Chapter 2: Amplitude Modulation Flashcards
Definitions of AM:
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- The process of changing the amplitude of a relatively high frequency carrier signal in proportion with the instantaneous value of modulating signal (information).
- A process of translating information signal from low band frequency to high band frequency.
Amplitude Modulation:
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- Information signal cannot travel far. It needs carrier signal of higher frequency for long distance destination.
- Inexpensive, low quality form of modulation.
- Amplitude of the carrier signal varies with the information signal.
- The modulated signal consists of carrier signal, upper sideband and lower sideband signals.
- The modulated AM signal needs to go through demodulation process to get back the information signal.
The AM Envelope:
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- AM double side-band full carrier (AM DSBFC) is the most commonly used and the oldest and the simplest form of AM modulation.
- Sometimes called conventional AM or simply AM.
- The outline of the positive and negative peaks of the carrier frequency re-create the exact shape of the modulating signal known as envelope.
- Note that the repetition rate of the envelope is equal to the frequency of the modulating signal.
The generation of AM envelope (diagram)
Refer to final folder in ECOM file.
What type of devices is an AM modulator?
An AM modulator is a non-linear device.
AM Frequency Spectrum and Bandwidth:
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- An AM modulator is a non-linear device.
- Nonlinear mixing results in a complex output envelope consists of the carrier frequency and the sum (f c + f m) and difference (f c - f m) frequencies (called cross-products).
- The cross-products are displaced from the carrier frequency by f m on both sides of it.
- AM modulated wave contains no frequency component of f m.
Frequency spectrum of an AM DSBFC wave diagram:
Refer to final folder in ECOM file.
Bandwidth:
- The BW of an AM DSBFC wave is equal to the difference between the highest upper side and the lowest lower side frequency:
(i) BW = [f c + f m (max)] - [f c
- f m (max)]
= 2 f m (max). - For efficiency transmission, the carrier and
sidebands must be high enough to be propagated thru earth’s atmosphere.
Information signal, carrier signal and AM DSBFC. (frequency continuous and distinct wave)
Refer to final folder in ECOM file.
Modulation index and percent of modulation:
- Used to describe the amount of amplitude change (modulation) present in an AM waveform.
- Percent modulation gives a percentage change in the amplitude of the output wave when the carrier is acted on by a modulating signal.
Modulation index and percentage of modulation formula:
m = E m / E c %m = E m / E c x 100%
Modulation index formula, if:
1. modulating signal is pure, single-freq sine wave and the process is symmetrical.
E m = 1/2 (V max - V min)
E c = 1/2 (V max + V min)
Therefore:
m = E m / E c
= [1/2 (V max - V min)]
---------------------------------
[1/2 (V max + V min)]
= V max - V min
-----------------------
V max + V min
Formula of E usb and E lsb:
E usb = E lsb = E m / 2
= (1/4)(V max -
min)
Modulation index for trapezoidal patterns formula:
m = E max - E min / E max
+ E min
= E m / E c
= (A - B) / (A + B)
% modulation of AM DSBFC envelope
Refer to final folder in ECOM file.
Proper AM operation in terms of E c, E m and m:
E c > E m, which means:
0 < = m < = 1.
If E c < E m:
means that m > 1 leads to severe distortion of the modulate wave.
If V c = V m
The percentage modulation index (%m) goes to 100%, means the maximum information signal is transmitted. In this case:
(i) V max = 2 V c
(ii) V min = 0
When m = 1, when m > 1 (diagram):
Refer to final folder in ECOM file.
