# FM transmission

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### Abstract:

The main task of the experiment is to demonstrate and analyze the basic principle of the FM transmission and to determine its characteristics. The experiment focuses on measuring the deviation constant of a FM modulator using different techniques, effect of filtering method, capture effect and the threshold effect and bandwidth noise reduction trade off in FM.

First there is a brief theoretical reference on the modulation and different modulation techniques. The frequency modulation technique is further explained and proved mathematically. It is also been described in FM spectrum analyzer mode. In this section particularly the fields which were closely related with the experiment are analyzed in theory in order to be easier later to proceed in the appropriate comparisons.

The experiment section is divided in to four parts. The first part of the experiment analyzes the values of the deviation constant of the FM modulator using three methods: Time domain method, Spectrum analyzer method and FSK method. The sinusoidal and square ware input in used in frequency domain to made the observations. The purpose of the second part of the experiment is to demonstrate the effect the band pass filtering in case of FM transmission. The third part of the experiment shows how the complete suppression of the weaker signal occurs at the receiver limiter considered as noise and rejected, called the capture effect and the last part of the experiment is the trade-off between the required bandwidth and the signal to the noise ratio (SNR).

In the following text there are some graphs made in Matlab software and a large set of real images from the several parts of the experiment taken with a digital camera provided by the member of the staff of the lab.

### Answers to the Pre lab Questions:

&sect; &beta; is termed as modulation index, it is the ratio of the deviation constant multiplied by the amplitude of the modulating signal to the frequency of the modulating signal. The unit of &beta; is radians.[1]

&sect; No, Frequency modulation is a non-linear process. Frequency deviation constant is represented by &lsquo;&Delta;F', it is the multiple function of deviation constant and the amplitude of the modulating signal.[1]

&sect; The [SNR]o is directly proportional to the square of the modulating index &lsquo;&beta;' in frequency modulation this termed as increasing the value of &beta; would increase the value of the [SNR]o this is known as the bandwidth and noise reduction trade-off in FM system.[1]

&sect; There is a sudden decay in the output when SNR is very low is known as the threshold effect.[1]

&sect; Capture range can be defined as the range of frequencies over which the PLL will lock the signal. [2]

&sect; Lock range is the range of frequencies over which PLL can track the input variation.[3]

&sect; If m (t) =2cos (200&#1055;t) + 3.5 cos (50&#1087;t), kf = 10khz/volt, fc = 100khz, find range of instantaneous frequency of the modulated signal.

### Solution

Ft (t) = 2&#1087;fc + 2&#1087;kfAmcos (2&#1087;fmt).

Also, Ft (t) = Fc + Kf m (t)&hellip;&hellip;&hellip;&hellip;&hellip;&hellip;&hellip;&hellip; (1)

After Substituting the values in equation 1.

We get,

Ft = 100x10-3 + 10x10-3 2cos(200&#1087;t) + 3.5 cos (50&#1087;t)

= 1 + (0.1 x 2cos6284) + 3.5cos157.1

= 1 + (0.1 x -1.9225) + (-3.224)

= 1 - 0.19225 - 3.224

= -2.42Hz

### 1.1 Objective

The experiment deals with the basic performance of the FM modulation and plotting its characteristics. Upon the completion of this experiment the one would:[4]

&sect; Understand the concept of FM modulation

&sect; Learn how to generate an FM signal

&sect; Learn how to generate demodulated signal

&sect; Understand the difference between the non-linear and linear modulation techniques.

### 1.1.1 Necessary background

To understand the properties of FM modulation waveform, we need a working knowledge of Fourier transform theory. We also have to use the Bessel function so we will use the basic theory as it would be needed in the experiment.

### 1.2.1 Modulation

Modulation is the process of changing the carrier signal with respect to the characteristic of the another signal (called as message signal).[1]

### 1.2.2 Need of modulation

There are several reasons for that some of them are follows:[3]

&sect; In broadcasting main use of modulation is to reduce the length of the antenna.

