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Communication Principles - 3

AM double-sideband full carrier (DSBFC) – commonly used amplitude modu...
Course

Electronics Engineering (CR 061)

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Samar State University

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LESSON CONTENT

AM modulators are non-linear devices with two inputs and one output. One input is a single, high frequency carrier signal of constant amplitude and the second input is comprised of relatively lowfrequency information signals that may be a single frequency or a complex waveform made up of many frequencies.

Radio Frequencies – frequencies that are high enough to be efficiently radiated by an antenna and propagated through free space.

The AM Envelope AM double-sideband full carrier (DSBFC) – commonly used amplitude modulation. - Sometimes called conventional AM or simply AM.

Figure 4-1 illustrates the relationship among carrier (𝐀 𝐀 sin[ 22222222222222 2 𝐀𝐀]), the modulating signal ((((((((((((((( 𝐀 sin[ 22222222222222 2 𝐀𝐀]), and the modulated wave (((((((((((((((𝐀𝐀 [[[[[[[[[[[[[[[]) for conventional AM. The output waveform contains all the frequencies that make up the AM signal and is used to transport the information through the system.

AM Envelope – the shape of the modulated signal

AM Frequency Spectrum Bandwidth Output envelope – a complex wave made up of a dc voltage, the carrier frequency, and the sum (fc + fm) and difference (fc - fm) frequencies. The sum and difference frequencies are displaced from the carrier frequency by an amount equal to the modulating signal frequency.

Figure 4-2 shows the frequency spectrum for an AM wave. Spectrum extends from fc – fm(max) to fc + fm(max), where fc is the carrier frequency and fm(max) is the highest modulating signal frequency.

Lower Sideband (LSB) – band of frequencies between fc – fm(max) and fc and any frequency within this band is called lower side frequency (LSF)

Upper Sideband (USB) - band of frequencies between fc + fm(max) and fc and any frequency within this band is called upper side frequency (LSF)

Bandwidth (B) – is equal to the difference between the highest upper side frequency and the lowest lower side frequency, or two times the highest modulating signal frequency (i., B = 2fm(max))

Example: For an AM DSBFC modulator with a carrier frequency fc = 100 kHz and a maximum modulating signal frequency fm(max) = 5 kHz, determine a. Frequency limits for the upper and lower sidebands b. Bandwidth c. Upper and lower side frequencies produced when the modulating signal is a single-frequency 3-kHz tone. d. Draw the output frequency spectrum

Solution: a. Lower Sideband

[[[[[[[[[[[[[[[ = [ 𝐀 𝐀 − ((((((((((((((( ) ] 𝐀 ) 5) 5 = (100 − 5) 5) 5) 5) 5) 5) 5) 5) 5) 5) 5) 5) 5 ) 100 = 9 5 100 Upper Sideband = 𝐀 𝐀 [[[[[[[[[[[[[[[𝐀 + 𝐀(max)] = 100 (100 + 5) = 100 105 b. Bandwidth

222222222222222 = 2𝐀 𝐀 ((((((((((((((() = 2(5 ) = 10 c. Upper side frequency 𝐀𝐀𝐀𝐀 = 𝐀 + 𝐀 = 100 + 3 = 103 Lower side frequency 𝐀𝐀𝐀𝐀= 𝐀 − 𝐀 = 100 − 3 = 97 d. The output frequency spectrum is shown in the figure below.

Coefficient of Modulation - a term used to describe the amount of amplitude change (modulation) present in an AM waveform.

