AB80
RLC Series and Parallel Resonance
Operating Manual
Ver.1.1
An ISO 9001 : 2000 company
94-101, Electronic Complex Pardesipura,
Indore- 452010, India
Tel : 91-731- 2570301/02, 4211100
Fax: 91- 731- 2555643
e mail : info@scientech.bz
Website : www.scientech.bz
Toll free : 1800-103-5050
AB80
Scientech Technologies Pvt. Ltd.
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AB80
AB80
RLC Series and Parallel Resonance
Table of Contents
1.
Introduction
4
2.
Theory
6
3.
Experiments
•
Experiment 1
Study of the resonance in RLC Series Circuit
13
•
Experiment 2
Study of the resonance in RLC Parallel Circuit
15
4.
Warranty
17
5.
List of Accessories
17
RoHS Compliance
Scientech Products are RoHS Complied.
RoHS Directive concerns with the restrictive use of Hazardous substances (Pb,
Cd, Cr, Hg, Br compounds) in electric and electronic equipments.
Scientech products are “Lead Free” and “Environment Friendly”.
It is mandatory that service engineers use lead free solder wire and use the
soldering irons upto (25 W) that reach a temperature of 450°C at the tip as the
melting temperature of the unleaded solder is higher than the leaded solder.
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Introduction
AB80 is a compact, ready to use RLC Series and Parallel Resonance experiment
board. This board is useful for students to understand the resonance condition in RLC
networks. It can be used as stand alone unit with external DC Power Supply or can be
used with Scientech Analog Lab ST2612 which has built in DC power supply, AC
power supply, function generator, modulation generator, continuity tester, toggle
switches, and potentiometer.
List of Boards :
Model
Name
AB01
AB02
AB03
AB04
AB05
AB06
AB07
AB08
AB09
AB10
AB11
AB12
AB13
AB14
AB15
AB16
AB17
AB18
AB19
AB20
AB21
AB22
AB23
AB25
Diode characteristics (Si, Zener, LED)
Transistor characteristics (CB NPN)
Transistor characteristics (CB PNP)
Transistor characteristics (CE NPN)
Transistor characteristics (CE PNP)
Transistor characteristics (CC NPN)
Transistor characteristics (CC PNP)
FET characteristics
Rectifier Circuits
Wheatstone Bridge
Maxwell’s Bridge
De Sauty’s Bridge
Schering Bridge
Darlington Pair
Common Emitter Amplifier
Common Collector Amplifier
Common Base Amplifier
Cascode Amplifier
RC-Coupled Amplifier
Direct Coupled Amplifier
Class A Amplifier
Class B Amplifier (push pull emitter follower)
Class C Tuned Amplifier
Phase Locked Loop (FM Demodulator & Frequency Divider /
Multiplier)
Multivibrator ( Mono stable / Astable)
F-V and V-F Converter
V-I and I-V Converter
Zener Voltage Regulator
Transistor Series Voltage Regulator
Transistor Shunt Voltage Regulator
DC Ammeter
Instrumentation Amplifier
Differential Amplifier (Transistorized)
Operational Amplifier (Inverting / Non-inverting / Differentiator)
AB28
AB29
AB30
AB31
AB32
AB33
AB35
AB39
AB41
AB42
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AB43
AB44
AB45
AB49
AB51
AB52
AB54
AB56
AB57
AB58
AB59
AB64
AB65
AB66
AB67
AB68
AB82
AB83
AB84
AB85
AB88
AB89
AB90
AB91
AB92
AB93
AB96
AB97
AB101
AB102
AB106
Operational Amplifier (Adder/Scalar)
Operational Amplifier (Integrator/ Differentiator)
Schmitt Trigger and Comparator
K Derived Filter
Active filters (Low Pass and High Pass)
Active Band Pass Filter
Tschebyscheff Filter
Fiber Optic Analog Link
Owen’s Bridge
Anderson’s Bridge
Maxwell’s Inductance Bridge
RC – Coupled Amplifier with Feedback
Phase Shift Oscillator
Wien Bridge Oscillators
Colpitt Oscillator
Hartley Oscillator
Thevenin’s and Maximum power Transfer Theorem
Reciprocity and Superposition Theorem
Tellegen’s Theorem
Norton’s theorem
Diode Clipper
Diode Clampers
Two port network parameter
Optical Transducer (Photovoltaic cell)
Optical Transducer (Photoconductive cell/LDR)
Optical Transducer (Phototransistor)
Temperature Transducer (RTD & IC335)
Temperature Transducer (Thermocouple)
DSB Modulator and Demodulator
SSB Modulator and Demodulator
FM Modulator and Demodulator
………… and many more
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Theory
In many of the electrical circuits, resonance is a very important phenomenon. The
study of resonance is very useful particularly in the area of communications. For
example, the ability of a radio receiver to select a certain frequency, transmitted by a
station and to eliminate frequencies from other stations is based on the principle of
resonance. The resonance condition can be achieved by connecting RLC components
either in series or in parallel depending on the requirement.
Series RLC resonance circuit :
Series RLC circuit is as shown in figure 1. In a series RLC circuit, the current lags
behind, or leads the applied voltage depending upon the values of XL and XC. XL
causes the total current to lag behind the applied voltage, while XC causes the total
current to lead the applied voltage. When XL > XC, the circuit is predominantly
inductive, and when XC > XL, the circuit is predominantly capacitive. However, if one
of the parameters of the series RLC circuit is varied in such a way that the current in
the circuit is in phase with the applied voltage, then the circuit is said to be in
resonance.
R
L
C
Figure 1
The total impedance for the series RLC circuit is
1 

