Course Web Page • http://people.physics.tamu.edu/depoy/PHYS225.html
• Up now • Contains – All lecture notes (PDF) – All assignments – Useful links
Last lecture • 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
Ceramic disk Monolithic ceramic Dipped silvered-mica Mylar or polyester Aluminum electrolytic (+/-) Tantalum (+/-)
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/dt V ≈ RC dVin/dt Circuit differentiates the incoming signal
For square wave input, output is a series of pulses
