Basic electronics
Optical interfaces:
Detect and control
Ohm’s law
Current = voltage / resistance
• I=V/R
• V=IxR
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
V1
I
R
V2
Schematics
• Symbols represent circuit elements
• Lines are wires
+
Battery
Sample circuit
V
Resistor
Ground
+
I
R
Ground voltage
defined = 0
Parallel and series resistors
Series
• same current flows through all
Parallel
• save voltage across all
+
I
R2
I
V
R1
I1
R2
R1
V
Parallel circuit
I = V/R1 + V/R2 = V/Reff
1/Reff = 1/R1 + 1/R2
+
Series circuit
V = R1 I + R2 I = Reff I
Reff = R1 + R2
I2
Note: these points are
connected together
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
Resistive divider
I = Vin/Reff = Vout/R2
Vout = Vin (R2 / (R1 + R2) )
Vin
+
I
Vout
R1
R2
I
New schematic symbol:
external connection
Variable voltage divider
• Use potentiometer (= variable resistor)
• Most common: constant output resistance
Variable voltage divider
Vout = Vin (Rout / (Rvar + Rout) )
New schematic symbol:
potentiometer
I
Vin
+
Vout
Rvar
Rout
I
Capacitors
• Charge = voltage x capacitance
• Q=CV
Definitions
• Charge = integrated current flow , units = Coloumbs = Amp - seconds
• I = dQ/dt
• Capacitance = storage capacity, units = Farads
Capacitor charging curve
time constant = RC
Example
• Capacitor charging circuit
Vin
• Time constant = RC = t
Vout
I
t = RC
Vout
t
V
R
+
C
New schematic
symbol:
capacitor
Q
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
• 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
Capacitive ac circuit
• 90 degree phase lag
Resistive ac circuit
V0 cos(2 p f t)
New schematic
symbol:
AC voltage source
I=
(V0/R) cos(2 p f t)
V0 cos(2 p f t)
R
I=
- 2 p f CV0 sin(2 p f t)
C
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
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
Capacitive ac circuit
V0 cos(2 p f t)
I = V/ZC
C
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
Capacitor charging circuit
= Low-pass filter
Vin = V0 cos(2 p f t)
Low-pass filter response
• time constant = RC = t
I
Vout
R
C
I
log(Vout)
logVin
Single-pole rolloff
6 dB/octave
= 10 dB/decade
knee
f=1/2pt
log( f )
Inductors
• 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 charging circuit
= Low-pass filter
Vin = V0 cos(2 p f t)
High-pass filter response
I
R
New schematic
symbol:
Inductor
logVin
Vout
L
I
log(Vout)
f=R/2pjL
log( f )
Capacitor filters circuits
• Can make both low and high pass filters
Low-pass filter
Vin = V0 cos(2 p f t) I
High-pass filter
Vin = V0 cos(2 p f t) I
Vout
R
Vout
C
C
R
I
Gain response
I
Gain response
logVin
logVin
log(Vout)
knee
log(Vout)
f=1/2pt
f=1/2pt
log( f )
Phase response
log( f )
0 degrees
phase
-90 degrees
f=1/2pt
log( f )
Phase response
phase
log( f )
0 degrees
-90 degrees
f=1/2pt
Summary of schematic symbols
+
Battery
AC voltage
source
Resistor
Potentiometer
Capacitor
Potentiometer
2-inputs plus
center tap
Inductor
Diode
Ground
External
connection
Non-connecting
wires
+
Op amp
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 Number
black
brown
red
orange
yellow
green
blue
violet
gray
white
0
1
2
3
4
5
6
7
8
9