Mathematical Representation and Analysis of AM (all formulas)
(i) v m (t) = V m sin (2 pi
f m t)
(ii) v c (t) = V c sin (2 pi
f c t)
(iii) v am (t) =
(a) [V c + V m sin (2 pi f m t)]
[sin (2 pi f c t)]
(b) [V c + m V c sin (2 pi f m
t)][sin (2 pi f c t)]
(c) [1 + m sin (2 pi f m t)][V c
sin (2 pi f c t)]
(d) V c sin (2 pi f c t) + V c [m sin (2 pi f m t)][sin (2 pi f c t)]
(e) V c sin (2 pi f c t) -
(m V c / 2) cos (2 pi
(f c + f m) t) + (m V c / 2)
cos (2 pi (f c - f m) t)[1 + m sin (2 pi f m t)][V c sin (2 pi f c t)]
From this formula name each part:
- [1 + m sin (2 pi f m t)]
- [V c sin (2 pi f c t)]
- Constant + modulated signal
2. Unmodulated signal
V c sin (2 pi f c t) - (m V c / 2) cos (2 pi (f c + f m) t) +
(m V c / 2) cos (2 pi
(f c - f m) t)
From this formula, determine each part:
1. V c sin (2 pi f c t)
2. (m V c / 2) cos (2 pi (f c +
f m) t)
3. (m V c / 2) cos (2 pi
(f c - f m) t)
- Carrier frequency signal. (volts)
- Upper side frequency signal. (volts)
- Lower side frequency signal. (volts)
From the equations it is obvious that:
amplitude of carrier
From the equation it is obvious that the amplitude of the carrier is unaffected by the modulation process.
From the equations it is obvious that:
amplitude of the side frequencies
The amplitude of the side frequencies depend
on the both the carrier amplitude and modulation index.
From the equations it is obvious that:
At 100% modulation, the amplitude of side frequencies
At 100% modulation the amplitudes of side frequencies are each equal to one half the amplitude of the carrier.
Generation of AM DSBFC envelope showing the time domain of the modulated wave, carrier & sideband signals: (diagram)
Refer to final folder in ECOM file.
AM Power Distribution and its formula:
In any electrical circuit, the power dissipated is equal to the voltage squared (rms) divided by the resistance.
P c = [( V c / (2)^(1/2))^2] / R
= [(V c)^2] / [2R]
Upper and lower side band powers formula:
P usb = P lsb
= [(m V c / 2)^2] / [2R]
= [(m^2)(V c)^2] / [8R]
P usb and p lsb in terms of P c:
P usb = P lsb = ([m^2] / [4])
([Vc]^2 / [2R])
= ([m^2] / [4])(P c)
Total power in an AM wave:
P t = P c + P usb + P lsb
Substituting the sidebands powers in terms of P c yields
P t = P c + ([m^2] / [4])(P c) +
([m^2] / [4])(P c)
= P c + ([m^2] / [2])(P c)
= P c [ 1 + ([m^2] / [4]) ]
Carrier power in modulated and unmodulated wave:
Since carrier power in modulated wave is the same as unmodulated wave, obviously power of the carrier is unaffected by modulation process.
Power spectrum for AM DSBFC wave with a single frequency modulating signal:
Refer to final folder in ECOM file.
The most significant disadvantage of AM DSBFC:
DSBFC is with m = 1, the efficiency of transmission is
only 33.3% of the total transmitted signal. The less wasted in the carrier which brings no information signal.
The advantage of AM DSBFC:
The use of relatively simple, inexpensive demodulator circuits in the receiver.
Transmitter Efficiency
Ratio of average side band powers to the total power absorbed.
% T E = m²/ ( 2+m² ) X 100
Modulation by a complex information signal (formula):
Refer to final folder in ECOM file.
Frequency spectrum for complex information signal:
Refer to final folder in ECOM file.
Modulation index for complex information signal:
m t = [ (m 1)^2 + (m 2)^2 +
(m 3)^2 + … +
(m n)^2 ]^1/2
Power calculation for complex information signal
P usb = P lsb = [P c (m t)^2]
/ [4]
P sbt = [P c (m t)^2] / [2]
P t = (P c) ( 1 + [(m t)^2]) / [2] )
Low Level AM Transmitter:
Refer to final folder in ECOM file.
High Level AM Transmitter:
Refer to final folder in ECOM file.
