Frequency Modulation (FM)

This tutorial is part of the National Instruments Measurement Fundamentals series. Each tutorial in this series, will teach you a specific topic of common measurement applications, by explaining the theory and giving practical examples. This tutorial covers an introduction to RF, wireless and high-frequency signals and systems.

For the complete list of tutorials, return to the NI Measurement Fundamentals Main page or for more RF tutorials refer to the NI RF Fundamentals main subpage. For more information on National Instruments RF products, visit www.ni.com/rf.

Frequency Modulation (FM) is a form of modulation in which changes in the frequency of the carrier wave correspond directly with changes in the baseband signal. This is considered an analog form of modulation, because the baseband signal is typically an analog waveform without discrete, digital values.

Common Applications

FM is most commonly used for radio and television broadcast. In fact, FM radio, which operates from 88 Mhz to 108 MHz, uses FM modulation to transmit audio signals. Each radio station utilizes a 38 kHz frequency band to broadcast audio. Analog television implements FM modulation as well. In fact, television channels 0 through 72 utilize various bandwidths between 54 MHz and 825 MHz. This bandwidth is divided between a variety of purposes, of which FM radio is one.

FM Theory

The basic principle behind FM modulation is that the amplitude of an analog baseband signal can be represented by a slightly different frequency of the carrier. We represent this relationship in the graph below:


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As this graph illustrates, various amplitudes of the baseband signal (shown in white) relate to specific frequencies of the carrier signal (shown in red). Mathematically, we will represent this by describing the equations which characterize FM modulation.

First, we represent our message signal, by the simple designation:

Second, we can represent a sinusoidal carrier by the equation:

The actual mathematical process to modulate a baseband signal, m(t), onto the carrier requires a two step process. First, the message signal must be integrated with respect to time to get an equation for phase with respect to time, Ө(t). This enables the modulation process because phase modulation is fairly straightforward. With typical IQ modulator circuitry. A block diagram description of a FM transmitter is shown below:


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As the block diagram above illustrates, the integration of a message signal results in an equation for phase with respect to time. This equation is defined by the following equation:



Again, the resulting modulation that must occur is phase modulation, which involves changing the phase of the carrier over time. This process is fairly straightforward and requires a quadrature modulator, shown below:


As a result of phase modulation, the resulting FM signal, s(t), now represents the FM modulated signal. This equation is shown below:

More simply, we can also represent this equation as:

Modulation Index

One important aspect of frequency modulation is the modulation index. We have already established that changes in amplitude of the baseband correspond to changes in frequency of the carrier. The factor which determines exactly how much the carrier deviates from its center frequency is known as the modulation index. Mathematically, have already identified our integrated baseband signal as:

We can actually simply this equation to the following:

In the equation above, ∆ƒ is the frequency deviation and it represents the maximum frequency difference between the instantaneous frequency and the carrier frequency. In fact, the ration of ∆ƒ to the carrier frequency is the modulation index. This index, β, is thus defined by the equation:

Thus, the integrated message signal can be represented as:

As a result, we can substitute this new representation of Ө(t) into our original formula to represent the final modulated FM signal as the following equation:

The affect of the modulation index on the modulated sinusoid is that the larger the modulation index, the greater the instantaneous frequency can be from the carrier. Below, we illustrate an FM modulated signal in which the center frequency is 500 kHz. In addition, observe in the graph below that the FM deviation has been selected as 425 kHz. As a result, the modulated signal will have instantaneous frequencies from 75 kHz to 925 kHz. The wide range of frequencies is evident by observing the minimum amplitude of the baseband, when the modulated frequency is very small.

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The image above can be contrasted to an FM signal where the frequency deviation is comparatively small. Below, we have chosen a FM deviation of 200 kHz instead.

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As the image illustrates, the range instantaneous frequency in the modulated signal is much smaller with a smaller FM deviation.

This property can be more fully observed by selecting the FM modulation example, linked here.

Conclusions

Frequency Modulation (FM) is an important modulation scheme both because of its widespread commercial use, and because of its simplicity. As we have seen in this document, frequency modulation can be simplified to phase modulation with a simple integrator. As a result, frequency modulated signals can be generated with the National Instruments vector signal generator, because they require nothing more than an IQ modulator.

Related Products

NI PXI-5660 2.7 GHz RF Vector Signal Analyzer
The National Instruments PXI-5660 is a modular 2.7 GHz RF vector signal analyzer with 20 MHz of real-time bandwidth optimized for automated test.

NI PXI-5671 2.7 GHz RF Vector Signal Generator
The National Instruments PXI-5671 module is a 3-slot RF vector signal generator that delivers signal generation from 250 kHz to 2.7 GHz, 20 MHz of real-time bandwidth and up to 512 MB of memory.

NI PXI-5652 6.6 GHz RF and Microwave Signal Generator
The National Instruments PXI-5652 6.6 GHz RF and microwave signal generator is continuous-wave with modulation capability. It is excellent for setting up stimulus response applications with RF signal analyzers.

NI RF Switches
The National Instruments RF switch modules are ideal for expanding the channel count or increasing the flexibility of systems with signal bandwidths greater than 10 MHz to bandwidths as high as 26.5 GHz.

NI LabVIEW
National Instruments LabVIEW is an industry-leading graphical software tool for designing test, measurement, and automation systems.

NI Modulation Toolkit
The National Instruments Modulation Toolkit extends the built-in analysis capability of LabVIEW with functions and tools for signal generation, analysis, visualization, and processing of standard and custom digital and analog modulation formats.

References

1. Simon Haykin, Communications Systems.
2. B.P. Lathi, Modern Digital and Analog Communications Systems.

   Conclusion
   

For the complete list of tutorials, return to the NI Measurement Fundamentals Main page or for more RF tutorials refer to the NI RF Fundamentals main subpage. For more information on National Instruments RF products, visit www.ni.com/rf.

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