&sect; It is to be used to modulate the weak signal to strong.

&sect; It is used to encrypt data.

&sect; Used to send signals over large distances.

&sect; Noise immunity.

&sect; To increase the signal strength.

&sect; Multiplexing, channel allocation for thousands of users.

### 1.2.3 Types of modulation

Basically there are two types of modulation based on the carrier signal they are:[1]

&sect; Continuous wave (CW) modulation in which the carrier is continuous sinusoidal waveform and

&sect; Discrete pulse modulation in which the carrier is a periodic set of pulses.

The CW modulation is further divided in to two sub-categories:[5]

&sect; Amplitude modulation: In AM frequency of a carrier wave is kept constant while the amplitude is varied with respect to the voltage of the modulating signal.

&sect; Angle modulation: Angle modulation is the system where the frequency or phase of the carrier signal is varied while the amplitude is kept constant with respect to the modulating signal.

Modulation techniques

Continuous Wave Modulation Discrete Pulse Modulation

Amplitude Modulation Angle Modulation

Frequency Modulation Phase Modulation

FM Modulation FSK Modulation

Now we will study the FM modulation in detail:

### 1.3 Frequency modulation:[6],[7]

In frequency modulation, the amplitude of the modulated carrier signal is kept constant while its frequency is varied by the modulating message signal. The basic idea of frequency modulation is shown in (2). The carrier frequency is controlled at each instant by the voltage of the modulating signal. The frequency of the modulated signal is increased if the input signal is positive, whereas the frequency is reduced if the input signal is negative.

### 1.3.1 Mathematical modeling:

The general definition of frequency modulated signal SFM(t) is given by the formula:[6],[7]

(1)

where,

is the modulating signal.

is the amplitude of the carrier.

is the carrier frequency.

is the deviation constant measured in Hz/V.

For the case of a single frequency sinusoidal modulating signal, , the frequency modulated signal SFM(t) will be expressed as:

(2)

The factor is called the frequency deviation. It is defined as the maximum frequency shift away from fc.

The modulation index &beta; is expressed as:

(3)

So, the SFM (t) signal can be represented as:

(4)

Frequency modulated signals are classified into two categories based on the value of .

### &sect; Narrow Band Frequency Modulation (NBFM)

For small values of the frequency modulation index (&lt;&lt;1), we have Narrow Band Frequency Modulation (NBFM). In this case, the frequency modulated signal SFM (t) becomes:

(5)

The derivation of equation (5) can be found in reference [6].

### &sect; Wide Band Frequency Modulation (WBFM)

As the modulation index increases, the signal occupies more bandwidth. In this case the modulation scheme is called Wide Band Frequency Modulation (WBFM).

Therefore, for a single frequency sinusoidal modulating signal the frequency modulated signal could be written in the form:

(6)

The derivation of equation (6) can be found in reference [6].

### 1.3.2 FM spectrum

As with amplitude modulation, the modulation process causes sidebands to be produced at frequencies above and below the carrier. However, for a frequency modulation based system, there are a lot more, all spaced at multiples of fm from the carrier frequency fC. As a result, the bandwidth needed to accommodate a frequency modulated signal is considerably larger than that for amplitude modulated signal having the same modulating frequency.

### 1.3.3 FM demodulation

There are many ways to recover the original information from a frequency modulated signal. The frequency demodulator should produce an output voltage with instantaneous amplitude that is directly proportional to the instantaneous frequency of the input frequency modulated signal. Thus, a frequency-to-amplitude converter circuit is a frequency demodulator.

Various techniques such as slope detection, zero-crossing detection, phase locked discrimination and quadrature detection are used to demodulate the frequency modulated signal.

Universally, demodulators use a phase-locked loop (PLL), an extremely useful circuit that finds its way into all sorts of electronic systems. Briefly, it consists of an oscillator whose frequency can be varied by means of a voltage (that is, a voltage-controlled oscillator or VCO), and a feedback loop, which results in the frequency of the oscillator being locked to the frequency of the incoming signal. In the process the circuit produces a voltage, which is proportional to the variation in the signal frequency.

