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Angle modulation. Angle modulation can be divided into frequency (FM) and phase modulation (PM) Both FM and PM are widely used in communication systems The most important advantage of FM or PM over AM is the possibility of improved signal to noise ratio. Frequency modulation. Frequency.

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## Angle modulation

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**Angle modulation**Angle modulation can be divided into frequency (FM) and phase modulation (PM) Both FM and PM are widely used in communication systems The most important advantage of FM or PM over AM is the possibility of improved signal to noise ratio**Frequency modulation**Frequency Implementation Amp VCO**Frequency modulation**Cos(ωc t + θ), ωc is the modulating signal Frequency deviation: fsig = fc + kf Em(t) Where kf is the modulator deviation constant**Example 4.1**kf = 30 kHz/v, carrier frequency is 175 MHz, find out the frequency for an modulating signal equal to: 150 mV and –2V**Frequency modulation index**Peak frequency deviation δ = kf Em Fsig( fc + δ sin ωm t) Frequency modulation index mf = δ / fm**Example 4.3**An FM transmitter operates at its maximum deviation of 75 kHz, find out the modulation index for a sine modulation signal with a frequency of 15 kHz and 50 Hz.**Phase modulation**kp = Φ/em Kp: phase modulator sensitivity Φ: phase deviation em: signal amplitude θ(t) = θc + kp em(t) in case of sin signal: θ(t) = θc + mp sinωmt**Relationship between frequency modulation and phase**modulation f Phase shift θ = ωt = Integral(ω dt)**The angle modulation spectrum**Angle modulation produces an infinite number of sidebands even for single-tone modulation In most cases, the bandwidth is much larger than that of an AM signal Consider V(t) = A sin(ωc t + m sin ωm t) m can be mf or mp The signal can be expressed by Bessel function of the first kind**Bessel expression of modulation spectrum**V(t) = A sin(ωc t + m sin ωm t) = A {J0(m)sin ωc t - J1(m)[sin(ωc - ωm)t - sin(ωc + ωm)t] +J2(m)[sin(ωc - 2ωm)t - sin(ωc + 2ωm)t] - J3(m)[sin(ωc - 3ωm)t - sin(ωc + 3ωm)t] + … Different from AM modulation, the total power remains the same therefore the power at the carrier must be reduced below its un-modulated value**Power of the angle modulated signals**PT = J02 + 2J12 + 2J22… J1 J0 J2 J3 J4 J0 could be zero under certain conditions Phase modulation can be utilized to generate suppressed carrier signals See a recent paper by J. Yu et al.**Carson’s rule**B = 2(δmax + fm(max)) Typically δmax is larger than fm(max), therefore B is primarily determined by the frequency deviation**Narrowband and Wideband FM**Larger values of frequency deviation result in an increased signal-to-noise ratio and bandwidth Narrowband FM: mf < 0.5, one pair of sidebands with significant power The criterion does not always apply**FM and Noise**Resultant Noise Phase Signal Amplitude ΦN = sin-1(EN/Es) FM detection does not care about the amplitude, but the frequency Limiting amplifier is typically applied in the receiver before frequency detection**Example 4.9 – SNR improvement using FM detection**Input: 5kHz FM and a modulation frequency of 1kHz, SNR = 20 dB Find the SNR at the output En/Es = -20 dB = 0.1 ΦN = 0.1 Remember the equation mf = δ / fm mf corresponds to the max frequency deviation Therefore considering the phase error, the corresponding frequency error is δ= mf fm = 0.1 x 1kHz δ s/δn = 5k / 0.1k = 50 = 34 dB**Threshold and capture effects**The superior SNR performance of FM does not always hold As long as the desired signal is considerably stronger than the interference, the ratio of desired to interfering signal strength will be grater at the output of the detector than at the input. The stronger signal captures the receiver. Output SNR FM Threshold AM Input SNR**Pre-emphasis and de-emphasis in FM systems**δ = mf fm mf corresponds to the peak phase deviation, which is random for noise. mf is evenly distributed Thus the resulting noise spectrum is linearly increasing with the frequency En Need pre-emphasis in the transmitter and de-emphasis in the receiver fm**Pre-emphasis and de-emphasis circuits**Time constant is 2.12 kHz in both circuits**FM measurement**Time domain measurement is difficult In theory it would be possible to perform measurements by observing the amplitude of each sideband It is usually the deviation that needs to be measured**FM measurement setup**δ = mf fm Function generator Spectrum analyzer Transmitter Load mf= 2.4 to observe the first suppression of the carrier, by measuring the modulation frequency, the peak deviation can be obtained Example 4.10

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