Analog Circuits
Seth Price
Department of Chemical Engineering
New Mexico Tech
Rev. 1/13/16
Ohm’s Law
• E = IR
–E is the voltage across a component
–I is the current through a component
–R is the resistance of the component
Resistor Color Code
Series/ Parallel Combinations
• Series: the same current passed through
multiple components
• Req = R1 + R2 + …
• Parallel: the same voltage is across multiple
components
• 1/Req = 1/R1 + 1/R2 + ….
Kirchoff’s Current Law (KCL)
• Any current flowing into a node must also
leave the node:
– The sum of all currents = 0
– Think “conservation of mass”
Kirchoff’s Voltage Law (KVL)
• The sum of the voltages around any closed
loop must equal zero
– Any voltage generated must be dissipated
– Think “conservation of mass”
Using a Multimeter
• Measure voltage in parallel
– Meter tries to have infinite impedance
• Measure current in series
– Meter tries to have no impedance
• 3 Point Safety Check
– Measure known voltage (ex wall outlet)
– Measure voltage on what you think has no power
– Measure known voltage again
Current Limiter
• All devices have a
maximum
allowable current
• A resistor in
series drops
current in loop
http://tinkerlog.com/2009/04/05/driving-an-led-with-or-without-a-resistor/
Shunt Resistor
• High currents are hard to
measure
• Instead, place a small
resistance (of known
value) in series
• Measure voltage drop
across resistor
• From Ohm’s law: I= V/R
http://www.reuk.co.uk/What-is-a-Shunt.htm
Wheatstone Bridge
• Easy to detect small
voltages
• R1, R2 and R3 are known
• Rx is adjustable
– Perhaps a sensor
• As Rx changes, the current
from A->C changes, Vg
changes
http://en.wikipedia.org/wiki/Wheatstone_bridge
Diodes (PN Junction)
•
•
•
•
Diodes conduct in only one direction
Semiconducting device
Resistance is non-linear
Require a “knee” or “turn-on” voltage
– Silicon: 0.6-0.7V
– Germanium: 0.3V
– LED: 1.7V
Diode Vs. Sine Wave
• http://www.duncansonelectric.com/blog/wpcontent/uploads/2009/08/23-half-wave-rectifier-1024x368.gif
IV Curve for Diodes
https://learn.sparkfun.com/tutorials/diodes/real-diode-characteristics
Capacitors
• Store energy in an electric field
• Measured in Farads (F)
• Two physical configurations
– Parallel plates
– Concentric cylinders
Capacitor Combinations
• Series Combination:
• 1/Ceq = 1/C1 + 1/C2 + … + 1/Cn
• Parallel Combination:
• Ceq = C1 + C2 + … + Cn
Capacitor Voltage
Vc(t) = Vs(1-e-t/T)
• Vc(t): Voltage across
capacitor at any time
• Vs: Source voltage
• T: Time constant
• t: elapsed time
Inductors
• Store energy in a magnetic field
• Measured in Henries (H)
• Typically a coil of wire
• Adjustable inductor: slug
Inductor Combinations
• Series Combinations
• Leq = L1 + L2 + … + Ln
• Parallel Combinations
• 1/Leq = 1/L1 + 1/L2 + … + 1/Ln
Inductor Voltage
V(t) = -L * di/dt
• V(t): Voltage across
Inductor as a function of
time
• L: inductance in Henries
• di/dt: change in current
with respect to time
Time Constants
• Time Constant (T): way to characterize time to
charge/discharge a capacitor or inductor
• 1*T: 63% of the maximum charge
• 5*T: fully charged
• For a capacitor: T = R*C
• For an inductor: T = L/R
Solenoids
• Changing current induces magnetic field
• Magnetic field moves plunger
• Used in starter motors, valves, latches, etc.
Solenoid Valve
Transformers
• Two adjacent inductors that can
influence each other
• Can add an iron core to transformer
to increase magnetic field
• No electron travels between
inductors
– Isolation Transformer
Putting it all together…
• DC Power Supply