Ground or Virtual Ground and thus destabilize your Positive and Negative Voltage Rails.
  3. Coupling an ac signal from one stage of a circuit to another by eliminating any DC bias or common mode Voltage before an amplifier or output stage. In a broader sense you see them isolating parts of a circuit from other parts by only passing AC signals. This keeps parts of a circuit using different Steady State Voltages from influencing eachother.

I would have said RC Filters but you only see that building block in Analog Music Hardware usually. Or any circuit that is concerned with Frequencies.

Here are uses for Capacitors I have experience with and if I can explain what the cap does in the circuit I’ll try my best!

  1. Op-Amp Integrator: Imagine an inverting Op-Amp but with a Capacitor in the feedback path. The Non-Inverting node is Grounded so their is a Virtual Ground at the node between the Input Resistor and the Feedback Capacitor. Now Imagine an unchanging DC Voltage is applied to the input through Rin. The input Resistor creates a constant Current that can’t go into the Inverting input and therefore must charge the Capacitor in the Feedback Loop lest the Virtual Ground be disturbed. A Voltage develops across a Capacitor as a function of the Rate of Change in a charging current. At the Inverting input the Op-Amp sees an incoming Current and adjusts it’s output to divert that current through the feedback path. so that both inputs remain 0-volts. So in order to have an input current charging a capacitor while not changing that nodes voltage away from zero volts the output voltage will be heading negative at a slope that is constant so that it creates the inverse constant current on the capacitors other plate evening out the Charge on the across the Cap.
  2. The Voltage on a Capacitor is independent of the voltage at the capacitors lead. It value is equal to the Charge it holds over its capacitance (makes sense being that capacitance is defined as the ability to hold a charge “Q” when the plates have a specific Voltage Potential formed by the Electric Field created by the charge “Q”.
  3. In a Time varying signal the Voltage will be related to the rate of change of that charge. This allows for charge pumps and switched capacitor voltage doublers or negative voltage inverters. The change in Voltage as it charges and discharges is relative to the voltage on the other plate. So when the Op-Amp changes it’s output it is doing so to keep that Inverting input at 0-volts, so if a positive voltage flows through Rin then Vout goes negative accordingly.
  4. So what does the Op-Amp Integrator do? The Capacitor Equation relation Capacitance to Voltage is Coulombs “Q” = voltage ” x “Capacitance”: Q=C*V; or, C=Q/V, that is, 1 Farad (The SI unit of Capacitance) provides that Two

Resistors

Resistors – they are everywhere because they serve two functions:

  • They limit current flowing into a node in a circuit and thus out of the node as well so they limit current into other components that can get all bent out of shape when the current is higher than the component following the resistor is rated to handle according to its “Datasheet” (Get used to googling a sequence of letter followed by some numbers followed by “datasheet” and clicking the PDF in the top three search results from google. These “Datasheets” will be necessary to pick out components or solve for component values when creating circuits…I will explain later)
  • They can create voltage levels between the Supply Voltage and Ground using a simple formula and a circuit building block called a voltage divider.

Every unique component in a circuit will need a specific current and voltage at which it will function at its optimum performance and therefore you will use resistors to set the optimum current in a circuit building block and the optimum voltage in a circuit building block.

What else do resistors do that you will need to know?

  • Resistor-Capacitor Networks add a time delay to circuitry allowing for all the digital processes of a computer because things need to be done in a specific order and sequence and the “RC-Network” serves the purpose of creating a signal within the “time-domain”
  • Resistors are frequently drawn ni schematics as a representation of this thing called a “Load” which I’ll just define for you right now: it’s the the “end-game” power consuming, work-performing, purposeful part of the circuit. That is to say, the circuit you are designing is usually created to provide power to a “Load”.  Imagine a guitar amplifier: the speaker that makes the sound is the load; a simple LED circuit: the LED is the Load; a DC Motor used to spin something: the motor is the Load; A lamp: the light-bulb, or more precisely, the  tungsten filament is the load. The Resistor is used in schematics because Resistance=(Voltage/Current) and since -as previously stated- Circuit components have optimum Voltages and Currents, they can be neatly defined as the ratio of one to the other. That ratio is the Load’s Resistance.

