CHAPTER 25 RESONANCE
Resonance – What is it?
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WVSS example
Vibration Report
Much like pumping your legs on a swing
Singing and Breaking Windows
Building earthquake (Skip to 30 seconds):
https://www.youtube.com/watch?v=LV_UuzEznHs
Tacoma Narrows Bridge
http://www.youtube.com/watch?v=j-zczJXSxnw
http://youtu.be/wvJAgrUBF4w resonance using salt
Electronic Resonance
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Electronic Resonance is when the capacitive reactance
and inductive reactance cancel each other out, resulting
in low total impedance and HIGH CURRENT.
Thus when XC = XL , then in series circuits:
 ZT
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= R – jXC + jXL = 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?
VR = 50A x 2Ω = 100V
What is the voltage across the capacitor?
VC = 50A x –j5Ω = 250-90˚V
What is the voltage across the inductor?
VL = 50A x j5Ω = 25090˚V
Kirchoff’s Voltage Law still holds
Although it seems like there is no
VT = VR + VC + VL
voltage left for the capacitor and
100 = 100 + 250-90˚ + 25090˚
inductor to have, they still do. The
voltages are at opposite angles so they
100 = 100 + 0
cancel out.
Notice that the voltage across the capacitor (and inductor
as well) have more voltage than the source voltage!
Current
What is fo in
this circuit?
This is what
current looks
like at
resonant
frequency.
Resonant
Frequency is
labeled fo.
fo
On either side
of fo
impedance
increases
rapidly so
current goes
down.
Current
Explaining
Frequency
Domain vs.
Time Domain
Frequency
At frequencies greater than fo, the load is Inductive and vice versa.
When XC=XL , (fO) the circuit is purely resistive.
So what frequency will cause the
circuit to resonate???
There is only one
frequency that
causes XL and XC
to be equal to
each other. (fo)
This is what we
are solving for
𝑋𝐿 = 𝑋𝐶
1
2𝜋𝑓𝑜 𝐿 =
2𝜋𝑓𝑜 𝐶
1
2
𝑓𝑜 =
2𝜋𝐿 ∙ 2𝜋𝐶
2
𝑓𝑜 =
Notice R is not used for
calculating resonant
frequency
𝒇𝒐 =
1
2𝜋𝐿 ∙ 2𝜋𝐶
𝟏
=
𝟐𝝅 𝑳 ∙ 𝑪
𝟏
𝟐𝝅 𝟐𝟎𝟎𝒎𝑯 ∙ 𝟏𝟎𝒏𝑭
=3559 Hz
Make sure they can all do this in their calculator
Calculate the Resonant Frequency
𝒇𝒐 =
=
𝟏
𝟐𝝅 𝑳 ∙ 𝑪
𝟏
𝟐𝝅 𝟖𝒖𝑯 ∙ 𝟓𝟎𝟎𝒏𝑭
= 𝟕𝟗. 𝟔𝒌𝑯𝒛
What is the current at resonant frequency?
100𝑉
𝐼𝑇 =
= 10𝑚𝐴
10,000Ω
Calculate other stuff
Calculate VCL at fo
0V
Calculate VC at fo
+
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1
𝑉𝐶 = 𝐼𝐶 ∙ 𝑋𝐶 = 10𝑚𝐴 ∙ −𝑗
2𝜋𝑓𝐶
1
𝑉𝐶 = 𝐼𝐶 ∙ 𝑋𝐶 = 10𝑚𝐴 ∙ −𝑗
2𝜋79600 ∙ 500𝑛
= 10𝑚𝐴 ∙ −𝑗 4 Ω
Just because the circuit is at
resonance, doesn’t mean there
will be more voltage across the
capacitor or inductor than the
source voltage.
= 40 − 90˚𝑚𝑉
What is the voltage across the inductor?
It must be the same size as VC just in the
opposite direction!
𝑉𝐿 = 4090˚𝑚𝑉
Calculate the Resonant Frequency
𝒇𝒐 =
=
𝟏
𝟐𝝅 𝑳 ∙ 𝑪
𝟏
𝟐𝝅 𝟑𝑯 ∙ 𝟏𝟎𝒖𝑭
= 𝟐𝟗𝑯𝒛
What is the current at resonant frequency?
400𝑉
𝐼𝑇 =
= 20𝐴
20Ω
Calculate other stuff
Calculate VCL at fo
0V
Calculate VL at fo
+
𝑉𝐿 = 𝐼𝐿 ∙ 𝑋𝐿 = 20𝐴 ∙ 𝑗 2𝜋𝑓𝐿
= 20𝐴 ∙ 𝑗 2𝜋29 ∙ 3
= 10,93290˚𝑉 ‼‼!
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What is the voltage across the capacitor?
Again, it must be the same size as VL just in
the opposite direction
What is the magnification from
input voltage to VL or VC?
Q = 27
𝑉𝐶 = 10,932 − 90˚𝑉
Calculating L and C when given fo
Suppose you have a 100uF capacitor and want to have a resonant frequency of
1000Hz. What size inductor must you use?
𝒇𝒐 =
𝟏
𝟐𝝅 𝑳 ∙ 𝑪
L = 253uH
Calculating L and C when given fo
Suppose you have a 20nF capacitor and want to have a resonant frequency of
50kHz. What size inductor must you use?
L = 507uH
Calculating L and C when given fo
Suppose you have a 14mH inductor and want to have a resonant frequency of 60Hz.
What size capacitor must you use?
𝒇𝒐 =
𝟏
𝟐𝝅 𝑳 ∙ 𝑪
C = 503uF
RVOTD
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Random Video of the Day
Another RVOTD
Cutoff Frequency
Leave up on white board and see notes
Reminder of 4 question problem set