Arroyo, Stephanie Nicole B.
ECE 401
ASSIGNMENT #1: FREQUENCY SHIFT KEYING (FSK)
I.
INTRODUCTION
Frequency-shift keying (FSK) is a low performance, simple type of digital
modulation. FSK is a type of constant-amplitude angle modulation (CAAM) that is like FM,
except that the modulating signal is a binary signal that varies between two discrete
voltage levels rather than a continuously changing analog waveform. As a result, FSK is
sometimes referred to as binary FSK (BFSK). The general expression for FSK is:
Figure 1: FSK General Equation based on Advanced Electronic Communications Systems (6 th
Edition) by Wayne Tomasi
FSK defines frequency deviation as the difference between either the mark or the
difference between the mark and the space frequency, or half the difference between
the mark and the space frequencies. Frequency deviation is illustrated and expressed
mathematically as:
Figure 2:: Frequency deviation formula based on Advanced Electronic Communications Systems
(6th Edition) by Wayne Tomasi
II.
FSK BIT RATE AND BAUD RATE
The time of one bit (tb) is the same as the time the FSK output is a mark of space
frequency (ts), as shown in the figures below . Thus, bit time equals FSK signaling element
time, and bit rate equals baud rate.
Figure 3: FSK in the Time domain based on Advanced Electronic Communications Systems (6 th
Edition) by Wayne Tomas
III.
BANDWIDTH CONSIDERATIONS OF FSK
When designing an FSK transmitter, bandwidth is a primary consideration, just as it is in
all electronic communications systems. FSK is comparable to conventional frequency modulation
and thus can be described similarly.
An FSK modulator is depicted in Figure 13-3. An FSK modulator is a type of FM modulator.
and is frequently a voltage-controlled oscillator (VCO). It can be seen that when the binary input
is a series of alternating signals, the input rate of change is the fastest.
Figure 4 & 5: BFSK transmitter in Electronic Communications Systems by Wayne Tomasi
A square wave is made up of l's and 0's. One-half of the bit rate is equal to the
fundamental frequency of a binary square wave. As a result, if only the fundamental
frequency is considered, the highest modulating frequency to the FSK modulator is
considered, it is equal to one-half of the input bit rate.
The VCO's rest frequency is chosen to be halfway between the mark and space
frequencies. A logic 1 condition at the input moves the VCO from its rest frequency to the
mark frequency, while a logic 0 condition moves the VCO from its rest frequency to the
space frequency. As a result, as the input binary signal changes from logic 1 to logic 0, the
VCO output frequency shifts or deviates between the mark and space frequencies.
Because FSK is a type of frequency modulation, the modulation index formula used in FM
also applies to FSK.
Figure 6 & 7: Modulation Index formulas based on Electronic Communications Systems by
Wayne Tomasi
The modulation index with the greatest output bandwidth (deviation ratio) is
known as the worst-case modulation index. When both the frequency deviation and the
modulating frequencies are at their maximum, the worst-case or widest bandwidth
occurs.
The bandwidth of conventional FM is directly proportional to the modulation
index. As a result, the modulation index in FSK is generally kept below 1.0, resulting in a
relatively narrowband FM output spectrum. The minimum Nyquist bandwidth is the
amount of bandwidth required to propagate a signal (Fn). The minimum bandwidth is
obtained when modulation is used and a double-sided output spectrum is generated. The
minimum double-sided Nyquist bandwidth, also known as the minimum IF bandwidth.
Because FSK is a form of narrowband frequency modulation, the minimum bandwidth is
dependent on the modulation index. For a modulation index between 0.5 and 1 , either two or
three sets of significant side frequencies are generated. Thus the minimum bandwidth is two to
three times the input bit rate.
Figure 8: Bessel Function Chart based on on Electronic Communications Systems by Wayne
Tomasi
IV.
MINIMUM SHIFT-KEYING FSK
MSK (minimum shift-keying) is a type of continuous-phase frequency shift keying
(CPFSK). MSK is like binary FSK except that the mark and space frequencies are
synchronized with the binary bit rate of the input. Synchronous simply means that the
two have a precise time relationship; it does not imply that they are equal. The mark and
space frequencies in MSK are chosen so that they are an exact odd multiple of one-half
of the bit rate apart from the center frequency [Fm and Fs = n(Fb/2), where n = any odd
integer]. This guarantees a smooth phase transition when the analog output signal
changes from a mark frequency to a space frequency, or vice versa. A noncontinuous FSK
waveform is shown in Figure 13-6. The analog output signal shows an abrupt phase
discontinuity when the input changes from a logic 1 to a logic 0, and vice versa. When this
happens, the demodulator has difficulty following the frequency shift, and an error may
occur.
A continuous-phase MSK waveform is shown in Figure 13-7. It is worth noting that
when the output frequency changes, the transition is smooth and continuous. Each
transition takes place. As a result, there are no phase discontinuities at a zero crossing.
MSK has a higher. For a given signal-to-noise ratio, bit-error performance is better than
conventional FSK. MSK has the disadvantage of requiring synchronizing circuits, which
makes it more expensive to be applied.
Figure 9: Non- continuous and continuous waveforms of FSK AND MSK based on on Electronic
Communications Systems by Wayne Tomasi