### Modulation Index and Deviation Ratio

Modulation is the term for varying a waveform to carry a signal, that’s why AM is named Amplitude Modulation. By the same token FM is Frequency Modulation and PM is Phase Modulation.

We’re coming around to two questions in a row that people struggle with on our practice tests. It’s around the terms “modulation index” and “deviation ratio.” Let’s go through them.

What is the modulation index of an FM signal? It is **the ratio of frequency deviation to modulating signal frequency****.** We’re measuring the level of how much a frequency changes when it is modulated. Throw out the two answers related type of modulation or bandwidth. While amplitude is a component of the wave, it’s not used in determining the FM modulation index. So, toss out the answer that has amplitude too.

Now let’s turn to the question of “What is deviation ratio?” Deviation ratio is **the ratio of the maximum carrier frequency deviation to the highest audio modulating frequency****.** All the other answers look good but the key terms for this ratio are *maximum* and *highest.* Only one answer includes both of those terms.

Let’s recap those two before we go on:

- Modulation index is the ratio of frequency deviation to modulating signal frequency. How much a frequency changes when it’s modulated. This is good to know so you are not interfering outside your bandwidth.
- Deviation ratio is a type of modulation index. It is the ratio of maximum carrier frequency deviation to the highest audio modulating frequency. For an FM signal frequency deviation is the difference between the minimum and maximum extent of the signal. This can be a factor of signal quality. If your deviation is too high your signal could be distorted.

Modulation index is different depending on the modulation type.

- We just discussed the FM modulation index. It is the ratio of frequency deviation to modulating signal frequency.
- For AM it’s the ratio between the modulation and carrier amplitudes. This makes sense because we are measuring the ratio of modulation, which is amplitude for AM.
- For phase modulation, the modulation index depends on the phase change. So know that for a PM emission, the modulation index
**does not depend on the RF carrier frequency****.**This is because the frequency is not being modulated! Even if the RF carrier frequency increases or decreases for a phase modulated signal, the modulation index will not change.

Now it’s time to calculate the modulation index and deviation ratio of an FM signal. Let’s start with the modulation index.

The modulation index is calculated by the amount of modulation divided by the carrier signal. That formula is deviation / modulating frequency.

Here’s the math for the modulation index questions:

- An FM-phone signal has a frequency deviation of 3000 Hz on either side of the carrier frequency. The modulating frequency is 1000 Hz. With a deviation of 3000 and a frequency of 1000, that divides out to a modulation index of
**3.** - Now, an FM-phone signal has a maximum carrier deviation of 6 kHz. The modulating frequency is 2 kHz. Since they are both in kilohertz, simply divide 6 by 2 to get the modulation index of
**3.**

In case you didn’t notice, both modulation index answers work out to be 3. That’s an easy trick to help on the exam. Just remember the answer to both of these is 3.

Time to calculate the deviation ratio of some signals. We’re going to use the same formula, deviation / modulating frequency:

- An FM-phone signal has a maximum frequency swing of plus-or-minus 5 kHz. Its maximum modulation frequency is 3 kHz. Plugging this into our formula, we see that 5 divided by 3 gives us a deviation ratio of
**1.67.** - Finally, an FM-phone signal has a maximum frequency swing of plus or minus 7.5 kHz. The maximum modulation frequency is 3.5 kHz. When we take 7.5 and divide it by 3.5 the answer is a deviation ratio of
**2.14.**

They are all just simple divisions. These four questions are a great example of why you should take advantage of having a simple calculator with you for the exam. The easy formulas will ensure you choose the correct answer.

*Simple calculator*

### Frequency and Time Division Multiplexing

While it seems like available frequencies go on forever, the usable radio spectrum is limited. Because of this, RF engineers have figured out very clever ways to get the most out of our finite spectrum. Two techniques they have invented are frequency division multiplexing and time division multiplexing. The term multiplexing is just an easier way of saying – combining multiple signals into one.

The cable TV in your home is a great example of frequency division multiplexing. FDM’s job is **dividing the transmitted signal into separate frequency bands that each carry a different data stream.** On your cable, over 100 unique frequency channels are combined into one signal into your home. Technologically this is done using Quadrature Amplitude Modulation or QAM. That is **transmission of data by modulating the amplitude of two carriers of the same frequency but 90 degrees out of phase. **

QAM and QPSK transmissions are closely related. Each can be mapped on what’s called a constellation diagram. That diagram shows **the possible phase and amplitude states for each symbol.**

What is digital time division multiplexing? It’s when **two or more signals are arranged to share discrete time slots of a data transmission****.** In amateur radio an example of this is Digital Mobile Radio, or DMR. DMR signals have two time slots. So while one user may be interacting on a local reflector, another can be listening to a net on a distant reflector. If you don’t use DMR, you definitely use time division multiplexing when you talk on your mobile phone. The use of two time slots (or more) means managing a signal in the “time domain.” That just means the signal has **amplitude at different times** in the cycle.

*Digital time division multiplexing diagram*

A more complex type of multiplexing is Orthogonal Frequency Division Multiplexing or OFDM. OFDM is a **digital modulation technique using subcarriers at frequencies chosen to avoid intersymbol interference****.** In amateur radio OFDM is used for **high-speed digital modes** similar to WiFi internet data.