Z= R+j(X L − X C ) = R + j  ω L –

ω
C

It is clear from the circuit that the current I =
VS
Z
The circuit is said to be in resonance if the current is in phase the applied voltage. In a
series RLC circuit, series resonance occurs when XL = XC. The frequency at which
the resonance occurs is called resonant frequency.
Since XL = XC, the impedance in a series RLC circuit is purely resistive. At the
resonant frequency fr, the voltages across capacitance and inductance are equal in
magnitude. Since they are 180o out of phase with each other, they cancel each other
and, hence, zero voltage appears across the LC combination.
At resonance,
XL = XC
Solving for resonance we have,
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2πf r L=
f r2 =
1
2πf r C
1
4π 2 LC
fr =
1
2π LC
(1)
In a series RLC circuit, the resonance may be produced by varying frequency,
keeping L and C constant; otherwise, resonance may produced by varying either L or
C for a fixed frequency.
Impedance and phase angle of a series Resonant circuit :
The impedance in series RLC circuit is,
Z = Z = R 2 +  ω L −

1 

ωC 
2
.…….(2)
The variation of XC and XL with frequency is shown in figure 2
At zero frequency, both XC and Z are infinitely large, and XL is zero because the
capacitor acts as an open circuit at zero frequency and the inductor acts as a short
circuit at zero frequency. As the frequency increases, XC decreases and XL increases.
Since XC is larger than XL, at frequencies below resonant frequency fr, Z decreases
along with XC. At resonant frequency fr, XC = XL, and Z=R. At frequencies above the
resonant frequency fr, XL is larger than XC, causing Z to increase. The phase angle as
a function of frequency is shown in figure 2
At a frequency below the resonant frequency, the current leads the source voltage
because the capacitive reactance is greater than the inductive reactance. The phase
angle decreases as the frequency approaches the resonant value, and is 0° at
resonance. At frequencies above resonance, the current lags behind the source
voltage, because the inductive reactance is greater than capacitive reactance. As the
frequency goes higher, the phase angle approaches 90°
XC = –1/ ω C
Figure 2
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Figure 3
Voltages and current in a series resonant circuit :
The variation of impedance and current with frequency is shown in figure 3. At
resonant frequency, the capacitive reactance is equal to inductive reactance, and hence
the impedance is minimum. Because of the minimum impedance, maximum current
flows through the circuit. The current variation with frequency is plotted.
The voltage drops across resistance, inductance and capacitance and also varies with
frequency. At f = 0, the capacitor acts as an open circuit and blocks current. The
complete source voltage appears across the capacitor. As the frequency increases, XC
decreases and XL increases, causing total reactance XC – XL to decrease. As a result,
the impedance decreases and the current increases. As the current increases, VR also
increases, and both VC and VL increase.
Figure 4
When the frequency reaches its resonant value fr, the impedance is equal to R, and
hence, the current reaches its maximum value, and VR is at its maximum value.
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As the frequency is increased above resonance, XL continues to increase and XC
continues to decrease, causing the total reactance, XL–XC to increase. As a result there
is an increase in impedance and a decrease in current. As the current decreases, VR
also decreases, and VC and VL decrease. As the frequency becomes very high, the
current approach zero, both VR and VC approaches zero, and VL approaches Vs.
The response of different voltages with frequency is shown in figure 5
Figure 5
The drop across resistance reaches its maximum when f = fr . The maximum voltage
across capacitor occurs at f = fC. Similarly, the maximum voltage across inductor
occurs at f = fL.
The voltage drop across inductor is
VL =IX L
Where,
V
Z
I=
VL =
ωLV
1 

