Modulation Index (μ)

In two ways, radio broadcasts and radio communications, we need to adjust the frequency. That’s why modulation is supplied to an amplitude signal so that it can be adjusted. If there isn’t much modulation, the audio (assuming it’s an audio broadcast) will be difficult to understand or modulate.

However, distortion can occur if too much frequency is applied, making communications difficult to hear. It may also cause increasing interference that might harm the users who are using surrounding frequencies or channels. So for accomplishing this, it is essential to have a method for specifying and monitoring the level of modulation that is applied to an amplitude modulated signal. 

What do you mean by modulation index? 

A measure of the degree of frequency modulation stated numerically for a pure tone modulation as the ratio of the frequency deviation to the frequency of the modulating signal is known as the modulation index.

Offset or Triangular Zero-Sequence Injection PWM

Adding an offset voltage to the references is another technique to boost the modulation index. This will essentially perform the same purpose as the previous method. The offset voltage is calculated as follows:

Where Vmax  = min ( Va + Vb + Vc ……..)

Why are modulation index values kept?

Let’s understand this with an example: 

The modulation index is a term that can be defined in a variety of ways. Why is its value kept at less than one in practice?

Question: A sinusoidal wave with a frequency of 10 kHz modulates a carrier wave with a frequency of 1.5 MHz and an amplitude of 50 V, resulting in 50% amplitude modulation. Find the amplitude of the AM wave as well as the frequencies of the created sidebands.

Explanation: The extent of modulation done on a carrier wave is measured using a modulation index. It can also be stated as the ratio of the amplitude of the modulating signal to that of the carrier signal.

m= Am / Ac 

It is important to keep the value of the modulation index below 1 so that overmodulation can be avoided. This overmodulation can cause distortions in the modulated signal and makes demodulating and extracting the original carrier signal extremely difficult.

So, from the information given,

m = Am / Ac 

= Am/ 50 

= 25 V 

AM wave is given by,

x(t) = Ac (1+mcos(ωm t))cos(ωωct)

Therefore amplitude can be calculated as follows,

Ax =Ac (1+mcos(ωωmt))

=50(1+0.5cos(2π×104t))

The maximum value of AM wave is 

xmax = 50x ×1.5 = 75V

Modulation index mathematical equation: 

The mathematical equation for amplitude modulation index: 

Modulation index, m = M/A

Here, m is the modulation amplitude that changes at its peak as in the RF amplitude from its unmodulated carrier and A is the amplitude carrier. 

For example, A modulation index of 0.75 using the equation means that the signal will increase by a factor of 0.75 and then reduce to 0.25 to find its original intensity.

The level of modulation that can be applied is a modulation index of the given equation. It happens when the envelope climbs by a factor of one, i.e., it becomes twice the steady-state value and then falls back to zero.

Examples: 

Let’s explain it with some examples with amplitude-modulated waveforms with various levels of modulation index. A signal with 100% modulation is the most seen with a modulation level. If there is no modulation, the signal level drops to zero and then rises to twice its original value. 

The voltage will also rise to its maximum of twice the given level in this example —— implying that the power is four times that of the quiescent value, or say 2² times that of the no modulation level.

The carrier will also not fall to zero, nor will it rise to double the level if, in the given example, less than 100 percent modulation is used. Also, the deviation value from the quiescent level will be less.

What if the levels are greater than 100% modulation? 

Over-modulation occurs when the level of modulation is increased above a modulation index of 1, i.e., more than 100% modulation. And if the carrier goes through 180° phase reversals, the carrier level will try to go below zero. These phase reversals will produce additional sidebands due to reversals (phase modulation). When we talk about theory, these phase reversal-induced sidebands go up to infinity. If these modulations are not filtered properly, users may have witnessed some interference. 

Limiters are designed in transmitters to restrict over modulation. Broadcast stations usually incorporate automated audio gain settings to maintain the audio levels of about 100% modulation most of the time. 

When demodulated, these signals sound cleaner and clearer. If the audio is over-modulated or near to the 100 percent modulation level, the audio processor clips it. Clipping helps in reducing the carrier from becoming over-modulated. After the audio clipper, an audio filter is used to minimise the audio harmonics. 

Many communication companies and broadcasting stations nowadays use the maximum level of the carrier to provide you with louder and clearer audio signals without modulation of any signal. 

How to monitor the modulation level? 

Transmitting stations use amplitude modulation to ensure that the signal is not over-modulated. These stations need to monitor the amount of interference produced. The signals are monitored because they are over-modulated. High levels of interference will be looked upon by monitoring units and users will suffer because of this. 

Despite the use of audio limiters, it is still necessary to monitor the setup and check that everything is working properly. Nowadays, all systems that use amplitude modulation look after these problems beforehand. All machines are designed in such a way that there is no need to constantly monitor them for overmodulation. Even the basic radio device doesn’t need any calibration or limiting. 

Conclusion 

When defining the modulation applied to an amplitude modulated signal, the modulation index and modulation depth figures are applied. If you use too little, the signal will not provide enough audio volume. If the signal is too strong, it will cause interference over the channels being broadcasted.