06. Frequency Modulation

Frequency Modulation and Phase Modulation

Two types of Angle Modulation

Frequency Modulation

It is a technique of modulation in which the frequency of carrier is varied in accordance with the amplitude of modulating signal.

TRUE

(TRUE or FALSE) In FM, amplitude and phase remain constant.

TRUE

(TRUE or FALSE) In FM, the information is conveyed via frequency changes.

modulation index

It is defined as the ratio of frequency deviation (δ) to the modulating frequency (f_m).

M.I. = δ/f_m

Formula of modulating index (M.I.)

TRUE

(TRUE or FALSE) In FM, M.I. > 1

i. Bandwidth of the FM wave

ii. Number of sidebands in FM wave

Modulation Index of FM decides these 2 factors (HINT: BN)

Deviation Ratio

It is the modulation index corresponding to maximum deviation and maximum modulating frequency.

Deviation Ratio = Maximum Deviation (δmax) / Maximum Modulating Frequency (f_max)

Formula for deviation ratio

75 kHz

In FM broadcasting, what is the maximum value of deviation?

15 kHz

In FM broadcasting, what is the maximum modulating frequency?

percentage modulation

It is defined as the ratio of the actual frequency deviation by the modulating signal to the maximum allowable frequency deviation.

%M.I. = Actual deviation / Maximum allowable deviation

Formula for percentage modulation (% M.I.)

e_m = E_m cos ω_mt …(1)

where:

e_m = Instantaneous amplitude

ω_m = Angular velocity

= 2πfm

f_m = Modulating frequency

This equation mathematically represents the modulating signal.

e_c = E_c sin (ω_mt + φ) …(2)

where:

e_m = Instantaneous amplitude

ω_m = Angular velocity

= 2πf_c

f_c = Carrier frequency

φ = Phase angle

This equation mathematically represents the carrier signal.

TRUE

(TRUE or FALSE) FM is nothing but a deviation of frequency.

f = f_c (1 + K E_m cos ω_mt) … (3)

where, f_c = Unmodulated carrier frequency

K = Proportionality constant

E_m cos ω_mt = Instantaneous modulating signal

(Cosine term preferred for simplicity otherwise we can use sine term also)

Instantaneous frequency ‘f’ of the FM wave is given by this formula.

frequency spectrum

It is a graph of amplitude versus frequency.

frequency spectrum

It tells us about the number of sideband present in the FM wave and their amplitudes.

TRUE

(TRUE or FALSE) The expression for FM wave is not simple. It is complex because it is a sine of sine function.

Bessels Function

The only solution for the complexity of FM wave expression is?

• Carrier (First term in equation)

• Infinite number of sidebands (All terms except first term ar sidebands)

From the Bessels Function, it is seen that the FM wave consists of these two factors.

‘J’ coefficient

The amplitudes of carrier and sidebands depend on this coefficient.

TRUE

(TRUE or FALSE) The ideal frequency spectrum of FM has a positive infinity bandwidth.

TRUE

(TRUE or FALSE) The bandwidth of FM wave is infinite.

TRUE

(TRUE or FALSE) Practically, the bandwidth is calculated based on how many sidebands have significant amplitudes.

BW = 2f_m x Number of significant sidebands

What is the first, simple method to calculate the bandwidth?

TRUE

(TRUE or FALSE) With increase in modulation index, the number of significant sideband increases. So, bandwidth also increases.

Carson’s Rule

What is the second method in calculating the bandwidth?

Carson’s Rule

It states that, the bandwidth of FM wave is twice the sum of deviation and highest modulating frequency.

BW = 2(δ + f_mmax)

Formula of bandwidth according to Carson’s rule.

Narrowband FM (NBFM) and Wideband FM (WBFM)

What are the two types of frequency modulation (FM)?

Narrowband FM

Modulation index is small

Wideband FM

Modulation index is large.

Less than or slightly greater than 1

Modulation index of NBFM

Greater than 1

Modulation index of WBFM

5 kHz

Maximum deviation of NBFM

75 kHz

Maximum deviation of WBFM

20 Hz - 3 kHz

Range of modulating frequency of NBFM

20 Hz - 15 kHz

Range of modulating frequency of WBFM

slightly greater than 1

Maximum modulation index of NBFM

5-2500

Maximum modulation index of WBFM

Small. Approximately same as that of AM

BW = 2f_m

Bandwidth of NBFM

Large about 15 times greater than that of NBFM.

BW = 2(δ+f_mmax)

Bandwidth of WBFM

FM mobile communication like police wireless, ambulance, short range sip to shore communication etc.

NBFM applications

Entertainment broadcasting (can be used for high quality music transmission)

WBFM applications

time domain and frequency domain

What are the two representations of FM?

FM in Time Domain

It means continuous variation of voltage with respect to time.

frequency spectrum

Frequency Domain is also known as what?

