CHAPTER 25 RESONANCE

Resonance – What is it?  WVSS example  Vibration Report Vibration Report  Much like pumping your legs on a swing  Tacoma Narrows Bridge Tacoma Narrows Bridge

Electronic Resonance  Electronic Resonance is when the capacitive reactance and inductive reactance cancel each other out, resulting in low total impedance and HIGH CURRENT.  Thus when X C = X L, then in series circuits:  Z T = R – jX C + jX L = R + 0 = R  Therefore, resonance is the frequency at which the circuit phase angle  is 0˚.  The reason for this is because the circuit is purely resistive when the reactances cancel each other out

When the capacitor and inductor have the same reactance, they cancel each other out. AKA they combine to be a short. What is the current at resonance? 50A What is the voltage across the resistor? What is the voltage across the capacitor? What is the voltage across the inductor? Kirchoff’s Voltage Law still holds V R = 50A x 2Ω = 100V V C = 50A x –j5Ω = 250  -90˚V Although it seems like there is no voltage left for the capacitor and inductor to have, they still do. The voltages are at opposite angles so they cancel out. V L = 50A x j5Ω = 250  90˚V V T = V R + V C + V L 100 =  -90˚  90˚ 100 = Notice that the voltage across the capacitor (and inductor as well) have more voltage than the source voltage!

This is what current looks like at resonant frequency. Resonant Frequency is labeled f o. What is f o in this circuit? fofo Current On either side of f o impedance increases rapidly so current goes down.

Explaining Frequency Domain vs. Time Domain Frequency Current

At frequencies greater than fo, the load is Inductive and vice versa. When X C =X L, (f O ) the circuit is purely resistive.

So what frequency will cause the circuit to resonate??? There is only one frequency that causes X L and X C to be equal to each other. (f o ) This is what we are solving for =3559 Hz Make sure they can all do this in their calculator Notice R is not used for calculating resonant frequency

Calculate the Resonant Frequency What is the current at resonant frequency?

Calculate other stuff Calculate V CL at f o 0V Calculate V C at f o Just because the circuit is at resonance, doesn’t mean there will be more voltage across the capacitor or inductor than the source voltage. What is the voltage across the inductor? It must be the same size as V C just in the opposite direction!

Calculate the Resonant Frequency What is the current at resonant frequency?

Calculate other stuff Calculate V CL at f o 0V Calculate V L at f o What is the voltage across the capacitor? Again, it must be the same size as V L just in the opposite direction

Calculating L and C when given f o Suppose you have a 100uF capacitor and want to have a resonant frequency of 1000Hz. What size inductor must you use? L = 253uH

Calculating L and C when given f o Suppose you have a 20nF capacitor and want to have a resonant frequency of 50kHz. What size inductor must you use? L = 506uH

Calculating L and C when given f o Suppose you have a 14mH inductor and want to have a resonant frequency of 60Hz. What size capacitor must you use? C = 503uF

RVOTD  Random Video of the Day Random Video of the Day

Cutoff Frequency Leave up on white board and see notes