Circuit Calculations for your Wearable Design.

7 min readDec 3, 2015

So I’ll be hosting a wearable workshop in January 2016, a first of many for WearHacks and myself. Montreal being the first to host, following Toronto.

But this article isn’t about the workshop. It’s about doing and finding the tools to do the calculations needed when designing your circuit design and how you want it to behave without any coding.

First off, I laid out what I wanted to use in my wearable project and this is what I came up with initially:

[ L ] 14 LEDs (3.2 ohms)
[ Pwr ] 3V Coin Cell Battery + Holder
[ PzS ] Piezo Sensor (or) [ PhS ] Photocell Sensor (has built-in resistor capacity)
[ r ] Resistors

I calculated what resistor(s) I needed so I won’t short the LEDs and the sensors.

[ Pwr ] =( [ L ] * 14 ) + [ PzS ] or [ PhS ]

[ Pwr ] is in ohms

It’s not obvious for a newbie that the 3V coin cell battery isn’t enough to power all 14 LEDs. Fact is, 9V would be just the right amount. But who wants three 3V coin cell batteries, nevermind one bulky 9V battery? Well, sometimes technology isn’t as fast as our wants.

This is where one would consider alternating one’s initial materials for the design. We haven’t touched based as to what order of these components will go in order yet, so here goes —

My logic would have been the following:

[ Pwr ] — [ PhS ] — [ r ] — [ L ] — [ r ] — [ Pwr ]

[ Pwr ] — [ PhS ] — [ L ]— [ Pwr ]

[ Pwr ] — [ PzS ] — [ r ] — [ L ] — [ r ]— [ Pwr ]

Note:
When wiring your design, a resistor should always be placed before any LEDs and not just a direct connection between the battery and the LEDs.
Also, almost all LEDs also have one longer wire [anode (+)] and a shorter wire [ cathode (-) ]. The negative will most likely have an arrow-looking head inside the LED.

Resist overflowing current

LED Series/Parallel Resistor Array Calculator — (current limiting resistor value)

If you need help calculating how much power resistance you’ll need before the current hits your light source, DigiKey has a no frills calculator on their site. Hobby-hour has one also along with a small tutorial and factual description.

Now you know what resistance value you’ll need to place before your LED sequence, it’s time to find the resistor with the right Ohms.

For the visual, there’s this Wizard. If you need a rundown of why we need resistors, Frank’s Training is a moderately understandable guide. If not, All About Circuits as a 101 on Basic Electricity on Resistors. Here’s a video if you need something quick:

http://www.allaboutcircuits.com/assets/videos/chp_3/3-3b-electroniccomponents.ogv

Resistor Color Decoder

DigiKey has a simple 4–6 Band Resistor Colour Code Calculator on their site. But before you go anywhere, check out the chart below as the DigiKey site won’t explain this.

http://www.resistorguide.com/pictures/resistor_color_codes_chart.png

Notice the fun colour and its sequence:
“Bad Beer Rots Our Young Guts But Vodka Goes Well — Get Some Now!”
Black / Brown / Red / Orange / Yellow / Green / Blue / Violet / Grey / White — Gold / Silver / None

More explanation is found for those who are more visual learners like myself on All About Circuits’ Chapter 2 Resistor Colour Code.

Okay, now if you have any resistors laying around, decode those colours on DigiKey.

So Hey, did you notice that the resistors are represented by the value in Ohms (Ω) with a numeric percentage i.e.:

4.7 kΩ ±1% 0.6W ±50ppm/°C
[ (# kΩ ) ( ± # % ) ] [ ( # W ) ( ± # ppm/°C ) ]
[ ( A ) ( B ) ] [ ( C ) ( D ) ]
A (Ω) = resistor value in kilo ohms that can withold current value that’s suitable for the next material
B (%) = max and min tolerance support of kilo ohms
C (W) = power of the resistor compared at 70°C
D (ppm/°C) = Temperature Coefficient / the resistance to change factor per degree Celsius of temperature (α)

Electronic Engineering Tolerance Structure

[ numeric value of ‘x’ unit ] [ +/ — ] [ numeric/percentage degree of how + (max) and — (min) it can go ]

Electrical Formulas

Oh god, I hate math but it is important.

You don’t want to blow anything up and replace all your expensive goodies, do you? Or, blow things up in a nonsense way because you’re a pyro at heart? ❤

Then you’ll need these formulas below to help you out.

This wheel diagram of Electrical Engineering is your formula cheat sheet to Ohm’s Law.

These Ohm’s and Watt’s calculations can be found using low-fi JS input.

Hey this wheel is overwhelming as hell, you say? No worries, I’ve got something for you.

DigiKey is another go-to place if you want something no frills. They don’t explain anything and are straight talkers. Wie Deutsch!

The copy and pasted calculators are as follow from the Digi-Key site:

Online Conversion Calculators

General Electronic Circuit Design help:

Tux Graphic’s — Voltage divider / resistor for a number of parallel resistors / First order RC-filter / Ohm’s Law / Electric power consumption
Sengpiel Audio’s Tontechnik Rechner — Ohm’s Law / Time Constant (Δ t : µs > fc : Hz) / frequency to wavelength ( f > λ ) / …

Formulas of Audio Acoustics ( I or J p v Z )

Formulas of Electrical Engineering ( V I R Z P ) (repeat)

Decipher your formula symbols with this Electrical Engineering + Electroacoustics (SI) metric chart in alphabetical order

Electrical Engineering + Electroacoustics Formula Symbols

More formula symbol-deciphering but this time it’s in alphabetical order of Units of Measurement

Electrical Engineering + Electroacoustics Units of Measurement

Just a side note:
It’s not a bad idea to know the parameter of a wire gauge and the length it needs to be – as current can wee off, just like trickling water at the end of pipe, resulting with little water at the end of a stream.

Circuit Schematic Drawing

Wow.. so we finally get to the fun part.

There are three ways we can test these logics and their schematics out before simulation:

We can draw the logic by hand and figure it out from there. However, you will have to familiarize yourself with circuit symbols (here’s also one by Circuits Today)
Breadboard prototyping.

Invention of the breadboard: 20+ years ago, there was a time where there was no product where you could map your electrical circuit components together in a blueprint. So hackers would steal their mother’s or wives’ kitchen cutting boards and nail on screws where wires could connect to hardware components, wires wrapped around and have these be placed solidly. The name never left.

Digitally draw your schematic using circuit editing software.

Drawing Tools

There are some cloud services that can help you create your own circuit schematics. These online tools are generally easy to use but they might not necessarily have the simulation capabilities you need.

123d Circuits by Autodesk *
Fritzing by FH Potsdam
Circuit Simulator / Applet by falstad.com

Downloadable available software are the following:

Eagle CAD by CadSoftware
Upverter * [ Mac OS / Win ] — [ schematic file converter on GitHub ]

* Account required

Other reading resources

Standard Electronic Design Documentation breakdown (PDF)
StackExchange’s Electrical Engineering Forum
All About Circuits — Lessons in Electric Circuits Online Textbook
Electronics Club — Beginner’s Quick Reference
Programming with Linear Logic by Chris Martens

As you can see, it’s a lot to know.

Come to my Montreal workshop and you will become a beginner wearable ninja in the first month of the new year ❤

— Cyclist Cyborg Hacker Girl from the Future. / CCHGF