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# 3 Basic Electronics 3

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### 3 Basic Electronics 3

1. 1. Basic electronics Optical interfaces: Detect and control
2. 2. Ohm’s law <ul><li>Current = voltage / resistance </li></ul><ul><li>I = V / R </li></ul><ul><li>V = I x R </li></ul><ul><li>Definitions </li></ul><ul><li>Voltage = potential energy / unit charge, units = Volts </li></ul><ul><li>Current = charge flow rate, units = Amps </li></ul><ul><li>Resistance = friction, units = Ohms </li></ul><ul><li>Example </li></ul><ul><li>Voltage drop when current flows through resistor </li></ul><ul><li>V 1 - V 2 = I R </li></ul>I R V 1 V 2
3. 3. Schematics <ul><li>Symbols represent circuit elements </li></ul><ul><li>Lines are wires </li></ul>Battery Resistor Ground V R I Sample circuit Ground voltage defined = 0 + +
4. 4. Parallel and series resistors <ul><li>Series </li></ul><ul><li>same current flows through all </li></ul><ul><li>Parallel </li></ul><ul><li>save voltage across all </li></ul>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 + Note: these points are connected together I V R 1 R 2 + V R 1 R 2 I 1 I 2 I
5. 5. Resistive voltage divider <ul><li>Series resistor circuit </li></ul><ul><li>Reduce input voltage to desired level </li></ul><ul><li>Advantages: </li></ul><ul><ul><li>simple and accurate </li></ul></ul><ul><ul><li>complex circuit can use single voltage source </li></ul></ul><ul><li>Disadvantage: </li></ul><ul><ul><li>dissipates power </li></ul></ul><ul><ul><li>easy to overload </li></ul></ul><ul><ul><li>need R load << R 2 </li></ul></ul>New schematic symbol: external connection Resistive divider I = V in /R eff = V out /R 2 V out = V in (R 2 / (R 1 + R 2 ) ) + V in R 1 R 2 I I V out
6. 6. Variable voltage divider <ul><li>Use potentiometer (= variable resistor) </li></ul><ul><li>Most common: constant output resistance </li></ul>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 +
7. 7. Capacitors <ul><li>Charge = voltage x capacitance </li></ul><ul><li>Q = C V </li></ul><ul><li>Definitions </li></ul><ul><li>Charge = integrated current flow , units = Coloumbs = Amp - seconds </li></ul><ul><li>I = dQ/dt </li></ul><ul><li>Capacitance = storage capacity, units = Farads </li></ul><ul><li>Example </li></ul><ul><li>Capacitor charging circuit </li></ul><ul><li>Time constant = RC =  </li></ul>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 V out t V in  = RC Capacitor charging curve time constant = RC
8. 8. AC circuits <ul><li>Replace battery with sine (cosine) wave source </li></ul><ul><li>V = V 0 cos(2  f t) </li></ul><ul><li>Definitions </li></ul><ul><li>Frequency f = cosine wave frequency, units = Hertz </li></ul><ul><li>Examples </li></ul><ul><li>Resistor response: I = (V 0 /R) cos(2  f t) </li></ul><ul><li>Capacitor response: Q = CV 0 cos(2  f t) </li></ul><ul><ul><li>I = - 2  f CV 0 sin(2  f t) </li></ul></ul><ul><ul><li>Current depends on frequency </li></ul></ul><ul><ul><li>negative sine wave replaces cosine wave </li></ul></ul><ul><ul><li>- 90 degree phase shift = lag </li></ul></ul>V 0 cos(2  f t) C I = - 2  f CV 0 sin(2  f t) <ul><li>Capacitive ac circuit </li></ul><ul><li>90 degree phase lag </li></ul>V 0 cos(2  f t) R I = (V 0 /R) cos(2  f t) Resistive ac circuit New schematic symbol: AC voltage source
