Sinh học - Chapter 7: Analog modulators

Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT1 Chapter 7: Analog Modulators Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT2 References [1] J. J. Carr, RF Components and Circuits, Newnes, 2002. Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT3 Analog Modulation  Amplitude Modulation:  Standard amplitude modulation (AM) with carrier.  Suppressed-carrier double-sideband modulation (DSB).  Single-sideband modulation (SSB).  Vestige-sideband modulation (VSB).  Frequency Modulation  Phase Modulation Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT4 Standard AM (1)  AM signal and spectra: The AM signal is: where µ is positive constant called AM modulation index, x(t) is message, Accosωct is carrier signal. Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT5 Standard AM (2) Message spectrum with bandwidth W: AM spectrum: AM bandwidth is 2W Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT6 Standard AM (3) AM transmitted power: where Pc represents unmodulated carrier power: and Psb represents power per sideband: where Sx is average message power. If fc >>W and µ ≤ 1, then the message can be extracted from xc(t) by a simple envelope detector. Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT7 Standard AM (4)  Product modulator for AM:  Using Multiplier: Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT8 Standard AM (5)  Using square-law element: Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT9 Standard AM (6) We assumed that the nonlinear element approximates the square law transfer curve: Thus, with  High-level modulation using class C amplifier: Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT10 Standard AM (7)  AM demodulation:  Synchronous detection (coherent detection): The oscillator of demodulator is exactly synchronized (both phase and frequency) with the carrier. Using PLL for carrier synchronization. Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT11 Standard AM (8)  Envelop detection: Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT12 (Suppressed-Carrier) DSB (1)  DSB signal and spectra: The wasted carrier power in AM can be eliminated by setting µ = 1 and suppressing the carrier-frequency component. The resulting DSB signal is: Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT13 (Suppressed-Carrier) DSB (2) DSB transmitted power:  Product DSB modulator:  Balanced modulator: Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT14 (Suppressed-Carrier) DSB (3)  Ring modulator: Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT15 (Suppressed-Carrier) DSB (4)  DSB demodulator:  Synchronous detection (coherent detection): As AM demodulator. Required carrier synchronization.  Envelope reconstruction (for suppressed carrier modulation): Required carrier synchronization. Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT16 (Suppressed-Carrier) DSB (5)  Using pilot carrier: Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT17 (Suppressed-Carrier) SSB (1)  SSB signals and spectra: SSB bandwidth and power: Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT18 (Suppressed-Carrier) SSB (2)  SSB modulator:  Based on DSB and filter: Two-step SSB modulator: Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT19 (Suppressed-Carrier) SSB (3)  Phase-shift method: HQ(f): 90o phase shifter Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT20 (Suppressed-Carrier) SSB (4)  Weaver method: Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT21 (Suppressed-Carrier) SSB (5)  SSB demodulator: Similar to DSB demodulator. Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT22 Carrier Synchronization for Coherent Detection (1)  Squaring loop: Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT23 Carrier Synchronization for Coherent Detection (2)  Costas loop: Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT24 PM/ FM (1)  PM and FM signals: Considering a signal with time-varying phase: The total instantaneous angle: Therefore: If θc(t) contains the message information x(t), then it is exponential modulation (or angle modulation). The phase modulation (PM) is defined by so that Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT25 PM/ FM (2) The constant φ∆ (φ∆ ≤ 180o) represents the maximum phase shift (or PM index, or phase deviation) produced by x(t). In the case of frequency modulation (FM), the instantaneous frequency is defined as: The constant frequency f∆ called frequency deviation, represents the maximum shift of f(t) relative to the carrier frequency fc By definition: where Then, the FM signal has and integration yields the PM: Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT26 PM/ FM (3) If t0 is selected such that φ(t0) = 0, then Therefore, The FM signal is written as: Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT27 PM/ FM (4) Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT28 PM/ FM (5)  Average transmitted power (for PM and FM): regardless of message x(t):  Narrowband PM and FM: Representing the exponential modulation as: where If so that Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT29 PM/ FM (6) Then the spectrum of xc(t) in term of the message spectrum is: where Therefore, we conclude that if the message has bandwidth of W << fc, then the bandwidth of the signal after narrowband modulation is 2W.  Tone modulation (single frequency modulation): Consider the tone message as: Then , where Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT30 PM/ FM (7) The parameter β is the modulation index for PM and FM in the case of tone modulation.  Narrowband PM/FM tone modulation requires β << 1, then after modulation we obtain: Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT31 PM/ FM (8)  For arbitrary β (wideband PM/FM tone modulation): using The coefficient Jn(β) are Bessel function of first kind. Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT32 PM/ FM (9) Finally, we obtain: Using the property: Then, we obtain the compact form: Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT33 PM/ FM (10) Selected values of Jn(β) Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT34 PM/ FM (11)  Bandwidth of PM/FM tone modulation: According to Carson’s rule: where Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT35 PM/ FM (12)  Direct FM and VCO: Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT36 PM/ FM (13) Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT37 PM/ FM (14)  Phase modulators and indirect FM:  Narrowband phase modulator:  Indirect FM transmitter: Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT38 PM/ FM (15)  FM/PM detector (demodulator) using PLL: Dept. of Telecomm. Eng. Faculty of EEE CSD2012 DHT, HCMUT39 PM/ FM (16)