Lab 5 The AC Circuit, Impedance, High-Pass and Low-Pass Filters This experiment requires only a spreadsheet upload

Crystal radio (AM radio) Where is the crystal? No longer in there. Modern crystal radios use diodes instead. Today: AC circuits with a capacitor or an inductor AM operates from 535 to 1605 kHz.

Lab #5: RC and RL AC Circuits remember how AC circuits containing capacitors and resistors, as well as inductors and resistors, behave. First, remember how to describe a sine (or cosine)

Capacitors and AC sources Voltage across cap is the same as the voltage from supply. When the voltage is changing quickly, the charge also has to change quickly -> big current Size of the current depends on the frequency Get biggest currents at high frequencies

Presence of the capacitor affects the size of the current in the circuit in a frequency-dependent way. “phases” of signals across voltage source, resistor, and capacitor differ math is most easily done by modeling the voltage source as instead of and an imaginary reactive impedance for the capacitor (to shift its affect on the current by 90 degrees) and then taking the real part at the end. AC RC Circuits As before, be careful with the grounds!

The Math What is the current? Any complex number can be written as a magnitude and an angle in the complex plane. Easy to read off mag of current. Current (and thus voltage across the resistor) is shifted in phase from the voltage source by φ What is the current at very large ω?

Voltage across R and across C V R (t) leads V(t) by  V C (t) lags V(t) by  /2 - 

Inductive Impedance L X L = i  L Z = [R 2 + (  L) 2 ] 1/2  = L/R tan  =  L/R =  As with the RC circuit, the current can be written as

lab For a fixed frequency, measure the phase shift  two ways and “compare” (using a  2 test) Measure the phase shift versus frequency two ways and use to extract RC. Compare to RC calculated directly.

hints Include systematic errors for R and C measurements, but not for t and V measurements with scope. MAKE SURE DUTY CYCLE IS ALL THE WAY COUNTER CLOCKWISE! phase shift can not be greater than  remember “compare” is a mathematical operation involving a  2 test make sure the voltage oscillates around zero (using the offset knob). Make sure there is no dc offset. remember, V R leads V IN by  If your wave form looks funny, your amplitude is too big for the instrumentation amplifier. Make it smaller

Error Propagation

You measure  t. Calculate y = cotan(2  f  t). What is error in y?