Chapter 2: Amplitude Modulation Transmission EET-223: RF Communication Circuits Walter Lara
Introduction • As see before, modulation is needed to: – Avoid interference since intelligence signals are at approximately the same frequency – Avoid impractical large antennas since intelligence signals have low frequencies • Problem: how to put intelligence signal onto a carrier (high frequency) signal for transmission • Simplest solution: put intelligence into carrier’s amplitude
AM Fundamentals • Combining (“mixing”) the intelligence and carrier signals can be done: – Using linear device (e.g. resistor) – simple addition, but not suitable for transmission (receiver cannot detect intelligence) – Non-linear device (e.g., BJT or OpAmp) – method used in practice • Non-linear mixing results on: – DC Component – Components at original frequencies (intelligence & carrier) – Components at sum & difference of original frequencies – Harmonics of original frequencies
AM Fundamentals – Cont’d • Only the following components resulting from non- linear mixing are used on an AM waveform: – Carrier frequency (f c ) – Lower-side frequency (f c - f i ) – Upper-side frequency (f c + f i )
Figure 2-1 Linear addition of two sine waves.
Figure 2-2 Nonlinear mixing.
AM Waveforms • An AM modulated signal can be expressed as: e(t) = (E c + E i sin w i t) sin w c t where: E c = peak value of carrier signal E i =peak value of intelligence signal w c = angular frequency of carrier signal w i = angular frequency of intelligence signal • It can be demonstrated that: e(t)= E c sin w c t + (E i /2)cos (w c - w i )t - (E i /2)cos (w c + w i )t
Figure 2-3 AM waveform under varying intelligence signal ( e i ) conditions.
Figure 2-4 Carrier and side-frequency components result in AM waveform.
Figure 2-5 Modulation by a band of intelligence frequencies.
Figure 2-6 Solution for Example 2-1.
Percentage Modulation • Aka Modulation Index or Modulation Factor • Measure of extend to which carrier voltage is varied by intelligence • Defined as: %m = E i / E c * 100 – E i : Peak value of intelligence signal – E c : Peak value of carrier signal • Can also be computed using the peak-to-peak value of the AM waveform (see Fig. 2-8) – Convenient in graphical (oscilloscope) solutions.
Figure 2-8 Percentage modulation determination.
Overmodulation • Overmodulation is a condition that occurs when an excessive intelligence signal overdrives an AM modulator making %m > 100% (because E i > E c ) • Modulated carrier amplitude reach value greater than double of unmodulated value • It produces a distortion known as sideband splatter , which results on transmission at frequencies outside the allocated range • It is unacceptable because it causes severe interference with other stations and causes a loud splattering sound to be heard at the receiver.
Figure 2-9 Overmodulation.
AM Analysis • Recall: e(t) = (E c + E i sin w i t) sin w c t = E c sin w c t + (E i /2)cos (w c - w i )t + (E i /2)cos (w c + w i )t • Since E i = m E c , then: e(t) = E c sin w c t + (mE c /2) cos (w c - w i )t + (mE c /2) cos (w c + w i )t • Therefore, the side-frequency amplitude is: E SF = mE c /2
Why is important to use a high %m? • The higher m, the more transmitted power gets to our sidebands, which contain the intelligence. • The total power can be computed as: P T = P C + 2P SF = P C (1 + m 2 / 2) Where: P C : carrier power P SF : single sideband power • The total current can be computed as: 𝟐 + 𝒏 𝟑 /𝟑 I T = I c • The power efficiency can be computed as: Efficiency = 2P SF / P T = m 2 / (2 + m 2 )
AM Transmitter System • Refer to block diagram at Fig. 2-18 (next slide). • Main components are: – Oscillator: generates carrier signal at high accuracy (crystal- controlled) – Buffer Amplifier: provides high impedance load to oscillator to minimize drift – Intelligence Amplifier: amplifies the signal from input transducer – Modulated Amplifier (aka Modulator): generates modulated/mixed signal – Linear Power Amplifier: amplifies modulated signal on high- power (commercial) systems
Figure 2-18 Simple AM transmitter block diagram.
Trapezoidal Patterns • Method to check proper modulation of AM signal – More revealing than viewing signal on scope • Procedure: – Put scope in XY Mode – Put AM signal on vertical – Put intelligence signal on horizontal (through RC phase-shift network • Possible Results (see Fig 2-23): – Top & bottom straight lines: proper modulation – Single vertical line: no intelligence (carrier only) – Concave curvature: poor linearity on modulation stage – Convex curvature: improper bias or low carrier signal – Half oval with inner Y : improper phase relationships
Figure 2-23 Trapezoidal pattern connection scheme and displays.
Spectrum Analyzers • Show plot of amplitude vs frequency • Swept-tuned (superhetereodyne) Analyzer – uses analog frequency sweep, can go up to GHz range • Fourier Analyzer – digitizes waveform and uses FFT algorithms. Limited to ~40 MHz (EET Labs) • Vector Signal Analyzer (VSA) – uses analog front- end and digitizes after down-convertion. – Best of both worlds, but expensive – Can measure Total Harmonic Distortion (THD)
Figure 2-24 Spectrum analysis of AM waveforms.
Figure 2-25 Spectrum analyzer and typical display. (Courtesy of Tektronix, Inc.)
Figure 2-25 (continued) Spectrum analyzer and typical display. (Courtesy of Tektronix, Inc.)
Relative Harmonic Distortion (RHD) • Ratio of fundamental with respect to the largest undesired harmonic – The greater, the better • Can be computed (in dB) as: RHD = 𝟑𝟏 𝒎𝒑𝒉 𝑾 𝟐 /𝑾 𝟑 Where: V 1 : desired component (fundamental frequency) V 2 : largest undesired harmonic component
Figure 2-26 Relative harmonic distortion.
Total Harmonic Distortion (THD) • Ratio of power from unwanted harmonics to desired frequency components – The greater, the worst – More descriptive distortion spec than RHD • Occurs in amplifiers and non-linear devices • Can be computed as: 𝟑 + 𝑾 𝟒 𝟑 + 𝑾 𝟓 𝟑 + … )/𝑾 𝟐 𝟑 THD = (𝑾 𝟑 Where: V 1 : desired component (fundamental frequency) V 2 , V 3 , … : undesired harmonic components
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