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RUKSHAN MUDLIYER - 101110641

Swinburne University of Technology TNE30003 Communication Principles

LAB REPORT-3

Angle Modulation and Detection

Student Name: Rukshan Mudliyer Student ID: 101110641

RUKSHAN MUDLIYER - 101110641

AIM 

The aim of this experiment is to understand the process of Angle modulation &detection. And also to understand about demodulation Angle Modulated System.

Theoretical Overview 



In Amplitude Modulation the amplitude of the carrier was varied according to the message signal. Angle Modulation is a scheme where the phase angle of the carrier is varied according to the message signal. The variation of phase of the carrier contains the message information is:

𝑚(𝑡) = 𝐴(𝑡) cos(𝜔𝑡 + ∅(𝑡))  Angular frequency can be defined as 𝜔 = 𝑑𝜃(𝑡) 𝑑𝑡 

Two common forms of angle modulation are:  Frequency Modulation (FM). 𝑡

𝑦(𝑡)𝐹𝑀 = 𝐴 cos[𝑡 + 𝑘𝑓 ∫0 𝑥(𝜏). 𝑑𝜏]  Phase Modulation (PM).

y(t)PM = A cos[ωc t + k p x(t)] Frequency Deviations, ∆𝑓 

Frequency deviation (∆f) is the change that occurs in the carrier frequency when it is acted on by a modulating signal. In a direct FM modulator, the frequency deviation is proportional to the amplitude of the modulating signal voltage (V m) and the rate at which the frequency change occurs is equal to the modulating signal frequency (fm). Therefore, the frequency deviation is a function of the deviation sensitivity of the modulator and the amplitude of the modulating signal (i.e. ∆f = Vm kf). ∆𝑓 𝑓 −𝑓 𝑘𝑓 = − 𝑐 0 ∆𝑉 0−𝑉𝐷𝐶

PM single tone modulation 

Modulation index:

 PM  k p Am   

The peak frequency deviation of a PM signal is directly proportional to the message frequency.

RUKSHAN MUDLIYER - 101110641

FM single tone modulation 

Modulation index:

 FM  

k f Am

m





m

The peak frequency deviation of a FM signal is not directly proportional to the message frequency.

Spectrum: Single Tone modulation  Single Tone Angle modulated signal can be expressed as: 

y (t )  Ac

J

n

(  ) cos( c  n m )t

n  

Bessel Functions   

When β >> 1 spectrum has several significant components. When β

Peak frequency Deviation  To generate an FM signal, an integrator is attached to the font of the modulator so that the message signal is integrated CS = fmax - fmin where CS = carrier swing. fmax = maximum frequency fmin = minimum frequency ∆f = CS/2 where ∆f = peak frequency deviation Tc=1/fc Tmin=1/fmax Waveform trigger reference

Tmax=1/fmin

RUKSHAN MUDLIYER - 101110641

Experimental Method Apparatus  TIMS unit (S/N:14094874)  PicoScope Module (PicoScope3204)  PicoScope Software (ATC101-010)  Enveloper Detector Box Modules in the TIMS unit  VCO (Voltage Controlled Oscillator)  Variable DC  Multiplier  Buffer Amplifier  Audio Oscillator  60kHz LPF  Scope Selector  Phase Shifter  Adder

1. Frequency Deviation constant, 𝒌𝒇 These steps were followed to find kf.  Connect the output of Variable DC module to the input of the VCO and adjusts the voltage to zero volts.  Then set the Hi Lo switch on the VCO module to Hi & connect the output of VCO to the Scope selector & measure the frequency of the signal.  Using the f0 knob set the output frequency to 100kHz  Set the DC output of Variable DC to 1.2v & use the GAIN control knob to adjust the GAIN on the VCO until the frequency is set to 94 kHz.  Record the frequencies of the signal when the input voltage is between +2V & -2V in 05V steps. Then Calculate k f using measured data.

