Frequency modulation and circuits

1
Frequency modulation and circuits

• Lecture 4

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Review of Modulation Circuits

• AM Generation
• DSBSC Generation
• FM Generation

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AM Generation

• The function of an AM modulator is to modulate a
  carrier wave using an intelligence signal, which
  results in sum and difference frequencies,
  together with the carrier.

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A possible way to achieve this is to use an
operational amplifier to electrically sum the two
signals as shown in the figure below. In such an
arrangement the two signals will remain
independent of each other.
5
The production of a typical AM wave requires the
use of a non-linear device, such as a transistor
or diode. A non-linear device is one that
produces an output, which is not proportional to
the input. An example of a circuit, which
produces an AM wave, is shown.
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The result of using the diode and resistor is to
clip the negative half of the composite signal.
The result is the output signal shown. It will be
noticed that this signal is only the top half of
the AM wave form.
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To produce the full AM wave will require the use
of a tank circuit. A diagram of the tank circuit
is shown together with its output
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If this circuit is incorporated into the original
non-linear modulator circuit, the full AM wave
can be produced
9
A diode ha s no gain. To produce gain, a
transistor could be used in place of a diode. The
circuit is as shown below.
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DSBSC Generation
Circuits used to obtain DSBSC are called balanced
modulators. The figure below shows an example of
a balanced modulator. It uses diodes as the
non-linear devices.
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Circuits used to obtain DSBSC are called balanced
modulators. The figure below shows an example of
a balanced modulator. It uses diodes as the
non-linear devices.
The diodes are paired and are turned on and off
during the positive and negative half of the
carrier frequency cycle.
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During the positive half, D1 and D4 are on and
the other two are off. The circuit will therefore
look as follows
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During the negative half, D2 and D3 are on and
the other two are off. The resulting circuit is
shown.
The modulating signal undergoes a 180o phase
shift.
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The current produced by the carrier signal is
split at the centre taps of the transformers and
flow in opposite directions. This leads to their
cancellation as they produce magnetic fields,
which are equal in magnitude but opposite in
phase.
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Frequency Modulation

• In this the instantaneous frequency of the
  carrier is caused to vary by an amount
  proportional to the amplitude of the modulating
  signal. The amplitude is kept constant.
• More complex than AM this is because it involves
  minute changes in frequency
• FM is more immune to effects of noise
• FM and PM are similar

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Assume we have a carrier at a frequency of
100MHz, called the resting frequency. If a
modulating signal is then applied, this will
cause the carrier to shift (deviate) from its
resting frequency by a certain amount. If the
amplitude is increased then the amount of
deviation also increases. The rate is
proportional to frequency of the intelligence
signal. If the signal is removed then the carrier
frequency shifts back to its resting
frequency. This shift in frequency compared with
the amplitude of the modulating voltage is called
the deviation ratio.
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The deviation ratio is also called the deviation
constant and it defines how much the carrier
frequency will change for a given input voltage
level. The units are kHz/V Example Given that
the deviation constant is 1kHz/10mV, what is the
shift in frequency for a voltage level of 50
mV? Frequency deviation
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Mathematical representation of FM
The following equation can be used to represent
FM where fc is the unmodulated carrier
frequency k is a proportionality constant and the
last term is the modulating voltage It will be
seen that the maximum deviation will occur when
the cosine term is unity and hence we
obtain maximum deviation
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It can be shown that the instantaneous value of
the FM voltage is given by The modulation
index for FM is defined as To solve for the
frequency components of the FM requires the use
of Bessel functions.
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This solution may be shown to be given by
To evaluate the individual values of J is quite
tedious and so tables are used.
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Observations

• Unlike AM where there are only three frequencies,
  FM has an infinite number of sidebands
• The J coefficients decrease with n but not in any
  simple form and represent the amplitude of a
  particular sideband. The modulation index
  determines how many sideband components have
  significant amplitudes
• The sidebands at equal distances from fc have
  equal amplitudes
• In AM increase depth of modulation increases
  sideband power and hence total transmitted power.
  In FM total transmitted power remains constant,
  increase depth of modulation increases bandwidth
• The theoretical bandwidth required for FM
  transmission is infinite.

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Examples
In an FM system when the audio frequency is 300
Hz and the audio voltage is 2.0V, the deviation
is 5kHz. If the audio voltage is now increased to
6V what is the new deviation? If the voltage is
now increased to 9V and the frequency dropped to
100Hz what is the deviation? Find the modulation
index in each case.
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Find the carrier and modulating frequencies, the
modulating index, and the max. deviation of an FM
wave below. What power will the wave dissipate in
a 10 ohm resistor?
Compare this with
Modulating index5 as given.
Power,
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What bandwidth is required to transmit an FM
signal with intelligence at 12KHz and max
deviation 24 kHz
Consult Bessel function table to note that for
modulating index of 2, components which exist are
J1,J2,J3,J4 apart from J0. This means that apart
from the carrier you get J1 at /-10kHz, J2 at
/- 20kHz, J3 at /- 30kHz and J4 at /- 40 kHz.
Total bandwidth is therefore 2x4080kHz.
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Carsons Rule
This is an approximate method used to predict the
required bandwidth necessary for FM transmission
About 98 of the total power is included in the
approximation.
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For an FM signal given by
If this signal is input into a 30 ohm antenna,
find

• the carrier frequency
• the transmitted power
• the modulating index
• the intelligence frequency
• the required bandwidth using Carson's rule and
  tables
• the power in the largest and smallest sidebands

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AM Vs FM systems
In both systems a carrier wave is modulated by an
audio signal to produce a carrier and sidebands.
The technique can be applied to various
communication systems eg telephony and
telegraphy Special techniques applied to AM can
also be applied to FM Both systems use receivers
based on the superheterodyne principle
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• In AM, the carrier amplitude is varied whereas in
  FM the carrier frequency is varied
• AM produces two sets of sidebands and is said to
  be a narrowband system. FM produces a large set
  of sidebands and is a broad band system
• FM gives a better signal to noise ratio than AM
  under similar operating conditions
• FM systems are more sophisticated and expensive
  than AM systems

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Transmitters In an AM transmitter, provision must
be made for varying the carrier amplitude whilst
for FM the carrier frequency is varied. AM and
FM modulators are therefore essentially different
in design. FM can be produced by direct frequency
modulation or by indirectly phase modulation.
The FM carrier must be high usually in the VHF
band as it requires large bandwidth which is not
available in the lower bands.
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Receivers The FM and AM receivers are basically
the same, however the FM receiver uses a limiter
and a discriminator to remove AM variations and
to convert frequency changes to amplitude
variations respectively. As a result they (FM)
have higher gain than AM. FM receivers give
high fidelity reproduction due to their large
audio bandwidth up to 15 kHz compared with about
8 kHz for AM receivers.