Printed Circuit Boards

Motivation: weak forces on DualPanto might be a result of a depleted battery. But how to find out?

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Analog Electronics

• digital output on Arduino: things happen one layer further down
  • analog electronics like resistors
  • power plays a role (LED might burn out, battery depletes, etc.)

Ohm’s law

$U=R\times I$ (Spannung $=$ Widerstand $\times$ Stromstärke)

• respectively $I=\frac{U}{R}$
• or $R=\frac{U}{I}$

Electrical power

$P=U\times I$ (Leistung $=$ Spannung $\times$ Stromstärke)

• which gives $P=U\times \frac{U}{R}=\frac{U^2}{R}$

Example I

• Red LED specs: 1.8 - 2.2V, 20mA
  • $\Rightarrow R_{\mathrm{LED}}=\frac{2V}{20mA}=\frac{2}{0,02}\Omega =100\Omega$ (using Ohm’s law)
• Battery specs: 2V
• result: voltage (Spannung) is chosen correctly, so LED will allow 20mA of current (Stromstärke) flow
  • $\Rightarrow$ 2V $\times$ 20mA $=$ 40mW of power in light (Leistung)

Example II

• 5V USB instead of battery
• 2.5 times the voltage $\Rightarrow$ 6.25 times the power (250mW)
• more energy accumulates than the LED can dispense $\Rightarrow$ gets hot $\Rightarrow$ boom

Example III

• still 5V USB
• LED specs now: 3.8V, 20mA
• 1.3 times the voltage $\Rightarrow$ 1.7 times the power (not a big factor)
• surprisingly, the LED blows too, because it does not follow Ohm’s law…

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Non-ohmic Devices / Behavior

Non-ohmic devices are pretty common and quite useful

Light bulb

• resistance of filament increases with its temperature (ingenious control loop)

LED

• resistance decreases with its voltage (steep slope)
  • $\Rightarrow$ large variations in current possible
  • $\Rightarrow$ works in small voltage interval

Resistors

• implement electrical resistance as a circuit element
• idea: fixing non-ohmic devices by adding an ohmic device in series
• resistor has high resistance $\Rightarrow$ $I=\frac{U}{R}$ almost constant $\Rightarrow$ we can increase the voltage and things will be fine
• variable resistor (i.e. using rotatable knob): can be used to adjust circuit elements (such as a volume control or a lamp dimmer), or as sensing devices for heat, light, humidity, force, or chemical activity.
• what resistance for LED?
  • subtract voltage drop over LED: $U=U_{\mathrm{in}}-U_{\mathrm{LED}}$, e.g. $U=5V-2V=3V$
  • apply Ohm’s law: $R=\frac{U}{I}$, e.g. $R=\frac{3V}{20mA}=150\Omega$
• what resistance for multiple LEDs?
  • principally same as above
  • LEDs in series: voltage drop adds up (limits possible amount of LEDs per branch)
  • LEDs in parallel: same voltage as for single LED on each branch (overall resistance drops $\Rightarrow$ battery delivers more current, strong enough source needed)
    • single resistor for same LED in parallel? Needs lower resistance for higher current $\Rightarrow$ has to be bigger to dissipate more heat
    • two identical resistors in parallel: $R_{\mathrm{total}}=\frac{1}{2}R$
    • two resistors in parallel (general): $R_{\mathrm{total}}=R_1||R_2=\frac{R_1\cdot R_2}{R_1+R_2}$
    • resistors in parallel (general): $\frac{1}{R_{\mathrm{total}}}=\frac{1}{R_1}+\cdots +\frac{1}{R_n}$

Zener diode

• is a special type of diode designed to reliably allow current to flow “backwards” when a certain set reverse voltage, known as the Zener voltage, is reached
• a modified diode (lets current through in just one direction), that lets current pass in the second direction as well, as soon as some specific voltage is reached
  • or scientifically speaking: an abrupt, heavily doped p–n junction, in which case the reverse conduction occurs due to electron quantum tunnelling in the short distance between p and n regions

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Battery tester

our batteries:

• 3 $\times$ 3.7V $=$ 11.1V (3S meaning three cells in series)
• 1500mAh: 1.5A $\times$ 11.1V $=$ 16.65W for 1 hour
• 40C: max discharge rate (current): 40 $\times$ 1500mA $=$ 60A (with 11.1V this discharges battery in 1.5 minutes) $\Rightarrow$ would explode in case of short circuit
• cut off voltage (red LED): 9.0V; nominal voltage (yellow LED): 11.1V; maximum voltage (green LED): 12.6V
• fitting Zener diode: subtract 2V drop over the LED
• fitting resistor: gets lower from red to yellow to green because of parallelity

Breadboard

issues:

• unreliable: cables fall out of the board
• unsafe: potential short circuit
• (large, impractical)

Electronic devices (historically)

1. case (structural)
2. electronic components
3. wiring (flexible)

Printed circuit board (PCB)

a board base for physically supporting and wiring the components in electronics

• combining structure + wiring
• components are soldered
• fiberglass board covered with copper layer
  • etch away areas to create conductive traces

side effects:

1. mass production (PCB vs. breadboard = injection molding vs. 3D printing)
2. reliability
3. miniaturization

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KiCad Process

essentially a large drawing program

1. Circuit design: paper / breadbord
2. Draw schematic: recreate circuit design in KiCad (symbolic / logical, not physical)
3. Assign footprints: use BIS library (true size etching plan, model of physical PCB)
4. Board layout: creative arrangement of components, routes, text, etc. (finished model of physical PCB)
5. Fabrication
6. Assembly (soldering)

Prototyping PCBs

• use fiber laser for engraving

Manufacturing PCBs in Shenzen

• using photoengraving
• photosensitive film selectively hardens
• then use chemicals to etch away the unprotected copper
• for more complex circuits (routes crossing), even multilayer PCBs are possible

Solder mask

• a thin layer of polymer to prevent oxidation and solder bridges between closely spaced solder pads on a PCB

Take home message

You can make your own electronics and PCBs for your own software / hardware start-up