9. 9. Simplified notation: ac-circuits <ul><li>V = V 0 cos(2  f t) = V 0 [exp(2  j f t) + c.c.]/2 </li></ul><ul><li>Drop c.c. part and factor of 1/2 </li></ul><ul><li>V = V 0 exp(2  j f t) </li></ul><ul><li>Revisit resistive and capacitive circuits </li></ul><ul><li>Resistor response: I = (V 0 /R) exp(2  j f t) = V / R = V/ Z R </li></ul><ul><li>Capacitor response: I = 2  j f CV 0 exp(2  j f t) = (2  j f C) V = V/ Z C </li></ul><ul><li>Definition: Impedance, Z = effective resistance, units Ohms </li></ul><ul><li>Capacitor impedance Z C = 1 / (2  j  f C) </li></ul><ul><li>Resistor impedance Z R = R </li></ul><ul><li>Impedance makes it look like Ohms law applies to capacitive circuits also </li></ul><ul><li>Capacitor response I = V / Z C </li></ul>
10. 10. Explore capacitor circuits <ul><li>Impedance Z C = 1/ (2  j  f C) </li></ul><ul><li>Limit of low frequency f ~ 0 </li></ul><ul><ul><li>Z C --> infinity </li></ul></ul><ul><ul><li>Capacitor is open circuit at low frequency </li></ul></ul><ul><li>Limit of low frequency f ~ infinity </li></ul><ul><ul><li>Z C --> 0 </li></ul></ul><ul><ul><li>Capacitor is short circuit at low frequency </li></ul></ul>V 0 cos(2  f t) C I = V/Z C Capacitive ac circuit
11. 11. Revisit capacitor charging circuit <ul><li>Replace C with impedance Z C </li></ul><ul><li>Charging circuit looks like voltage divider </li></ul><ul><li>V out = V in (Z C / (Z R + Z C ) ) = V in / (1 + 2  j  f R C ) </li></ul><ul><li>Low-pass filter </li></ul><ul><li>Crossover when f = 1 / 2  R C = 1 / 2   ,  is time constant </li></ul><ul><li>lower frequencies V out ~ V in = pass band </li></ul><ul><li>higher frequencies V out ~ V in / (2  j  f R C ) = attenuated </li></ul>log(V out ) log(  f ) logV in f = 1 / 2  <ul><li>Low-pass filter response </li></ul><ul><li>time constant = RC =  </li></ul>Single-pole rolloff 6 dB/octave = 10 dB/decade knee Capacitor charging circuit = Low-pass filter V in = V 0 cos(2  f t) R C I V out I
12. 12. Inductors <ul><li>Voltage = rate of voltage change x inductance </li></ul><ul><li>V = L dI/dt </li></ul><ul><li>Definitions </li></ul><ul><li>Inductance L = resistance to current change, units = Henrys </li></ul><ul><li>Impedance of inductor: Z L = (2  j  f L) </li></ul><ul><li>Low frequency = short circuit </li></ul><ul><li>High frequency = open circuit </li></ul><ul><li>Inductors rarely used </li></ul>Capacitor charging circuit = Low-pass filter V out log(V out ) log(  f ) logV in f = R / 2  j  L High-pass filter response V in = V 0 cos(2  f t) R L I I New schematic symbol: Inductor
13. 13. Capacitor filters circuits <ul><li>Can make both low and high pass filters </li></ul>0 degrees 0 degrees 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
14. 14. Summary of schematic symbols + Battery Resistor Ground External connection Capacitor AC voltage source Inductor Non-connecting wires - + Op amp Potentiometer Potentiometer 2-inputs plus center tap Diode
15. 15. Color code <ul><li>Resistor values determined by color </li></ul><ul><li>Three main bands </li></ul><ul><ul><li>1st = 1st digit </li></ul></ul><ul><ul><li>2nd = 2nd digit </li></ul></ul><ul><ul><li>3rd = # of trailing zeros </li></ul></ul><ul><li>Examples </li></ul><ul><ul><li>red, brown, black </li></ul></ul><ul><ul><li>2 1 no zeros = 21 Ohms </li></ul></ul><ul><ul><li>yellow, brown, green </li></ul></ul><ul><ul><li>4 1 5 = 4.1 Mohm </li></ul></ul><ul><ul><li>purple, gray, orange </li></ul></ul><ul><ul><li>7 8 3 = 78 kOhms </li></ul></ul><ul><li>Capacitors can have 3 numbers </li></ul><ul><ul><li>use like three colors </li></ul></ul>Color black brown red orange yellow green blue violet gray white Number 0 1 2 3 4 5 6 7 8 9