Basic electronics Optical interfaces: Detect and control

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 V 1 - V 2 = I R I R V1V1 V2V2

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

Parallel and series resistors Series same current flows through all Parallel save voltage across all + Note: these points are connected together I V R1R1 R2R2 Series circuit V = R 1 I + R 2 I = R eff I R eff = R 1 + R 2 Parallel circuit I = V/R 1 + V/R 2 = V/R eff 1/R eff = 1/R 1 + 1/R 2 + V R1R1 R2R2 I1I1 I2I2 I

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 R load << R 2 New schematic symbol: external connection + V in R1R1 R2R2 I I V out Resistive divider I = V in /R eff = V out /R 2 V out = V in (R 2 / (R 1 + R 2 ) )

Variable voltage divider Use potentiometer (= variable resistor) Most common: constant output resistance + V in R var R out I I V out Variable voltage divider V out = V in (R out / (R var + R out ) ) New schematic symbol: potentiometer

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 =  Capacitor charging circuit V = V R + V C = R dQ/dt + Q/C dQ/dt + Q/RC = V/R Q = C V (1 - exp(-t/RC)) V out = V in (1 - exp(-t/RC)) New schematic symbol: capacitor + V R C I V out Q t V in  = RC Capacitor charging curve time constant = RC

AC circuits Replace battery with sine (cosine) wave source V = V 0 cos(2  f t) Definitions Frequency f = cosine wave frequency, units = Hertz Examples Resistor response: I = (V 0 /R) cos(2  f t) Capacitor response: Q = CV 0 cos(2  f t) –I = - 2  f CV 0 sin(2  f t) –Current depends on frequency –negative sine wave replaces cosine wave –- 90 degree phase shift = lag V 0 cos(2  f t) R I = (V 0 /R) cos(2  f t) Resistive ac circuit New schematic symbol: AC voltage source V 0 cos(2  f t) C I = - 2  f CV 0 sin(2  f t) Capacitive ac circuit 90 degree phase lag

Simplified notation: ac-circuits V = V 0 cos(2  f t) = V 0 [exp(2  j f t) + c.c.]/2 Drop c.c. part and factor of 1/2 V = V 0 exp(2  j f t) Revisit resistive and capacitive circuits Resistor response: I = (V 0 /R) exp(2  j f t) = V / R = V/ Z R Capacitor response: I = 2  j f CV 0 exp(2  j f t) = (2  j f C) V = V/ Z C Definition: Impedance, Z = effective resistance, units Ohms Capacitor impedance Z C = 1 / (2  j  f C) Resistor impedance Z R = R Impedance makes it look like Ohms law applies to capacitive circuits also Capacitor response I = V / Z C

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

Revisit capacitor charging circuit Replace C with impedance Z C Charging circuit looks like voltage divider V out = V in (Z C / (Z R + Z C ) ) = V in / (1 + 2  j  f R C ) Low-pass filter Crossover when f = 1 / 2  R C = 1 / 2 ,  is time constant lower frequencies V out ~ V in = pass band higher frequencies V out ~ V in / (2  j  f R C ) = attenuated Capacitor charging circuit = Low-pass filter V in = V 0 cos(2  f t) R C I V out I log(V out ) log(  f ) logV in f = 1 / 2  Low-pass filter response time constant = RC =  Single-pole rolloff 6 dB/octave = 10 dB/decade knee

Inductors Capacitor charging circuit = Low-pass filter V out log(V out ) log(  f ) logV in f = R / 2  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: Z L = (2  j  f L) Low frequency = short circuit High frequency = open circuit Inductors rarely used V in = V 0 cos(2  f t) R L I I New schematic symbol: Inductor

Capacitor filters circuits Can make both low and high pass filters Low-pass filter V in = V 0 cos(2  f t) R C I V out I High-pass filter V in = V 0 cos(2  f t) C R I V out I log(V out ) log(  f ) logV in f = 1 / 2  Gain response log(V out ) log(  f ) logV in f = 1 / 2  Gain response knee phase log(  f ) f = 1 / 2  Phase response -90 degrees phase log(  f ) f = 1 / 2  Phase response -90 degrees 0 degrees

Summary of schematic symbols + BatteryResistor Ground External connection Capacitor AC voltage source Inductor Non-connecting wires - + Op amp Potentiometer 2-inputs plus center tap Diode

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 Mohm –purple, gray, orange – = 78 kOhms Capacitors can have 3 numbers –use like three colors Color black brown red orange yellow green blue violet gray white Number