Angle Modulation

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1. Communication Theory Angle Modulation

2. 2 Angle Modulation: Principle (1) Angle of the carrier is varied according to the message Carrier amplitude remain constant Provides better discrimination against noise and interference than AM Required higher transmission bandwidth than that for AM Trade-off between channel bandwidth and noise performance Angle modulated wave: A simple case of an unmodulated carrier: Relationship between instantaneous phase and frequency:

3. 3 Angle Modulation: Principle (2) Two common methods for angle modulation: 1. Phase Modulation (PM): 2. Frequency Modulation (FM): k p = Phase sensitivity factor (radians/volt) Phase-modulated signal: k f = Frequency sensitivity factor (Hz/volt) Frequency-modulated signal:

4. 4 Angle Modulation: Principle (3) Angle Modulated Signal: Example 1 Carrier Message PM signal FM signal

5. 5 Angle Modulation: Principle (4) Angle Modulated Signal: Example 2 Message PM signal FM signal

6. 6 Properties of Angle Modulated Signal (1) Property 1: Constancy of Transmitted Power Amplitude of PM and FM waves is maintained at a constant value equal to the carrier amplitude for all time t, irrespective of the sensitivity factors k p and k f => Average transmitted power of angle-modulated waves is a constant Property 2: Nonlinearity of the Modulation Process For m(t) = m 1 (t): For m(t) = m 2 (t): For m(t) = m 1 (t) + m 2 (t): Consider PM (Prove the nonlinearity for FM by yourself) :

7. 7 Properties of Angle Modulated Signal (5) Property 3: Tradeoff of Increased Transmission Bandwidth for Improved Noise Performance An important advantage of angle modulation over AM is the realization of improved noise performance This advantage is due to the fact that the transmission of a message signal by modulating the angle of a sinusoidal carrier wave is less sensitive to the presence of additive noise than transmission by modulating the amplitude of the carrier The improvement in noise performance is, however, attained at the expense of a corresponding increase in the transmission bandwidth requirement of angle modulation In other words, the use of angle modulation offers the possibility of exchanging an increase in transmission bandwidth for an improvement in noise performance. Such a tradeoff is not possible with amplitude modulation since the transmission bandwidth of an amplitude-modulated wave is fixed somewhere between the message bandwidth B and 2B Hz, depending on the type of modulation employed

8. 8 Relationship between PM and FM FM: PM: PM and FM are uniquely related to each other This means that the properties of PM can be deduced from those of FM and vice versa

9. 9 Frequency Modulation (FM) (1) Consider a case of single-tone modulation: Δ f = Frequency Deviation (Hz) = Maximum departure of f i of the FM wave from f c β = Modulation Index FM signal:

10. 10 Narrow-band FM (NBFM) For small β : 1. NBFM ( β is small compared to one radian):

11. 11 NBFM ( contd …) Block diagram of an indirect method for generating a narrow-band FM wave AM signal: BW of NBFM signal: 2 f m Amplitude of NBFM: Not constant

12. 12 Wide-band FM (WBFM) 2. WBFM ( β is large compared to one radian): Complex Envelope of s(t): => a periodic function of time with a fundamental frequency equal to f m

13. 13 WBFM ( contd …) Complex Fourier Coefficient J n ( β ) = n th order Bessel function of the first kind and argument β

14. 14 WBFM ( contd …) Thus, => S ( f ) consists of an infinite number of delta functions spaced at f = f c ± nf m

15. 15 WBFM ( contd …) Properties of FM for arbitrary β : 1. J n ( β ) = (-1) n J -n ( β ) for all n 3.

16. 16 WBFM ( contd …) The spectrum of an FM wave contains a carrier component and an infinite set of side frequencies located symmetrically on either side of the carrier at frequency separations of f m , 2 f m , 3 f m , …. For the special case of small β compared with unity, only the Bessel coefficients J ( β ) and J 1 ( β ) have significant values, so that the FM wave is effectively composed of a carrier and a single pair of side-frequencies at f c ± f m . This FM signal is essentially the NBFM signal. The amplitude of the carrier component varies with β according to J ( β ). This implies that the envelope of an FM wave is constant, so that the average power of FM signal is constant. Alternatively: Power of FM signal

17. 17 BW of FM Signals Carson’s Rule W = BW of m ( t ) Δ f = k f m ( t ) |max Single-tone Multi-tone Theoretically, BW of FM wave is finite BW of FM signals is effectively limited to a finite number of significant side frequencies Example: Commercial FM Broadcasting In North America, the maximum value of frequency deviation Δf is fixed at 75 kHz for commercial FM broadcasting by radio. Assume W = 15 kHz, which is typically the “maximum” audio frequency of interest in FM transmission. Carson’s rule: B T = 2∆f + 2W = 180 kHz