𝐀 𝐀

Example: For the AM waveform shown in Figure 4-7, determine a. Peak amplitude of the upper and lower side frequencies. b. Peak amplitude of the unmodulated carrier c. Peak change in the amplitude of the envelope. d. Coefficient of modulation e. Percent Modulation Solution:

a. 𝐀𝐀𝐀𝐀 = 𝐀𝐀𝐀 = 14 (18 − 2) = 4

b. 𝐀 1 𝐀 = 2 (18 + 2) = 10 c. 𝐀𝐀 = 12 (18 − 2) = 8 d. 𝐀 = = 0.

e. 𝐀 = 0 × 100 = 80%

AM Voltage Distribution Unmodulated Carrier 𝐀𝐀 ((((((((((((((( ) =𝐀 sin( 22222222222222 2 𝐀𝐀) (4-9) Where vc(t) = time-varying voltage waveform for the carrier Ec = peak carrier amplitude (volts) fc = carrier frequency (hertz)

Instantaneous amplitude of modulated wave can be expressed as 𝐀𝐀𝐀 ([([([([([([([([([([([([([([() = [𝐀 + 𝐀 sin( 22222222222222 2 𝐀)][sin(2𝐀𝐀 222222222222222 𝐀𝐀)] (4-10) Where [[[[[[[[[[[[[[[𝐀 + 𝐀 sin( 22222222222222 2 𝐀𝐀)] = amplitude of the modulated wave 𝐀𝐀 = peak change in the amplitude of the envelope 𝐀𝐀 = frequency of the modulating signal (hertz)

If 𝐀𝐀𝐀 is substituted for 𝐀𝐀, 𝐀𝐀𝐀 ([([([([([([([([([([([([([([() = [𝐀 + 𝐀 sin( 22222222222222 2 𝐀)][sin(2𝐀𝐀 222222222222222 𝐀𝐀)] (4-11) Where [[[[[[[[[[[[[[[𝐀 + 𝐀 sin( 22222222222222 2 𝐀𝐀)] = equal the amplitude of the modulated wave

Factoring Ec from previous equation and rearranging gives 𝐀𝐀𝐀 ( 2( 2( 2( 2( 2( 2( 2( 2( 2( 2( 2( 2( 2( 2() = [1 + sin( 2 𝐀)][𝐀[[[[[[[[[[[[[[[ 𝐀sin( 22222222222222 2 𝐀𝐀)] (4-12) Where [1 + 22222222222222 sin( 2 𝐀𝐀)] = constant + modulating signal [[[[[[[[[[[[[[[𝐀sin( 22222222222222 2 𝐀𝐀)] = unmodulated carrier

𝐀𝐀𝐀(((((((((((((( () = 𝐀sin( 22222222222222 2 𝐀𝐀) − 𝐀 2𝐀𝐀 cos[2(2(2(2(2(2(2(2(2(2(2(2(2(2( 2(𝐀 + 𝐀 )))))))))))))))] + 𝐀 2𝐀𝐀 cos[2(2(2(2(2(2(2(2(2(2(2(2(2(2( 2(𝐀 − 𝐀 )))))))))))))))] (4-14)

AM Power Distribution (0 77777777777777 7 𝐀) 2 𝐀𝐀 = 𝐀

(((((((((((((((𝐀) 2

𝐀𝐀 =

222222222222222

Where Pc = carrier power (watts) Ec = peak carrier voltage (volts) R = load resistance (ohms)

The upper and lower sideband power are expressed mathematically as 𝐀 2 𝐀𝐀 𝐀𝐀𝐀𝐀 = 𝐀𝐀𝐀 = 4

Total Power in an AM DSBFC envelope is

𝐀𝐀 = 𝐀 + 𝐀𝐀𝐀 + 𝐀𝐀𝐀

Where Pt = total power of an AM DSBFC envelope (watts)

Pc = carrier power (watts) Pusb = upper sideband power (watts) Plsb = lower sideband power (watts)

𝐀 2

𝐀𝐀 = 𝐀 (1 +

Example )

2 For an AM DSBFC wave with a peak unmodulated carrier voltage Vc = 10 Vp, a load resistance RL = 10 ohms, and a modulation coefficient m = 1, determine a. Powers of the carrier and the upper and lower sidebands b. Total sideband power c. Total power of the modulated wave

Solution

a. 𝐀𝐀 = 2 10(10 2 ) = 5

𝐀𝐀𝐀𝐀 = 𝐀𝐀𝐀 = = 1.

b. 𝐀𝐀𝐀𝐀 = 𝐀 2222222222222222 𝐀 = (1 2 2)(5) = 2 (1) 2

c. 𝐀𝐀 = 5 [1 + 2 ] = 7.