2. Frequency Deviation, ∆𝒇  Set the output frequency to 300Hz on the Audio Oscillator & connect to the Vin on

the VCO.  Using PicoScope measure the Amplitude of the message.  Using the software change Display mode to Persistence Mode & then set the timebase to 2𝜇s, then calculate the peak frequency deviation.

3. FM Spectrum The following steps were followed to clarify the functionality of Bessel function.  Set the frequency of the audio oscillator module to 2 kHz and now connect to input A of the buffer amplifier and then connect the output K1A to the input of VCO.  Increase the input voltage swing gradually, to a value that carrier frequency is zer0.  Observe all the sidebands.

RUKSHAN MUDLIYER - 101110641  Change the amplitude to 4V P-P & frequency to10kHz on the message signal and record the magnitude spectrum.  Then change the message frequency to 300Hz and record the magnitude spectrum again.

4. FM Detection  Setup the system on Figure 4-1. Use a capacitor from the envelop detector box as a differentiator.  Adjust the phase shift so that LPF gives the maximum output.  Then record the output result in both time & frequency domains. Message

~

Differentiator

Multiplier

LPF 60 kHz



d/dt

VCO

C xd(t)

R

2sin(4000t)

 Differentiator Use the envelope detector box

Phase Shifter Figure 4-1

5. Generation of NBPM  Setup the system on Figure 5.  Then we gave the carrier signal (2cos (200π x 10^3 t)) to the phase shifter and observed both the inputs and outputs of the phase shifter.  While observing the phase shift (Ф) was set to 0. Audio Oscillator Module



Adder Multiplier

A



Message 2cos(  t)

 Carrier

2cos(  x103t)



Output



B

Phase Shifter

g

RUKSHAN MUDLIYER - 101110641

Results 1. Frequency Deviation Constant – Results DC Input

Frequency

-2

108.5

-1.5

107.7

-1.0

105.8

-0.5

102.2

0

99.4

0.5

97.8

1.0

94.3

1.5

92.7

2.0

90.8

120 108.5 106.7 104.8 102.2 99.4 96.8 94.3 92.5 100

89.5

Frequency (Hz)

80

60

40

20

0 -3

-2

-1

0

1

2

DC input (volts)

3 Frequency

General expression for a straight line is: 𝑦 = 𝑚𝑥 + 𝑐 , but in our case its 𝑓𝑜𝑢𝑡 = 𝑘𝑓 ∗ 𝑉𝑖𝑛 + 𝑓0 From the table of results we know that f0 = 99.4 Hz. Gradient of the straight line can be found using: 𝐺𝑟𝑎𝑑𝑖𝑒𝑛𝑡 = 𝑘𝑓 =

𝑓 𝐿 − 𝑓𝐻 𝑉𝐿 − 𝑉𝐻

=

90.8 −108.5 2−(−2)

= −4.425

𝑓𝑜𝑢𝑡 = 99.4 − 4.425 ∗ 𝑉𝑖𝑛

RUKSHAN MUDLIYER - 101110641

 By using the values recorded on the table frequency vs. voltage graph was drawn. According to the values the graph shows a linear relationship between frequency & voltage.

 In the experiment after changing the DC input to 1.25v & using the reading from Pico scope we found out that the resulting frequency is 93.76 kHz. Therefore now we have to find the predicted resulting frequency using the expression that we found earlier. 𝑓𝑜𝑢𝑡 = 99.4 − 4.425 ∗ 1.25 𝑓𝑜𝑢𝑡 = 93.87 𝑘𝐻𝑧 Predicted Frequency = 93.87 kHz Observed Frequency = 93.76 kHz 𝑬𝒓𝒓𝒐𝒓 =

