resonance/electrical networks

ANALOG COMMUNICATION
Chandra Shekhar K NTFF-SIT Tumkur Centre
Unit2 ELECTRICAL NETWORK
2.1. RESONANCE CIRCUIT
Definition:
Resonance is a condition in an RLC circuit in which the capacitive and inductive
reactances are equal in magnitude at one particular frequency, thereby
resulting in purely resistive impedance.
Types of resonance:
1. Series resonance
2. Parallel resonance
APPLICATIONS OF RESONANCE:
1. Tuners
2. Oscillators
3. Filters
4. Mixers
5. Induction Heating
2.1.2 series resonance
Circuit Diagram of series resonance

Phasor diagram of Series Resonance
Resonance curve
I
VR
VL
Vc

2.1.3 Characteristics of series Resonance
1. Applied Voltage and resulting current are in phase
2. Power Factor is unity
3. Impedance of circuit will be purely resistive
4. Current is maximum
5. Acts as Voltage amplifier
6. BELOW RESONANCE ƒr The circuit is capacitive
7. ABOVE RESONANCE ƒr The circuit is inductive
2.1.4 Expressions of series Resonance
1. Condition for resonance
Resonance occurs when XL = XC
2. Frequency for resonance
3. Impedance
Note: Impedance at Resonance
RZ 0

4. Current Current at Resonance
R
V
Ir 
5.Voltage
Voltage drop across L
VL = I(2πfrL)
Voltage drop across C
Vc = I 





frC2
1
Voltage drop across R
VR = IR
6.Q Factor
1.Q = C
L
R
1
2.Q = R
frL2
3.Q = frCR2
1
7.Power Factor at Resonance
Power factor at Resonance is 1
Cosφ=1

8.Expression of Bandwidth in terms of Q
Bandwidth= Q
fr
Other expression for Bandwidth
1.Bandwidth= BW= f2-f1
2.Bandwidth= BW= L
R
2
Problems Based on Series Resonance
1.Follow class note
2. Write all Problems including assignments

2.1.5 Parallel resonance
Circuit Diagram
Phasor diagram of Parallel Resonance

Resonance curve
2.1.5 Characteristics of Parallel Resonance
1. Applied Voltage and resulting current are in phase
2. Power Factor is unity
3. At resonance Impedance is maximum & Current is minimum
4. Acts as current amplifier
5. BELOW RESONANCE ƒr the circuit is inductive
6. ABOVE RESONANCE ƒr the circuit is capacitive

2.1.4 Expressions of Parallel Resonance
1. Condition for resonance
Resonance occurs when YL = YC
Where YL = susceptance of Inductor and YC= susceptance of capacitor
2. Frequency for resonance
rf = 2
2
1
2
1
L
R
LC
L


3. Impedance at Resonance
RC
L
ZZ  0
Admittance(Y) is Reciprocal of Impedance (Z)
4. Current at Resonance
L
VRC
I r 
5.Voltage
Voltage drop across L
VL = I(2πfrL)
Voltage drop across C







L
Cj
R
Y


11

Vc = I 





frC2
1
Voltage drop across R
VR = IR
6.Q Factor
1.Q = L
C
R
2.Q = frL
R
2
3.Q = RCfr2
7.Power Factor at Resonance
Power factor at Resonance is 1
Cosφ=1
8.Expression of Bandwidth in terms of Q
Bandwidth= Q
fr
Problems Based on Parallel Resonance
1.Follow class note
2. Write all Problems including assignments
------------------- End of Resonance----------------------

2.2 Filters
2.2.1 Define Filter,Cut-off frequency, Pass band and Stop band
Filter:
Filters are circuits which freely pass a desire band of frequency and
totally suppress unwanted frequency.
Cut-off frequency:
It is the particular frequency which separates pass band and stop
band.
Pass band:
It is the Range of frequency in which attenuation is zero.
Stop band:
It is the Range of frequency in which attenuation is infinite.
2.2.2 Classification of filters
Classification based on component
1. Passive filters
2. Active filters
Classification based on frequency
1. Low pass filter (LPF)
2. High pass filter (HPF)
3. Band pass filter (BPF)
4. Band Reject filter (BRF)

Classification based on relation between series and shunt
impedance
1. Constant K filters or Prototype filters
2. M – derived filters
2.2.3 Plotting of ideal characteristics of passive filters
(LPF, HPF, BPF, BRF)

Explanation about passive filters
Low pass filter: passes low frequencies and stops high frequencies
High pass filter: passes high frequencies and rejects low frequencies
Band stop filter: passes frequencies outside a frequency band and
attenuates frequencies within the band

