FM or Frequency Modulation is the encoding of information in a carrier by varying the instantaneous frequency of the carrier wave.

But then the question is: by how much does the instantaneous frequency vary?

The modulation index indicates by how much the modulated frequency varies around the unmodulated carrier frequency. Another way to think of it is, how much will the frequency vary when you compare full silence (unmodulated carrier) to transmitting a loud tone? Or, the way the test prefers to describe it, The ratio of frequency deviation to the modulating signal frequency.

For the sake of remembering, just remember that this is a comparison between frequencies, not a comparison of frequency to amplitude.

For sine waves:

$ h = \frac{\Delta f}{f_{m}} = \frac{f_{\Delta}|x_m(t)|}{f_m}$

Where:

• \(h\) is the modulation index
• \(x_m(t)\) is the modulating signal
• \(f_m\) is the highest frequency component present in the modulating signal
• \(\Delta f\) is the peak frequency deviation

It is not necessary to remember the math. Just remember that it is peak frequency deviation divided by highest modulating signal frequency.

Mnemonic:
Modulation index=mod in=mod inverse=dom=
d over m
=deviation (one sideband) over modulating frequency

While this is related to the bandwidth, it is not exactly the same thing. The distractor answer about bandwidth is wrong. (The bandwidth is \(\approx \small{h \ll 1 :}\space 2f_m, \space \small{h \gg 1 :}\space 2f_\Delta\) for those who want an estimate.)

Memory Aid: FM is Frequency Modulation. The correct answer choice refers to “frequency” twice, whereas all the incorrect choices only mention it once.

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The modulation index for phase modulation is simply the peak phase deviation.

The maximum deviation is +/- 90 degrees, regardless of frequency.

https://en.m.wikipedia.org/wiki/Phase_modulation

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Simply divide the deviation by the modulation frequency to arrive at the correct answer:

\begin{align} \text{modulation index} &= \frac{\text{deviation}}{\text{modulation frequency}} \\ &= \frac{3000 \text{ Hz}}{1000 \text{ Hz}} \\ &= 3 \end{align} --wileyj2956

In other words, the modulation index tells you how efficient the modulation is. An index of 1 would mean that a 1000 Hz signal would cause a deviation of 1000 Hz on either side of the carrier. In this example, it takes a bandwidth of three times the modulating frequency on each side of the carrier to carry the information, a modulation index of 3.

Mnemonic:
Modulation index=mod in=mod inverse=dom=
d over m
=deviation (one sideband) over modulating frequency

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The FM modulation index is equal to the ratio of the frequency deviation to the modulating frequency.

\begin{align} \text{modulation index} &= \frac{\text{frequency deviation}}{\text{modulation frequency}} \\ &= \frac{6\text{ kHz}}{2 \text{ kHz}}\\ &= 3 \end{align}

See: https://www.radio-electronics.com/info/rf-technology-design/fm-frequency-modulation/modulation-index-deviation-ratio.php

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The deviation ratio is the maximum carrier frequency deviation divided by the highest (maximum) audio modulating frequency: \[\text{deviation ratio}=\frac{\text{max. carrier frequency swing}}{\text{max. modulation frequency}}\]

The carrier frequency deviation is defined by the frequency swing relative to the carrier, in this case \(+5\) kHz or \(-5\) kHz, the maximum being \(5\) kHz. Therefore, the deviation ratio is:

\begin{align} \text{deviation ratio}&=\frac{5 \text{ kHz}}{3\text{ kHz}}\\ &=1.666...\approx1.67 \end{align}

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\begin{align} \text{deviation} &= \frac{\text{frequency swing}}{\text{frequency}}\\ &= \frac{7.5 \text{ kHz}}{3.5 \text{ kHz}}=2.142857...\\ &\approx 2.14 \end{align}

The deviation ratio is calculated by dividing the maximum deviation by the maximum modulation: \[ \frac{\text{maximum deviation}}{\text{maximum modulation frequency}}\]

The deviation ratio of an FM-phone signal having a maximum frequency swing of \(\pm\) 7.5 kHz when the maximum modulation frequency is 3.5 kHz is 2.14.

Hint: 7.5 kHz and 3.5 kHz are a couple [2] of deviants [KQ4AEY]

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OFDM avoids the effects of multipath distortion on a single high speed data stream by distributing the data across a set of lower speed digital streams. Any type of modulation can be used on the individual signals, known as subcarriers.

Hint: multiple speeds

SILLY HINT: Question has "D"ivision "M"ultiplexing in it. Answer has "D"igital "M"ode in it.

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Orthogonal Frequency Division Multiplexing is a digital modulation technique using subcarriers at frequencies chosen to avoid intersymbol interference.

Orthogonal Frequency Division Multiplexing (OFDM) is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier modulation method. A large number of closely spaced orthogonal sub-carrier signals are used to carry data on several parallel data streams or channels.

Hint: The correct answer is the one that deals with subcarriers and frequencies

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TIP: It is the only answer that has 'deviation' in it.

In FM modulation, the two primary parameters of interest are deviation ratio and modulation index. Deviation ratio is the ratio of the maximum carrier frequency deviation to the highest audio modulating frequency.

The deviation ratio of an FM-phone signal having a maximum frequency swing of plus-or-minus 5 kHz when the maximum modulation frequency is 3 kHz is 1.67.

The deviation ratio of an FM-phone signal having a maximum frequency swing of plus or minus 7.5 kHz when the maximum modulation frequency is 3.5 kHz is 2.14.

Mnemonic: Deviant child = (Swing carrying child to the max swing height) over (Maximum length of Odd Mud)

Hint: Only the question and the correct answer have 'deviation' in it.

Stupid Hint: You want the "Maximum" points on this question.

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Multiplexing a signal is a method of combining multiple distinct streams of information over a shared medium. In our case, the medium is RF frequency spectrum.

Therefore, multiplexing using frequency division would be dividing different streams of information into separate frequencies for transmission.

Hint: The correct answer is the only one that contains both the terms "frequency" and "dividing"

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Time division multiplexing (TDM) is a communications process that transmits two or more streaming digital signals over a common channel. In TDM, incoming signals are divided into equal fixed-length time slots. After multiplexing, these signals are transmitted over a shared medium and reassembled into their original format after de-multiplexing. Time slot selection is directly proportional to overall system efficiency.

Time division multiplexing (TDM) is also known as a digital circuit switched.

per https://www.techopedia.com/definition/9669/time-division-multiplexing-tdm

Hint: The answer has time slot in it.

Hint: time division --> time slots

Hint: digital in question 'data transmission' last two words answer

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