𝑬𝒓𝒓𝒐𝒓 =

𝑷𝒓𝒆𝒅𝒊𝒄𝒕𝒆𝒅 − 𝑨𝒄𝒕𝒖𝒂𝒍 × 𝟏𝟎𝟎% 𝑨𝒄𝒕𝒖𝒂𝒍

𝟗𝟑.𝟖𝟕−𝟗𝟑.𝟕𝟔 × 𝟗𝟑.𝟕𝟔

𝟏𝟎𝟎% = 𝟎. 𝟏𝟏𝟕%

2. Frequency Deviation- Results

Peak Frequency Deviation: 105.4 kHz Message Amplitude: 2V Frequency deviation is calculated using following formulas: CS = fmax - fmin where CS = carrier swing. fmax = maximum frequency fmin = minimum frequency ∆f = CS/2 where 𝑇𝑚𝑖𝑛 = 9.2 × 10−6 𝑠

𝑇𝑚𝑎𝑥 = 11.26 × 10−6 𝑠

RUKSHAN MUDLIYER - 101110641 1𝜇 1𝜇 − 11.62 9.2 ∆f = = 11.32𝑘𝐻𝑧 2

3. .FM Spectrum



Modulation index is directly proportional to amplitude of the modulating signal, therefore when the modulation index changes bandwidth also changes.

Observed (10 kHz)

RUKSHAN MUDLIYER - 101110641

Observed (300 Hz)

Observation 

10kHz 𝜷=

𝒌𝒇 𝑨 𝒎 𝝎𝒎

=

(𝟏𝟎𝟓×𝟏𝟎𝟑 )(𝟐) 𝟐𝝅(𝟏𝟎×𝟏𝟎𝟑 )

= 𝟑. 𝟑

𝑩𝑻 = 𝟐(𝜷 + 𝟏)𝒇𝒎 𝑩𝑻 = 𝟐(𝟑. 𝟑 + 𝟏)(𝟏𝟎𝒌𝑯𝒛) 𝑩𝑻 = 𝟖𝟔 𝒌𝑯𝒛 

300Hz 𝑩𝑻 = 𝟐(𝜷 + 𝟏)𝒇𝒎 𝑩𝑻 = 𝟐(𝟑. 𝟑 + 𝟏)(𝟑𝟎𝟎𝑯𝒛) 𝑩𝑻 = 𝟐𝟓𝟖𝟎 𝑯𝒛

RUKSHAN MUDLIYER - 101110641

4. FM Detection Time Domain Graph:

Message Signal Period

522.5 𝜇𝑠

Recovered Message Signal 522.5 𝜇𝑠

P- P Amplitude

714.3mV

3.889V

Amplitude

357.15mV

1.9445V

Frequency Domain:



From the time domain it clearly shows that the amplitude of the recovered message signal has decreased.

RUKSHAN MUDLIYER - 101110641

5. Generation of NBPM

a = 6.64 𝑎−𝑏 𝛽= 𝑎+𝑏 Β = 0.308

b = 3.51

RUKSHAN MUDLIYER - 101110641 

When the phase shift is 0 (Ф = 0)

Ф=0

Time Domain when Ф = 0

RUKSHAN MUDLIYER - 101110641



When the phase shift is 90 degrees (Ф = 90)

Ф = 90

Time domain when Ф = 90 

The massage frequency was set to 10 KHz and the graphs were obtained.

RUKSHAN MUDLIYER - 101110641

Conclusion 



From the frequency deviation constant part of the experiment we learnt that the amount of frequency deviation of a carrier is directly proportional to the amplitude of the applied modulating signal From the FM Spectrum part of the experiment we learnt that Modulation index is directly proportional to amplitude of the modulating signal, therefore when the modulation index changes bandwidth also changes. Increasing modulated frequency increases the frequency separation in between sidebands.



Also this lab gave us the knowledge that in order to demodulate a FM it is necessary for the radio receiver tic invert the frequency variation into voltage variations.



In addition we gained a detailed knowledge about Bessel Function, Carson’s rule, detect a FM signal in order to retrieve the message, which will help in future when studying for exams.

Reference  

Angle modulation & Detection Lab manual Angle modulation lecture notes, Swinburne

RUKSHAN MUDLIYER - 101110641...