PHYS225Lecture 3

Electronic Circuits

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• Devices not like a resistor– Zener diode

– Tunnel diode

– Capacitor

• Signals– Sinusoid

• Frequency, phase, and amplitude

– Fourier transform• Can be used to characterize complex signals

Sinusoidal • Time variable signal

• Characterized by– Frequency

– Phase

– Amplitude

Sinusoidal

• Many sinusoids of top of each other– Many frequencies, phases, amplitudes added

• Fourier transform to sort out

Fourier transforms

Fourier transforms

Other kinds of signals

These have Fourier transforms too

Lots of combinations

Pulses

Machines available to generate these signals

• Function generator

• Pulse generator

• Signal generators

• Generally characterized by frequency, shape of pulse, etc.

Circuits with capacitors• Capacitors

– Q = CV– I = C dV/dT

• Current is proportional to rate of change of potential• Change in potential proportional to current

– Power stored as energy in internal electric field• Can get it back again later

• Parallel capacitance add– C = C1 + C2 + C3 + …

• Serial capacitors add like parallel resistors– 1/C = 1/C1 + 1/C2 + 1/C3 + …

• Many different kinds of capacitors– Each has unique and useful properties

Capacitors

Battery

Capacitor

Unit = Farad

Pico Farad - pF = 10-12FMicro Farad - uF = 10-6F

Capacitor types

Ceramic disk

Monolithic ceramic

Dipped silvered-mica

Mylar or polyester

Aluminum electrolytic (+/-)

Tantalum (+/-)

Ceramic disk Monolithic ceramic Dipped siver-mica Mylar Mylar

Solid tantalum, polarized Radial aluminum electrolytic Axial aluminum electrolytic

Capacitors

• Capacitance is determined by 3 factors– Plate surface area– Plate spacing– Insulating material (dielectric)

Capacitor ratings

Physical size of capacitors is related to voltage handling ability – WVDC – working voltage DC

Temperature coefficient may also be important –can be + or – or nearly zero

Temperature coefficient depends upon dielectric material

Circuits with capacitors

Potential across capacitor changes when a current flows through it

Circuits with capacitors

• C dV/dt = I = -V/R

• V = A e-t/RC

• Capacitors will “charge up” over time after application of an initial voltage

– Approaches the applied potential

• Will also “discharge” over time if the applied potential is reduced

Capacitor Charging

Capacitor Discharge

RC time constant

RC time constant• Product of RC in a simple circuit

– For R in ohms and C in farads, RC is in seconds

• 1 µF across 1KΩ = 1 ms

– Characteristic time of response for the circuit

• Sets “frequency response” of circuit

– How quickly circuit responds

– How much of which frequencies get through the circuit

Some applications

Time-delay circuit:Can induce a delay in a signal

Another application

I = C d/dt(Vin – V) = V/R

V = RC d/dt(Vin – V)

For small changes in dV/dtV ≈ RC dVin/dt

Circuit differentiates the incoming signal

For square wave input, output is a series of pulses

Unintentional capacitive coupling

Circuits with capacitors

• Integrators

– V << Vin

• Ramp generators

– If provide constant current,

• Voltage continues to increase

• All sometimes useful

Inductors

• V = L dI/dt; L is inductance– A simple coil of wire!

• Putting a voltage across an inductor causes the current to ramp

• Power stored in as energy in the magnetic field• 1 V across 1 henry produces 1 amp• Rare to use, but useful in some circumstances

– RF “chokes”– Transformers

• Two closely coupled inductors

Inductors

Values specified in henries (H), millihenries (mH) and microhenries (μH)

A coil of wire that may be wound on a core of air or other non-magnetic material, or on a magnetic core such as iron powder or ferrite.

Two coils magnetically coupled form a transformer.

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Inductor types

Molded inductor & air-wound inductor Adjustable air-wound inductor

Ferrite core toroidal transformer Iron powder toroidal inductorAir wound inductor

Inductor ratings

Wire gauge and physical size of the coil determine the current handling capacity.

Core material will have a temperature dependence. Air is best, followed by iron powder, then ferrites.

Transformers

• Two closely coupled coils

• AC voltage applied across one will appear across the other at a different voltage

– Change depends on ratio of the number of turns in the coil

• Power is conserved

– So if voltage goes up, current will go down

• Generally very efficient

Transformer

Transformers

• Useful to change “line” power to something else

– At the heart of everything used to power computers, cell phones, etc.

• Isolate circuit from actual connection to the power line