R 2 +  ωL −

ω
C

2
The maximum voltage across inductor is obtained at
fL =
1
2π LC
1
R 2C
1−
2L
The maximum voltage across capacitor is obtained at
fc =
1
1
2π
LC
–
R
2
2L
The maximum voltage across the capacitor occurs below the resonant frequency, and
the maximum voltage across the inductor occurs above the resonant frequency.
Here the frequency f1 is the frequency at which the current is 0.707 times the current
at resonant value, and it is called the lower cut off frequency.
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Bandwidth :
The bandwidth of any system is the range of frequencies for which the current or the
output voltage is equal to 70.7% of its value at resonant frequency, and is denoted by
BW. Figure 5 shows the response of series RLC circuit frequency. The frequency f2 is
the frequency at which the current is 0.707 times the current at resonant value (i.e.
maximum value), and is called the upper cut off frequency. The bandwidth, or BW, is
defined as the frequency difference of f2 and fl.
Figure 6
BW = f2 - fl
The unit of BW is the hertz (Hz).
If the current at PI is 0.707Imax, the impedance of the circuit at this point is
hence
BW =
2 R,
and
R
2π L
Parallel RLC resonance circuit :
Basically, parallel resonance occurs when XC = XL. The frequency at which resonance
occurs is called the resonant frequency. When XC = XL, the two branch-currents are
equal in magnitude and 180o out of phase with each other. Therefore, the two currents
cancel each other and the total current is zero. Consider the circuit shown in figure 6.
The condition for resonance occurs when XL = XC.
RL XL
Figure 7
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At resonance
X L =X C
Solving for resonance we have,
1
ω0 =
1  R 2L C-L  2
 2

