07-basic-electronics (1)

Basic electronics : 

Basic electronics Optical interfaces: Detect and control

Ohm’s law : 

Ohm’s law Current = voltage / resistance I = V / R V = I x R Definitions Voltage = potential energy / unit charge, units = Volts Current = charge flow rate, units = Amps Resistance = friction, units = Ohms Example Voltage drop when current flows through resistor V1 - V2 = I R I R V1 V2

Schematics : 

Schematics Symbols represent circuit elements Lines are wires Battery Resistor Ground V R I Sample circuit Ground voltage defined = 0

Parallel and series resistors : 

Parallel and series resistors Series same current flows through all Parallel save voltage across all Series circuit V = R1 I + R2 I = Reff I Reff = R1 + R2 Parallel circuit I = V/R1 + V/R2 = V/Reff 1/Reff = 1/R1 + 1/R2

Resistive voltage divider : 

Resistive voltage divider Series resistor circuit Reduce input voltage to desired level Advantages: simple and accurate complex circuit can use single voltage source Disadvantage: dissipates power easy to overload need Rload << R2 New schematic symbol: external connection Resistive divider I = Vin/Reff = Vout/R2 Vout = Vin (R2 / (R1 + R2) )

Variable voltage divider : 

Variable voltage divider Use potentiometer (= variable resistor) Most common: constant output resistance Vin Rvar Rout I I Vout Variable voltage divider Vout = Vin (Rout / (Rvar + Rout) ) New schematic symbol: potentiometer

Capacitors : 

Capacitors Charge = voltage x capacitance Q = C V Definitions Charge = integrated current flow , units = Coloumbs = Amp - seconds I = dQ/dt Capacitance = storage capacity, units = Farads Example Capacitor charging circuit Time constant = RC = t Capacitor charging circuit V = VR + VC = R dQ/dt + Q/C dQ/dt + Q/RC = V/R Q = C V (1 - exp(-t/RC)) Vout = Vin (1 - exp(-t/RC))

AC circuits : 

AC circuits Replace battery with sine (cosine) wave source V = V0 cos(2 p f t) Definitions Frequency f = cosine wave frequency, units = Hertz Examples Resistor response: I = (V0/R) cos(2 p f t) Capacitor response: Q = CV0 cos(2 p f t) I = - 2 p f CV0 sin(2 p f t) Current depends on frequency negative sine wave replaces cosine wave - 90 degree phase shift = lag V0 cos(2 p f t) C I = - 2 p f CV0 sin(2 p f t) Capacitive ac circuit 90 degree phase lag

Simplified notation: ac-circuits : 

Simplified notation: ac-circuits V = V0 cos(2 p f t) = V0 [exp(2 p j f t) + c.c.]/2 Drop c.c. part and factor of 1/2 V = V0 exp(2 p j f t) Revisit resistive and capacitive circuits Resistor response: I = (V0/R) exp(2 p j f t) = V / R = V/ ZR Capacitor response: I = 2 p j f CV0 exp(2 p j f t) = (2 p j f C) V = V/ ZC Definition: Impedance, Z = effective resistance, units Ohms Capacitor impedance ZC = 1 / (2 p j f C) Resistor impedance ZR = R Impedance makes it look like Ohms law applies to capacitive circuits also Capacitor response I = V / ZC

Explore capacitor circuits : 

Explore capacitor circuits Impedance ZC = 1/ (2 p j f C) Limit of low frequency f ~ 0 ZC --> infinity Capacitor is open circuit at low frequency Limit of low frequency f ~ infinity ZC --> 0 Capacitor is short circuit at low frequency V0 cos(2 p f t) C I = V/ZC Capacitive ac circuit

Revisit capacitor charging circuit : 

Revisit capacitor charging circuit Replace C with impedance ZC Charging circuit looks like voltage divider Vout = Vin (ZC / (ZR + ZC) ) = Vin / (1 + 2 p j f R C ) Low-pass filter Crossover when f = 1 / 2 p R C = 1 / 2 p t , t is time constant lower frequencies Vout ~ Vin = pass band higher frequencies Vout ~ Vin / (2 p j f R C ) = attenuated log(Vout) log( f ) logVin f = 1 / 2 p t Low-pass filter response time constant = RC = t Single-pole rolloff 6 dB/octave = 10 dB/decade knee

Inductors : 

Inductors Capacitor charging circuit = Low-pass filter Vout log(Vout) log( f ) logVin f = R / 2 p j L High-pass filter response Voltage = rate of voltage change x inductance V = L dI/dt Definitions Inductance L = resistance to current change, units = Henrys Impedance of inductor: ZL = (2 p j f L) Low frequency = short circuit High frequency = open circuit Inductors rarely used

Capacitor filters circuits : 

Capacitor filters circuits Can make both low and high pass filters 0 degrees 0 degrees

Summary of schematic symbols : 

Summary of schematic symbols

Color code : 

Color code Resistor values determined by color Three main bands 1st = 1st digit 2nd = 2nd digit 3rd = # of trailing zeros Examples red, brown, black 2 1 no zeros = 21 Ohms yellow, brown, green 4 1 5 = 4.1 Mohm purple, gray, orange 7 8 3 = 78 kOhms Capacitors can have 3 numbers use like three colors Color black brown red orange yellow green blue violet gray white Number 0 1 2 3 4 5 6 7 8 9