Analog Circuits Seth Price Department of Chemical Engineering New Mexico Tech Rev. 8/20/15

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/wp content/uploads/2009/08/23-half-wave-rectifier-1024x368.gif

IV Curve for Diodes https://learn.sparkfun.com/tutorials/diodes/real-diode-characteristics

Zener Diode • Diode that is meant to operate in reverse bias region – Very stable, consistent voltage • Can be used to replace battery, complex resistor network in some situations

Capacitors • Store energy in an electric field • Measured in Farads (F) • Two physical configurations – Parallel plates – Concentric cylinders

Capacitor Combinations • Series Combination: • 1/C eq = 1/C 1 + 1/C 2 + … + 1/C n • Parallel Combination: • C eq = C 1 + C 2 + … + C n

Capacitor Voltage V c(t) = V s (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 • L eq = L 1 + L 2 + … + L n • Parallel Combinations • 1/L eq = 1/L 1 + 1/L 2 + … + 1/L n

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