Band pass filter: passes frequencies within a frequency band and
attenuates frequencies outside the band
2.2.4 Constant- K filters
Draw the T and π type configuration of Constant K LPF and HPF
Constant- K LPF
Practical Characteristics
T- Configuration
π- Configuration
Design Formula
1. R0 =
C
L
2. fc =
LC
1
3. L =
cf
R

0
4. C =
cfR0
1


Constant- K HPF
Practical Characteristics
2.2.5 Design of Constant K LPF and HPF
Copy from AC Record
Design Formula
1. R0 =
C
L
2. fc =
LC4
1
3. L =
cf
R
4
0
4. C =
cfR04
1


2.2.6 Realization of BPF by using LPF & HPF
Block diagram
Signal input Signal Output
By the series combination of Low pass filter and High pass filter
forms Band pass filter circuit that will only allow passage of
frequencies that neither too high nor too low.
2.2.7 Realization of BRF by using LPF & HPF
Band Reject filter can be made by connecting the two filters in
parallel with each other
LPF HPF

2.2.8 Concept of m- derived filters, constant K and digital filters
Constant- K filters :
Draw backs of Constant-K filters are:
1. The attenuation does not increase rapidly beyond cut-off frequency
2. Characteristic impedance varies widely in passband from designed value of R0
Advantages of m derived filters over constant K filters :
1. M- derived filters impedance matching is possible but not in case of constant k
filters.
2. Compared to constant k filter m derived filter has a sharp cutoff frequency.
3. Maximum attenuation immediately in stop band.
Digital filters:
A digital filter is a system that performs mathematical operations
on a sampled, discrete-time signal to reduce or enhance certain
aspects of that signal.
Example :
Kalman filter, Butterworth filter, Chebyshev filters
--------- End of filters --------------

2.3 Attenuators
Attenuators :
Attenuators are two port resistive networks which are used to attenuate the
signals by desired amount.
Attenuation :
The process of introducing known amount of loss to signal is known as
attenuation.
Classification of attenuators :
1. Fixed attenuator
2. Variable attenuator
3. Symmetrical attenuators
4. Asymmetrical attenuators
Symmetrical attenuators are further classified into:
a. T-type attenuators
b. Π- type attenuators
c. L- type attenuators
Asymmetrical attenuators are further classified into:
a. T-type attenuators
b. Π- type attenuators
c. L- type attenuators
Symmetrical attenuators:
If the electrical properties are unaffected by interchanging the input and
output terminals then it is said to be Symmetrical attenuators

Asymmetrical attenuators:
If the electrical properties are affected by interchanging the input and output
terminals then it is said to be Asymmetrical attenuators
Applications of attenuators:
1. Attenuators are used to reduce the signal level by a given amount
2. Resistive attenuators are used for impedance matching
3. Variable attenuators are used as volume controller in broad cast
station
4. Capacitive attenuators are used for high frequency applications
5. These are also used as Buffer in telecommunication
2.3.2 Bel, Decibel and Neper :
Bel: is defined as the logarithm of a power ratio to the base 10
Bel = 





o
i
P
P
log
Decibel: is defined as the 10 times the logarithmic ratio between input power
and output power
D= 10 log10 





o
i
P
P
Neper:
Is defined as the natural logarithmic of the ratio of input voltage or current to
the output voltage or current respectively.
Neper =N= loge 





vout
vi
Or Neper =N= loge 





Iout
Iin

Relation between Decibel and Neper Units
Attenuation in dB = 8.686 * Attenuation in neper
Attenuation in Neper = 0.1151 * Attenuation in dB
2.3.3 Draw the Symmetrical T and Pi attenuator configurations
2.3.4 Design Symmetrical T and Pi attenuator configurations
Copy from AC Record

2.4 Equalizers
Define Equalizers:
Equalizers is an electrical network designed to counteract the attenuation or
phase distortion occurs in any part of the circuit due to the non-uniform
variations of attenuation or phase
Classification of Equalizers:
1. Amplitude or Attenuation equalizers
2. Phase or Delay Equalizers
Attenuation equalizers:
It is a network that designed to compensate attenuation distortion in
the network. It is also called as Amplitude Equalizers.
Phase Equalizers:
It is a network that designed to compensate phase distortion in the
network. It is also called as delay Equalizers.
Applications of Equalizers:
1. Telephone System
2. In feedback control system
3. T.V Signal Transmission

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