FM in Frequency Domain

It means graph or plot of amplitude versus frequency.

TRUE

(TRUE or FALSE) Pre- and de-emphasis circuits are used ONLY in frequency modulation.

pre-emphasis

It is the artificial boosting of higher audio modulating frequencies in accordance with prearranged response curve.

pre-emphasis circuit

It is a high pass filter.

transmitter

Which part of the communication system is pre-emphasis used?

TRUE

(TRUE or FALSE) In FM, the noise has a greater effect on the higher modulating frequencies. This effect can be reduced by increasing the value of modulation index (m_f), for higher modulating frequencies. This can be done by increasing the deviation ‘δ’ and ‘δ’ can be increased by increasing the amplitude of modulating signal at higher frequencies.

TRUE

(TRUE or FALSE) In a pre-emphasis circuit, AF is passed through a high-pass filter, before applying to FM modulator.

TRUE

(TRUE or FALSE) In a pre-emphasis circuit, as modulating frequency (f_m) increases, capacitive reactance decreases and modulating voltage goes on increasing. In other words, f_m ∝ voltage of modulating signal applied to FM modulation.

TRUE

(TRUE or FALSE) Boosting is done according to pre-arranged curve.

50 μs (In systems employing American FM and TV standards, networks having time constant of 75 μs is used)

In all CCIR standards, what is the time constant of pre-emphasis?

receiver

Which part of the communication systems is de-emphasis used?

de-emphasis

It is the artificial boosting of higher modulating frequencies in the process of pre-emphasis is nullified at receiver.

TRUE

(TRUE or FALSE) De-emphasis circuit is a low pass filter.

TRUE

(TRUE or FALSE) In the process of de-emphasis, as f_m increases, capacitive reactance X_c decreases. The output of de-emphasis circuit also reduces.

TRUE

(TRUE or FALSE) The de-emphasis circuit is used after the FM demodulator at the FM receiver.

50 μs

Time constant of de-emphasis.

Pre-emphasis

Boosting of higher frequencies

de-emphasis

Removal of higher frequencies

AM

Amplitude of carrier is varied in accordance with amplitude of modulating signal keeping frequency and phase constant.

FM

Frequency of carrier is varied in accordance with the frequency of modulating signal keeping amplitude and phase constant.

AM

In this type of modulation, frequency and phase are the constant parameters.

FM

In this type of modulation, amplitude and phase are kept constant.

m = Em/Ec

In AM, what is the formula for modulation index?

m = δ/fm

In FM, what is the formula for modulation index?

only 2

How many sidebands does an AM have?

infinite and depends on m_f

How many sidebands does FM have?

BW = 2f_m

In AM, what is the formula for Bandwidth?

BW = 2 (δ + f_m(max))

In FM, what is the formula for Bandwidth?

MW, SW band broadcasting, video transmission in TV

AM applications

broadcasting FM, audio transmission in TV

FM applications

direct and indirect method

What are the two methods for generation of FM wave?

reactance modulator and varactor diode

What are the two (2) direct methods when it comes to FM generation?

Armstrong method

Example of an indirect method for the generation of FM

reactance modulator

It is a circuit that uses a transistor amplifier that acts like either a variable capacitor or inductor. When the circuit is connected across the tuned circuit of an oscillator, the oscillator frequency can be varied by applying the modulating signal to the amplifier.

1. In this method, it is very difficult to get high order stability in carrier frequency because in this method the basic oscillator is not a stable oscillator, as it is controlled by the modulating signal.

2. Generally, in this method we get distorted FM, due to non-linearity of the varactor diode.

What are the limitations of direct method of FM generation?

TRUE

(TRUE or FALSE) In direct method of FM generation, it is very difficult to get high order stability in carrier frequency because in this method the basic oscillator is not a stable oscillator, as it is controlled by the modulating signal.

TRUE

(TRUE or FALSE) In direct method of FM generation, we get a distorted FM due to non-linearity of the varactor diode.

Amrstrong method

It generates a double sideband suppressed carrier signal, phase shifts this signal, and then reinserts the carrier to produce a frequency modulated signal.

uses stable crystal oscillator

Advantage of direct PM

limited phase deviation

Disadvantage of direct PM

TRUE

(TRUE or FALSE) Direct PM uses a stable crystal oscillator.

TRUE

(TRUE or FALSE) Direct PM uses a limited phase deviation.

1. Transmitted power remains constant.

2. FM receivers are immune to noise.

3. Good capture effect.

4. No mixing of signals.

Advantages of FM

1. It uses too much spectrum space.

2. The bandwidth is wider.

3. The modulation index can be kept low to minimize the bandwidth used.

4. But reduction in M.I. reduces the noise immunity.

5. Used only at very high frequencies.

Disadvantages of FM

1. FM radio broadcasting.

2. Sound transmission in TV.

3. Police wireless.

Applications of FM