What is Carson's Rule?
Carson's formula is used to calculate the bandwidth (BW) of a single tone wideband FM.According to carson's rule, the FM bandwidth is given as, twice the sum of frequency deviation and the highest modulating frequency.
But it should be noted here that this rule is just an approximation.
Watch the Complete Video Here
So Carson's rule can be written mathematically as-
BW = 2(∆w + wm)
But mf = ∆w/wm
Therefore
BW = 2(mfwm+ wm)
= 2wm (mf + 1)
Now we have two special cases for the carson's rule -
1 - If ∆w << wm and
2- ∆w >> wm
Derivation of Carson's Rule for Narrowband FM and Wideband FM
Case 1- If ∆w << wm
Since mf = ∆w/wm
If ∆w << wm
=> mf << 1
=> It is the case for narrowband FM
Since the bandwidth by the carson's rule is given
as-
BW = 2(∆w + wm)
BW = 2(mfwm+ wm)
= 2wm (mf + 1)
Therefore for mf << 1
BW = 2wm
Note here that this is equivalent to Amplitude Modulation (AM)
Case 2- ∆w >> wm
Since mf = ∆w/wm
Therefore if ∆w >> wm
=> mf >> 1 as is the case for wideband FM
Then, since by Carson's rule
BW = 2wm (mf + 1)
Therefore for mf >> 1
BW = 2wmmf
But wmmf = ∆w
Therefore
BW = 2∆w
Note- For large values of mf this BW relationship can be considered accurate for all practical purposes.
Read More-
Go To HOME Page
FREQUENCY SPECTRUM OF AMPLITUDE MODULATION (WAVEFORMS AND EQUATIONS DERIVATION)
AMPLITUDE MODULATION (TIME DOMAIN EQUATIONS AND WAVEFORMS)
ADVANTAGES AND DISADVANTAGES OF DIGITAL COMMUNICATION SYSTEM
ADVANTAGES OF OPTICAL FIBER COMMUNICATION
STEP INDEX OPTICAL FIBER (MULTIMODE AND SINGLE MODE STEP INDEX FIBERS)
PULSE MODULATION TECHNIQUES (PAM, PWM, PPM, PCM)
OPTICAL FIBER: STRUCTURE AND WORKING PRINCIPLE
PULSE AMPLITUDE MODULATION (PAM)
COMPARISON OF PAM, PWM, PPM MODULATION TECHNIQUES
PULSE WIDTH MODULATION (PWM)
CONTINUOUS TIME AND DISCRETE TIME SIGNALS (C.T. AND D.T. SIGNALS)
NEED AND BENEFITS OF MODULATION
PULSE POSITION MODULATION (PPM)
OPTICAL FIBERS IN COMMUNICATION: COVERS ALL IMPORTANT POINTS
OPTICAL FIBER SOURCES (DESIRABLE PROPERTIES)
AMPLITUDE MODULATION Vs FREQUENCY MODULATION (ADVANTAGES AND DISADVANTAGES)
PULSE CODE MODULATION (PCM) [ADVANTAGES AND DISADVANTAGES]
SAMPLING THEOREM AND RECONSTRUCTION (SAMPLING AND QUANTIZATION)
SUPERPOSITION THEOREM (BASICS, SOLVED PROBLEMS, APPLICATIONS AND LIMITATIONS)
Digital Modulation Techniques (ASK, FSK, PSK, BPSK)/ Amplitude, Frequency and Phase Shift Keying
Conventional AM Vs DSB-SC Vs SSB-SC Vs VSB (Comparison of AM Systems)
Quadrature Amplitude Modulation (QAM)/ QAM Transmitter and QAM Receiver Block Diagram
Single-Mode Optical Fiber Advantages
What are Microwaves and their Applications (Uses) in various fields
Microwaves Properties and Advantages (Benefits)
Basic Structure of Bipolar Junction Transistor (BJT) - BJT Transistor - Working and Properties
Polar Plots of Transfer Functions in Control Systems (How to Draw Nyquist Plot Examples)
Generation of Binary Phase Shift Keying (BPSK Generation) - Block Diagram of Binary Phase Shift Keying (BPSK)
Low Level and High Level Modulation Block Diagram (AM Transmitter Block Diagram)
Block Diagram of CRO (Cathode Ray Oscilloscope), Components of CRO and CRT with Structure and Working
Slope Overload Distortion and Granular (Idle Noise), Quantization Noise in Delta Modulation
Frequency Translation/Frequency Mixing/Frequency Conversion/Heterodyning (Basic Concepts and Need)
Quadrature Phase Shift Keying Modulation (QPSK) Basics, Waveform and Benefits
Pulse Code Modulation (PCM) Vs Differential Pulse Code Modulation (DPCM)