LC  R L C-L 
or, when RL=RC
fr =
1
……… (1)
2π LC
Variation in impedance with frequency :
The impedance of parallel resonant circuit is maximum at the resonant frequency and
decreases at lower and higher frequencies, as shown in figure 7.
XL>XC
fr
XC>XL
f
Figure 8
At very low frequencies, XL is very small and XC is very large, so the total impedance
is essentially inductive. As the frequency increases, the impedance also increases, and
the inductive reactance dominates until the resonant frequency is reached. At this
point XL=XC and the impedance is at its maximum. As the frequency goes above the
resonance, the capacitive reactance dominates and the impedance decreases.
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Reactance Curves in Parallel Resonance :
The effect of variation of frequency on the reactance of the parallel circuit is shown in
the figure 8
Figure 9
The effect of inductive susceptance,
BL =
−1
2π fL
Inductive susceptance is inversely proportional to the frequency or (ω ). Hence it is
represented by a rectangular hyperbola, MN. It is drawn in forth quadrant, since BL is
negative. Capacitive susceptance, BC = 2π fC; it is directly proportional to frequency
f or (ω ). Hence it is represented as OP, passing through the origin. Net susceptance
B= BC – BL. it is represented by the curve JK, which is a hyperbola. At point ω r, the
total susceptance is zero, and the resonance takes place. The variation of the
admittance Y and the current I is represented by curve VW. The current will be
minimum at resonant frequency.
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Experiment 1
Objective :
Study of resonance in series RLC Circuit
Equipments Needed :
1.
Analog board AB80.
2.
Function Generator Caddo 4062 are equivalent.
3.
Oscilloscope Caddo 802 or equivalent
4. 2mm patch chords.
Circuit diagram :
Circuit used to study the resonance in series RLC circuit is shown below :
Figure 10
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Procedure :
1.
Connect point a and c this will bring capacitor C1 in series with R1 and L1.
2.
Connect a 10Vp-p sine wave signal at the input Vin (for series RLC resonance
circuit) and Gnd.
3.
Observe the output waveform on Oscilloscope between test point tp1 and Gnd
CH 1.
4.
Gradually increase the frequency of input signal from 0Hz to 10KHz and note
the respective output signal amplitude (put Oscilloscope in XY mode to get
exact amplitude readings) in given table.
5.
Calculate the resonance frequency using equation 1 and crosscheck the results.
Results :
S.
Number
Frequency (Hz)
Voltage (Vp-p)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Theoretical value of resonant frequency = fr =
1
2π LC
= …………Hz
Calculate
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Experiment 2
Objective :
Study of Resonance in Parallel RLC Circuit
Equipments Needed :
1.
Analog board AB80.
2.
Function Generator Caddo 4062-10MHz or equivalent.
3.
Oscilloscope Caddo 802 or equivalent
4. 2mm patch chords.
Circuit diagram :
Circuit used to study the resonance in series RLC circuit is shown below :
Figure 11
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Procedure for Parallel RLC circuit :
a. Connect point e and point f.
b. Connect point g and point j.
This will bring L3 and C3 in parallel.
c.
Connect a 10Vp-p sine wave signal at the input Vin (for parallel RLC resonance
circuit) and Gnd.
d. Observe the output waveform on Oscilloscope between test point tp1 and Gnd
of CH 1.
e.
Gradually increase the frequency of input signal from 0 Hz to 50 KHz and note
the respective output signal amplitude (put Oscilloscope in XY mode to get
exact amplitude readings) in given table.
f.
Calculate the resonance frequency using equation 1 and crosscheck the result.
g. Follow the steps from 2 to 5 when
i.
Point e is connected to point h and point i to point j (R=1K, L= 65mH, C =
0.1uF)
ii.
Point e is connected to point f and point g to point k (R=1K, L=12mH,
C=2n2)
iii.
Point e is connected to point h and point I to point k (R=1K, L=65mH,
C=2n2)
Results :
S. Number
Frequency (Hz)
Voltage (Vp-p)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Theoretical value of resonant frequency = fr =
Scientech Technologies Pvt. Ltd.
1
2π LC
= …………Hz
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AB80
Warranty
1.
We guarantee the product against all manufacturing defects for 24 months from
the date of sale by us or through our dealers. Consumables like dry cell etc. are
not covered under warranty.
2.
The guarantee will become void, if
a)
The product is not operated as per the instruction given in the operating
manual.
b)
The agreed payment terms and other conditions of sale are not followed.
c)
The customer resells the instrument to another party.
d)
Any attempt is made to service and modify the instrument.
3.
The non-working of the product is to be communicated to us immediately giving
full details of the complaints and defects noticed specifically mentioning the
type, serial number of the product and date of purchase etc.
4.
The repair work will be carried out, provided the product is dispatched securely
packed and insured. The transportation charges shall be borne by the customer.
For any Technical Problem Please Contact us at service@scientech.bz
List of Accessories
1.
2mm Patch Cord (Red) 16” ................................................................... 4 Nos.
2.
2mm Patch Cord (Blue) 16” .................................................................. 2 Nos.
3.
2mm Patch Cord (Black) 16”................................................................. 5 Nos.
4.
e-Manual ................................................................................................1 No.
Updated 26-06-2009
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