Ohm’s Law (The thing you will use all the damn time)

There are lots of formulas in Electronics. The one you must know by heart came to use care of German Physicist Georg Ohm in his paper on the “Galvanisches Kettle”. Basically old Georg figured out that Voltage “Across a Conductor” is related to the Current “Through a Conductor” by the resistance of the conductor. You could say Resistance is the ratio of Current (“I”) To Voltage (“V”) and is represented i he equation:

R=I/V

But you will find Ohms law more helpful if it’s written as:

I=V/R

This is because a Resistor’s purpose is to limit current “I” and since Voltage is usually known and you are trying to produce a specific current, you can find the resistance necessary to produce the correct current by solving for R. But if you already have a circuit you are trying to analyze you will know voltage and resistance and so by dividing Voltage by Resistance you can reduce the current in that node of the circuit.

The defacto “LED Example”:

You have a 9-Volt Battery, a Red LED that wants a .02 Amp Current to function (to little current it won’t light up, too much current and it burns up and catastrophic failure occurs and you now have one less LED). So if I=.02 and V=9-Volts you pop those number in the equation and you get the resistor value necessary to make the LED function perfectly:

.02=9/R > R=9/.02 > R=4.5/.01 > R=450/1

The resistor value necessary is 450 Ohms.

(Resistor Values are measured in Ohms)

If your Resistor was 900 Ohms the LED would have half the current (10 milliAmps vs 20 milliAmps) and not light up. If the resistor Value was 100 Ohms the current would be 90 milliAmps and the LED would burn up aost instantly.

You must get used to this formula. Resistors are everywhere. Every component requires either a specific Voltage or Current to function properly and efficiently otherwise you waste energy, create waste heat and thus fire hazards, and your circuits either don’t work or have a lifetime that is shortened due to the stresses of too high of a current.

That’s enough for today but get a breadboard and connect a 9 volt battery to an LED with a 450, 330, or 220 ohm resistor between the positive battery terminal and the longer lead of the LED and see what happens!

(LEDs have a short lead which you connect to the negative battery terminal and a long lead to the positive terminal. If you don’t have a resistor between either leg and it’s respective terminal you will break the LED)

‘Till Next Time,

Danny

How I got started

Here are my prerequisites:

1. Economics Degrees from UCSB (so I know complex math, but had to learn engineering math)

2. First started to solder and toy with Electronics when I was mod-ingy Fender Telecaster

3. In Modifying my Telephone I replaced the capacitor on the tone pot and replaced the potentiometers

4. I was amazed that in spending $5 I made my $400 1975 Tell sound better than my $4,000 Les Paul…so I realized there was something there.

5. I picked up an O-scope, a Lab Bench Power Supply and Tons of $1 books on eBay from the 50s that were used textbooks for electrical engineering.

6. My goal was to make a synthesizer (which is probably the absolute hardest thing you can possibly make…I still haven’t done it) so along the way I learned how to make, well, lots of things. I’ll get into each project separately.

7. I researched thousands of hours how each Electronic component worked. Especially op amps. I bought a 1000 page text-book and read and copied every page, did every problem, and when I got through I felt pretty solid.

8. I bought books on Transistor theory and applications. I bought books on mathematics, physics, materials science, and EVERY book by Forrest Mimms until I felt like I could understand computers on a ‘spiritual’ level. Binary? Fuck ya! Boolean Logic? You know it, Bra! Frequency domain? What you want? Laplace or Fourier Transforms cuz I got that shiiit…

9. Some people think it’s a waste of time…but I got a job at a place called tech shop where I prototype products for people (I provided the Electronics Expertise). I was paid for it too. And people were impressed. Because iade things that worked.

So I want to walk you through how I learned this stuff and use my notes that hopefully anyone can learn from. Because the textbooks provide a university level knowledge that is dense because they are written under the assumption you know calculus and physics. I will present theory and physics necessary only to understand how it all works.

’til next time,

Danny