### AIM:

Determining the deviation constant &lsquo;Kf &lsquo;, the purpose of this part of the experiment is to measure the deviation constant of a FM modulator using three different methods:

### Required equipments:

Oscilloscope, spectrum analyzer, signal generator, mini circuit kit (VCO,PLL,ADDER), arbitrary waveform generator, CRO cables and wires.

### Theory:

This method is used to measure the deviation constant by determining the maximum change in the carrier frequency, F&Delta;

i.e. kf = F&Delta;/Am

### Procedure:

Apply I v PK-PK sine wave signal at frequency of 1KHZ to VCO, now observe the waveform at the o/p of the VCO and measure the frequency difference.

### Observations:

1v PK-PK input sine wave signal appears at the output of the VCO.

Input:

1v PK-PK sine wave, at 1 KHZ frequency

Shown below in fig. 2.0

### Calculations:

Output recorded

Fmax = 78.74 KHZ, 12.70 &mu;s

Fmim = 62.50 KHZ, 16.00 &mu;s

We know that,

kf = F&Delta;/Am, but

2F&Delta; = (Fmax - Fmin),

So, F&Delta; = (Fmax - Fmin) / 2

= 78.74 - 62.50 / 2

Putting the value in the formula of deviation constant

We get,

Kf = 16.24 KHZ/V Because, Am = 0.5

Ans. The more straight forward method for calculating the kf would be derived from the formula kf = F&Delta;/Am

We know that,

2F&Delta; = (Fmax - Fmin),

So, substituting the value of 2F&Delta; in the formula we get,

Kf = (Fmax - Fmin) / 2Am 1v PK-PK, so Am = 0.5

Kf = (Fmax - Fmin)

= 78.74 - 62.50

= 16.24 KHZ/V

### Conclusion:

After performing the experiment, I have understood the concept behind calculating the deviation constant of a FM modulator. I understood the linear relationship between the change in frequency and the applied voltage, the applied voltage is directly proportional to the change in frequency as the input voltage increases the change in frequency would also increases. I have matched the results and found the observations are same theoretically as well as practically.

### Theory:

The modulation index is defined by as:

&beta; = (KfAm/Fm).

This means it is the ratio of the deviation constant multiplied by the amplitude of the modulating signal to the frequency of the modulating signal.

However, If the voltage of the message signal is measured and the values of modulation index and frequency is known then the deviation constant can be calculated. This technique of calculating the deviation constant is considered to be the most precise technique of calculating deviation constant of the FM modulator. We have to use Bessel function behavior for finding out the value of the &beta;.

### Procedure:

Apply Sine wave signal at frequency of 1KHZ to the input of the VCO,

now bring the oscilloscope in the spectrum analyzer mode and observe the spectrum of the modulated signal.

### Observations:

The amplitude of the input signal measured is = 308 MV PK-PK at 1KHZ

### Calculations:

we know that,

&beta; = (KfAm/Fm).

the value of &beta; = 2.4048 is given in the experiment.

Fm = 1KHZ (given)

Am = 308 MV PK-PK (observed)

= 154 MV PK.

So, according to the formula,

Kf = &beta;Fm/Am

Substituting the values in the formula,

Kf = 2.4048 x 1 x 103 / 154 x10&#713;3

= 15.61 KHZ/V

Ans.

### Conclusion:

C. FSK method: [1]

### Theory:

FSK stands for frequency shift keying it is the special case of finding the deviation constant, we have used the digital input here i.e. the square wave input, in this method digital information is transmitted through the discrete frequency changes of a carrier signal.[2]

### Procedure:

Start the experiment by applying a square wave input signal at 300 HZ instead of 2KHZ printed in the lab sheet at the input of the VCO. Increase the amplitude of the signal applied until two definite peaks appeared and Observe the frequency difference between the two peaks.