LRC circuit Real Imag V  |I| = |1/Z| |V| I = (1/Z)V ext L R C I V ext Z must have amplitude & phase

Usually write: Z is IMPEDANCE (generalized resistance) But Z is ratio of applied voltage to resulting current, or "in/out" 1/Z (also Y) is ADMITTANCE Is a ratio of "out/in" 1/Z is a frequency-dependent, complex quantity that describes the system's response to a driving voltage. It is a "response function".

R circuit Look for independent of  Purely resistive circuit: Current in phase with driving voltage at all frequencies Magnitude indep. of frequency R I V=IR V ext Is there a phase shift?

R circuit drive R I V=IR V ext response Phasor diagram Impedance, Z Admittance, 1/Z

C circuit dependent on  Purely capacitive circuit: Current leads driving voltage (ICE) Magnitude depends on frequency C I V=q/C V ext Look for

C circuit C I V=q/C V ext input output Phasor diagram ICE Impedance, Z Admittance, 1/Z (sometimes Y)

L circuit dependent on  Purely inductive circuit: Current lags driving voltage (ELI) Magnitude depends on frequency V L  =LdI/dt I L V + - V ext Look for

L circuit I L V + - V ext input output Phasor diagram ELI Impedance, Z Admittance, 1/Z

L (inductance), C (capacitance), cause oscillation, R (resistance) causes damping LRC circuit L R C I

Real Imag V  |I| = |1/Z| |V| I = (1/Z)V L R C I V ext

12

Amplitude of I/V app Frequency,  -> What is the best variable to plot for the LRC lab? ADMITTANCE

Frequency,  -> Phase of I (rel to V app )

Q factor of an underdamped oscillator large if  is small compared to  0 Damping time or "1/e" time is  = 1/   (>> 1/   if  is very small) How many T 0 periods elapse in the damping time? This number (times π) is the Quality factor or Q of the system.

Current Amplitude |I 0 | Driving Frequency------> Find frequencies where POWER drops to half maximum (current drops to of max). These define . Find resonant frequency,  0 Max Amplitude Homework problem to show the two definitions are the same.

QUETSION: FM radio stations have broadcast frequencies of approximately 100 MHz. Most radios use a series LRC circuit similar to the one you used in the lab as part of the receiver electronics. Estimate the spacing of the broadcast frequencies of FM stations if typical receivers have a Q of 500 or better. Explain your reasoning, and include a graph. station 1 station 2 

QUETSION: FM radio stations have broadcast frequencies of approximately 100 MHz. Most radios use a series LRC circuit similar to the one you used in the lab as part of the receiver electronics. Estimate the spacing of the broadcast frequencies of FM stations if typical receivers have a Q of 500 or better. Explain your reasoning, and include a graph. station 1 station 2  Therefore, stations 99.3 and 99.5 FM are allowed, but 99.3 and 99.4 FM are not! They have cross-talk!

You should be able to: Calculate & plot the magnitude and phase of 1/Z Convert between the mag/phase and Re/Im forms Draw phasor diagrams of V ext, I, 1/Z (or Z) Express 1/Z (or Z) in terms of R, L, C or  0,  You should be able to discuss: The amplitude of the response and resonance The phase of the response The nature of the behavior at all frequencies The transfer of the series LCR circuit analysis to analogous oscillatory systems