2. ELECTRICAL NETWORK_ UNIT 2_chandra Shekhar K

ANALOG COMMUNICATION

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. Tuners2. Oscillators3. Filters4. Mixers 5. Induction Heating

2.1.2 series resonance

Circuit Diagram of series resonance

Chandra Shekhar K NTFF-SIT Tumkur Centre


Phasor diagram of Series Resonance

Resonance curve


Vc

VL

VRI


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

Z0=R



4. Current Current at Resonance

I r=

VR

5.Voltage

Voltage drop across L

VL = I(2πfrL)

Voltage drop across C

Vc = I (1

2π frC ) Voltage drop across R

VR = IR

6. Q Factor

1. Q = 1R √ LC

2. Q = 2π frLR

3. Q = 1

2π frCR

7. Power Factor at ResonancePower factor at Resonance is 1

Cosφ=1



8. Expression of Bandwidth in terms of Q

Bandwidth= frQ

Other expression for Bandwidth1. Bandwidth= BW= f2-f1

2. Bandwidth= BW=R2πL

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 BL = BC

Where BL = susceptance of Inductor and BC= susceptance of capacitor

2. Frequency for resonance

f r = 12π √ 1

LC−RL2

L2

3. Impedance at Resonance

Z=Z0=LRC

Admittance(Y) is Reciprocal of Impedance (Z)

4. Current at Resonance

I r=VRCL

5.Voltage

Voltage drop across L

VL = I(2πfrL)

Voltage drop across CChandra Shekhar K NTFF-SIT Tumkur Centre

Y= 1R

+ j (ωC− 1ωL )


Vc = I (1

2π frC ) Voltage drop across R

VR = IR

6. Q Factor

1. Q = R√CL

2. Q = R

2π frL

3. Q = 2πf rRC

7. Power Factor at ResonancePower factor at Resonance is 1

Cosφ=1

8. Expression of Bandwidth in terms of Q

Bandwidth= frQ

Problems Based on Parallel Resonance

1.Follow class note

2. Write all Problems including assignments

------------------- End of Resonance----------------------



2.2 Filters2.2.1 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 filters2. Active filters

Classification based on frequency

1. Low pass filter (LPF)2. High pass filter (HPF)3. Band pass filter (BPF)


ANALOG COMMUNICATION 4. Band Reject filter (BRF)

Classification based on relation between series and shunt impedance

1. Constant K filters or Prototype filters2. M – derived filters

2.2.3 Plotting of ideal characteristics of passive filters

(LPF, HPF, BPF, BRF)


ANALOG COMMUNICATION 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

Constant- K HPF


T- Configuration π- Configuration

Design Formula

1. R0 = √ LC2. fc =

1π √LC

3. L =

R0πf c

4. C =

1πR0 f c


Practical Characteristics

2.2.5 Design of Constant K LPF and HPF

Copy from AC Record

2.2.6 Realization of BPF by using LPF & HPF


Design Formula

1. R0 = √ LC2. fc =

14 π √LC

3. L =

R04 πf c

4. C =

14 πR0 f c


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


HPF LPF

ANALOG COMMUNICATION 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 frequency2. 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


https://en.wikipedia.org/wiki/Signal_(electrical_engineering)

https://en.wikipedia.org/wiki/Discrete-time

https://en.wikipedia.org/wiki/Sampling_(signal_processing)


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 attenuator2. Variable attenuator3. Symmetrical attenuators4. Asymmetrical attenuators

Symmetrical attenuators are further classified into:

a. T-type attenuatorsb. Π- type attenuatorsc. L- type attenuators

Asymmetrical attenuators are further classified into:

a. T-type attenuatorsb. Π- type attenuatorsc. 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


ANALOG COMMUNICATION 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 amount2. Resistive attenuators are used for impedance matching3. Variable attenuators are used as volume controller in broad cast

station4. Capacitive attenuators are used for high frequency applications5. 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 = log [ PiPo ]

Decibel: is defined as the 10 times the logarithmic ratio between input power and output power

D= 10 log10 [P iPo ]

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 [vivout ] Or Neper =N= loge [

IinIout ]

Relation between Decibel and Neper Units


ANALOG COMMUNICATION 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 Chandra Shekhar K NTFF-SIT Tumkur Centre


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 equalizers2. 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 System2. In feedback control system3. T.V Signal Transmission


2. ELECTRICAL NETWORK_ UNIT 2_chandra Shekhar K

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