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6 minute read time.

In the previous episode, we learned about amplitude shift keying (ASK) modulation schemes, in which the digital message modulates the carrier amplitude. In this fourth episode, we will analyze how a digital message can change the carrier frequency, known as frequency shift keying (FSK).

**FSK signal = A(t) . Sin(2π.f(t) + ɸ(t))** Where f(t) is a digital bits flow

Frequency shift keying or FSK is the digital form of FM modulation, which we covered briefly in the first episode. The carrier frequency can shift between a finite series of possibilities, the simplest being the case where only two frequencies are used to transport the bits, 0 and 1. It is then called binary frequency shift keying (BFSK) or 2FSK.

*Figure 1 - Frequency shift keying (FSK) modulation principle as seen in a transponder timing RFID chip. *

The FSK modulation principle is simple: when the message data is 0, the carrier frequency is F0, and when the message is 1, the carrier frequency is F1. Since the amplitude signal doesn’t carry the information, FSK is highly robust against perturbance; thus the different circuits (amplifiers, filters, etc.) don’t have to be highly linear.

*Figure 2 – Binary FSK Principle *

For some strange reason, the higher frequency F1 coding 1 is called “mark,” while the lower frequency F0 coding 0 is called “space.” The middle frequency between them, represented by (F1+F0)/2, is the virtual central carrier frequency FC. It can be used to calculate frequency deviation FD as either F1-FC or FC-F0.

Frequency deviation is an important parameter. The smaller it is, the greater the risk of inter-symbol interference, which can deteriorate the bit error rate (BER). The larger it is, the more easily an FSK receiver will be able to recognize the two distinct values—but one cannot push FD too far. Frequency deviation directly impacts the frequency band occupancy, and thus there is a trade-off between BER and bandwidth efficiency.

The frequency usage by FSK depends on the tone spacing and bit rate. For a BFSK, the bandwidth occupied is:

**BWBFSK = 2 (FD +FB) ** where FD is the frequency deviation and FB the message bit rate

Beyond the simple BFSK, things become more complicated. The bandwidth occupied by one bit of duration T is theoretically infinite, mainly due to the assumption that the transition 0 to 1 and 1 to 0 is brutal with zero delay. An abrupt transition contains many frequencies that can muddy the waters when trying to determine bandwidth. There are techniques to soften the transitions by applying filter interfacing to the data before modulation, and we’ll see one way to use them in a moment.

You can find a good approximation of bandwidth by ignoring all but the main lobe. Consider this lobe’s bandwidth to equal 1/T and you’ll have your answer.

*Figure 3 - BFSK Bandwidth Spectrum*

To quantify and appreciate the bandwidth usage, a specific parameter is set: the modulation index, h.

** h = 2.FD / FB ** where FD is the frequency deviation and FB the bit rate

Optimum FSK detection is quasi guaranteed when the modulation index is larger than 1 (h >1), but frequencies start to be “wasted” when h >0.5. By softening the bit transitions with a filter and keeping h=0.5, we reach an optimal tradeoff. This called minimum shift keying or MSK.

*Figure 4 – MSK operation*

MSK is a good trade-off between frequency usage, data flow and distortion performance. It's used for various applications, including the GSM mobile phone, which follows the Global System for Mobile Communications (GSM) protocols for 2G digital cellular networks. The well-known Gaussian minimum shift keying (GMSK) is a particular form of MSK: the filter shaping has a Gaussian profile.

*Figure 5 – FSK ideal implementation, in which the multiplexer selects the output frequency based on the state of the binary input. CC BY TutorialsPoint*

The implementation of a FSK modulator can be simple. Since the modulation is made by having a specific frequency when the data is 0 and a slightly different frequency when data is 1, all you need are two oscillators with two possible frequencies, F1 and F2, and a multiplexer that switches from one frequency to the other according to a binary signal.

This structure is easy to understand. It works, but switching between the two frequencies is often a source of noise and disturbances. That’s why this is also called a non-coherent FSK: the transition between frequencies can occur at any phase, causing a phase break, noise, and bad BER. In contrast, a coherent FSK signal will have the frequency changes occurring at the same phase value, usually when crossing zero.

*Figure 6 – Comparison of non-coherent and coherent FSK signals based on continuity of the frequency transition*

To ensure a coherent switch between the different FSK frequencies, one must use a single generator that gives a frequency depending on a tunable element inside the device, the voltage controlled oscillator (VCO). The varying element is a Varicap exhibiting a variable capacitance rather than an applied DC voltage.

*Figure 7 - Coherent FSK implementation using a varicap diode. *

Like the ASK modulation family, FSK schemes come in many forms. Here we will briefly mention them; however, a detailed analysis is outside the scope of this series.

**MSK**or Minimum BFSK: a 2-FSK with modulation index h=0.5**M-ary FSK**: Frequency modulation scheme using more than 2 tones. They are called M-FSK, with M being a multiple of 2. Usual values are 4 and 8. Note: M-FSK is not to be confused with MSK.**GFSK**or**Gaussian Frequency Shift Keying**: A coherent FSK where the data flow is shaped with a Gaussian filter, .**GMSK**or**Gaussian Minimum Frequency Shift Keying**: The principle of GFSK, applied to MSK.

Thanks to its robustness against interference, FSK is used in applications as wide-ranging as paging systems, metering, telemetry, remote controls, Bluetooth links, DECT, two-way digital radio, and more. However, today’s applications demand more and more data and throughput in wireless communications, so phase shift keying (PSK) and its variations are replacing FSK techniques for many applications.

Next post—check back soon!