Embedded Systems Analog ElectronicsUnitsTerminologyCircuit Analysis ToolsResistorsSlide 6Slide 7Voltage DividerCapacitorsSlide 10RC CircuitsSlide 12RC DifferentiatorRC IntegratorInductorsSlide 16TransformersSwitchesRelaysTuteBotSlide 21Laboratory for Perceptual Robotics – Department of Computer ScienceEmbedded SystemsAnalog ElectronicsLaboratory for Perceptual Robotics – Department of Computer ScienceUnitsphysical units = length [meter], mass [kilogram], time [second]force - [Newton]: kg m/s2 (F=ma)torque - [N m]energy - [joule]: 1N acting through distance of 1m - [calorie]: raise the temperature of 1 gram of water by 1 degree centigradepower - [Watts]: energy rate of 1 joule/seccharge - [coulomb]: -1(charge of 0.624142 x 1019) electronscurrent - [Amperes]: 1 coulomb/secvoltage - [Volts]: 1 joule of energy is required to push 1 coulomb up a 1 volt potential differenceLaboratory for Perceptual Robotics – Department of Computer ScienceTerminologyconductor - materials (metals) with a crystalline structure withloosely bound electrons in the (outer) valence shell donate electrons to the lattice easilyinsulators - materials with tightly bound electrons in the valenceshellsemiconductors - a material whose conductivity can becontrolledLaboratory for Perceptual Robotics – Department of Computer ScienceCircuit Analysis ToolsKirchoff’s Current Law - the sum of the current flowing into a junction is zero (conservation of electrical charge)Kirchoff’s Voltage Law - the sum of the voltagesTaken around any closed circuit is zeroI1 + I2 + I3 + I4 = 0V1+ V2 + V3 + V4 + V5 = 0Laboratory for Perceptual Robotics – Department of Computer ScienceResistorsresistance - [Ohms, ]: a resistance of 1  permits a 1 Acurrent flow given 1 V of electromotive potentialpower dissipated in resistors - P=VI=V2/R=I2RLaboratory for Perceptual Robotics – Department of Computer ScienceResistorsblack 0brown 1red 2orange 3yellow 4green 5blue 6violet 7grey 8white 91/8, 1/4, 1/2, 1, 10 Wcarbon film - up to 1/4 W, precision to 5%[d1 d2 exp precision]: for example: 4700 W at 5%yellow violet red goldLaboratory for Perceptual Robotics – Department of Computer ScienceResistorsseries combinationparallel combinationLaboratory for Perceptual Robotics – Department of Computer ScienceVoltage DividerLaboratory for Perceptual Robotics – Department of Computer ScienceCapacitors• capacitance - [Farads]: Michael Faraday • capacitor - two terminal device that storesenergy in the form of an electric charge• two conductors separated by a thin layer of dielectric• capacitance ~ conductor surface area, thinness of dielectric• two adjacent wires in a ribbon cable are subject to capacitive crosstalk(ground every other wire)• big capacitors are polarized , terrible accuracy, temperature stability,leakage, and lifetime---a loud buzzing noise from electronics couldbe an electrolytic capacitor has diedLaboratory for Perceptual Robotics – Department of Computer ScienceCapacitorsseries combination parallel combinationLaboratory for Perceptual Robotics – Department of Computer ScienceRC CircuitsLaboratory for Perceptual Robotics – Department of Computer ScienceRC Circuitstiming - RC is called the time constant, , of the circuit, voltage will fall to 37% of its initial value in RC seconds.smoothing - high frequency noise on top of a slowly varying signal can be rejected by observing the signal through a relatively large RC time constantLaboratory for Perceptual Robotics – Department of Computer ScienceRC Differentiatorchoose R and C small so Vout is smallnote - this can happen by accident, if a smooth signal is corrupted with noise, maybe it’s capacitive coupling---perhaps a digital line is too close to an analog signal.Laboratory for Perceptual Robotics – Department of Computer ScienceRC Integratorchoose R and C large so Vout is smallLaboratory for Perceptual Robotics – Department of Computer ScienceInductors• inductance - [Henries]: 1 volt across 1 Henryproduces a current that increases at 1 amp persecond• an inductor is normally formed from a coil of wire that may be wound on a core of magnetic material.• a voltage source across an inductor causes the current to rise as a ramp.• stopping a current going through an inductor generates a high voltage.Laboratory for Perceptual Robotics – Department of Computer ScienceInductorsseries combination parallel combinationno mutual inductanceLaboratory for Perceptual Robotics – Department of Computer ScienceTransformers• transformers are the main reason why AC power is used.• often first stage for low voltage DC power“gearbox” for AC voltage and currentprimary secondaryI ~ V ~ constant power: VI ()6 : 3 =6/3VinVoutstep-down:less voltagemore currentVoutVin3 : 6 =3/6step-up:more voltageless currentLaboratory for Perceptual Robotics – Department of Computer ScienceSwitchesSwitches are classified in terms of the number of poles and number of throws.Common types are SPST DPDT SPDT, sometimes with center-off position.Note that contacts bounce for about a millisecond after closing. This is noticeable to logic circuits, which can respond in nanoseconds.SPSTSPDTDPDTLaboratory for Perceptual Robotics – Department of Computer ScienceRelays• electro-magnetically operated switches• input behaves as an inductor with some loss (the energy required to operate the switch as well as the normal resistance)• the output circuit behaves as a switch• take milliseconds to operate• can only manage a few million operations• can take a lot of abuse, unlike electronic switches which can die from a very brief overvoltage.Laboratory for Perceptual Robotics – Department of Computer ScienceTuteBota circuit, a chassis, a sensor, a battery, and two motors…programmed by adjusting two potentiometersLaboratory for Perceptual Robotics – Department of Computer ScienceTuteBot• diode D alleviatesexcessive voltage on collector when the field in the inductor collapses• capacitor C2 smoothesvoltage spikes from the motor• with Vout(0) =