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

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
Advertisements

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