AM Current Calculations 𝐀𝐀 𝐀𝐀2𝐀 𝐀𝐀2 𝐀 2

= 2 = 𝐀 𝐀2 = 1 + 2 𝐀𝐀 𝐀𝐀

Where 𝐀𝐀 = total transmit power (watts) 𝐀𝐀 = carrier power (watts) 𝐀𝐀 = total transmit current (ampere) 𝐀𝐀 = carrier current (ampere) R = antenna resistance (ohms)

And 𝐀𝐀 𝐀𝐀

Modulation by a Complex Information Signal

𝐀𝐀𝐀 (2(2(2(2(2(2(2(2(2(2(2(2(2(2() = sin( 2 𝐀𝐀) + 2(2(2(2(2(2(2(2(2(2(2(2(2(2(cos[ 2(𝐀 − 𝐀1 )))))))))))))))] − 2(2(2(2(2(2(2(2(2(2(2(2(2(2(cos[ 2(𝐀 + 𝐀1 )))))))))))))))] + 2(2(2(2(2(2(2(2(2(2(2(2(2(2(cos[ 2(𝐀 − 𝐀2 )))))))))))))))] − 2(2(2(2(2(2(2(2(2(2(2(2(2(2(cos[ 2(𝐀 + 𝐀2 )))))))))))))))] Combine coefficient of modulation

𝐀𝐀

Where 𝐀𝐀 = total coefficient of modulation 𝐀 1 , 2 , 3 𝐀 = coefficients of modulation for input signals 1, 2, 3, and n

AM Modulating Circuits Low-level Modulation – the modulation takes place prior to the output element of the final stage of the transmitter

High-level Modulation – the modulation takes place in the final element of the final stage where the carrier signal is at its maximum amplitude

Emitter Modulation – the amplitude of the output signal depends on the amplitude of the input carrier and the voltage gain of the amplifier

𝐀 𝐀 = 𝐀[1 + 22222222222222 sin( 2 𝐀𝐀)] Where Av = amplifier voltage gain with modulation (unitless) Aq = amplifier quiescent (without modulation) voltage gain (unitless)

Collector Modulation – a class C modulator capable of nonlinear mixing and the modulating signal is applied directly to the collector

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Communication Principles - 3

Course: Electronics Engineering (CR 061)

95 Documents
Students shared 95 documents in this course

University: Samar State University

Was this document helpful?
LESSON CONTENT
AM modulators are non-linear devices with two inputs and one output. One input is a single, high frequency
carrier signal of constant amplitude and the second input is comprised of relatively lowfrequency information
signals that may be a single frequency or a complex waveform made up of many frequencies.
Radio Frequencies – frequencies that are high enough to be efficiently radiated by an antenna
and propagated through free space.
The AM Envelope
AM double-sideband full carrier (DSBFC) – commonly used amplitude modulation. -
Sometimes called conventional AM or simply AM.
Figure 4-1 illustrates the relationship among carrier (�� sin[22222222222222 2 ��]), the modulating
signal
((((((((((((((( � sin[22222222222222 2��]), and the modulated wave (((((((((((((((�� ])[[[[[[[[[[[[[[[ for conventional AM.
The output waveform contains all the frequencies that make up the AM signal and is
used to transport the information through the system.
AM Envelope – the shape of the modulated signal
AM Frequency Spectrum Bandwidth
Output envelope – a complex wave made up of a dc voltage, the carrier frequency, and
the sum (fc + fm) and difference (fc - fm) frequencies. The sum and difference frequencies
are displaced from the carrier frequency by an amount equal to the modulating signal
frequency.

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