Chapter 4: Linear CW Modulation

Transcription

1 Chapter 4: Linear CW Modulation Bandpass signals and systems Double-sideband amplitude modulation Modulation and transmitters Suppressed-sideband amplitude modulation Frequency conversion and demodulation

2 Bandpass signals and systems

3 Bandpass signal (a) Spectrum; Waveform

4 Bandpass signals Definition: V ( f) bp X( f) fc W < f < fc + W = 0 fc + W < f < fc W

5 (a) Rotating phasor; (b) Phasor diagram with rotation suppressed Figure 4.1-3

6 Quadrature-carrier representation: v () t = v ()cos2 t πf t v ()sin2 t πf t bp i c q c where: vi ( t) = A( t)cos φ( t) in-phase component v ( t) = A( t)sin φ( t) quadrature component q

7 Envelope-phase representation where [ ] v ( t) = A( t)cos 2 π f t+φ( t) bp A( t) v ( t) v ( t) and ( t) tan c v () t q = i + q φ = vi () t

8 Modulation to create a BP signal Modulation is the translation of a band limited LP signal to a band pass signal with some center frequency f c message spectrum bandpass spectrum

9 Analog message conventions Message signal: x( t) Amplitude: xt ( ) 1 1 S = x t = x t dt 2 2 Power: () x () 1 T0 T 0 Thus with a single tone message x( t) = Amcos2πfmt 2 Am 1 Am 1 Sx = 2 2 Message bandwidth = W f W m

10 Bandwidth Message bandwidth: W Transmission bandwidth: B T

11 Fractional bandwidth (a) Relevant to band pass signals (b) fractional bandwidth defined as BT (c) For practical systems we require 0.01< < 0.1 f (d) Upper limit fc > 10 BT prevents spillover into negative frequencies (e) Lower limit f < 100 B economics c T B f T c c

12 How is bandwidth defined? Absolute bandwidth: 100% of energy is within some frequency range 3 db, or half power bandwidth: frequency range where magnitude reduction is less than -3 db Noise equivalent bandwidth (see chapter 9) Occupied bandwidth: FCC definition where frequency range that contains 99% of energy Relative power bandwidth: frequency range where magnitude rolloff is less than a given level of db (e.g. -40 db)

13 Types of linear CW modulation Conventional Amplitude Modulation (AM) Suppressed carrier double sideband (SCDSB, or DSB) Single sideband (USSB and LSSB) Vesigal sideband (VSB)

14 AM, DSB, SSB, and VSB are considered AM because the message alters the carrier s amplitude However, AM conventional AM

15 Double-sideband amplitude modulation Conventional AM Suppressed carrier DSB, (SCDSB) or simply DSB

16 Conventional AM, or simply AM x () t = A[1 +μx()]cos2 t πf t c c c where Ac = carrier amplitude xt ( ) = message, and xt ( ) 1 μ= modulation index, μ 1 and μ=1 100% modulation f = carrier frequency, Hz c 1 1 xc( t) Xc( f) = Acδ ( f ± fc) + AcX( f ± fc) 2 2

17 AM waveforms (a) Message; (b) AM wave with μ < 1; (c) AM wave with μ > 1 (overmodulation)

18 AM Spectrum Note: (a) carrier impulse at ± f c this impulse carries no information (b) redundant sidebands: the lower and upper sidebands carry the same information increased bandwidth B = 2W T

19 AM Power Output power: carrier power + sideband power where S = P + 2P T c sb 1 2 Pc = Ac 2 1 P = A μ S sb c x Peak envelope power: P peak envelope 2 2 = Amax = A c 1 + u x( t) max 2

20 AM Systems Relatively simple transmitter and receiver hardware The first voice modulation system More than half power goes into carrier, but carrier carries no information inefficient Not suited for messages with low frequency content

21 Suppressed Carrier DSB Signals 1 x () t = A x()cos2 t πf t X ( f) = A X f ± f 2 Output power: ( ) c c c c c c Peak envelope power 1 S = 2P = A S 2 2 T sb c x P = A = A x( t) peak envelope 2 2 max c 2 max

22 DSB waveforms

23 DSB systems Suppressed carrier: typically db All power goes into sidebands more efficient than AM Demodulation more complicated than AM; requires synchronization Transmitter hardware more complex than AM Well suited to transmission of messages with low frequency or DC content

24 Modulation and transmitters AM DSB

25 AM transmitters Implemented using a nonlinear element or some nonlinear portion of a circuit. Often done where the message is superimposed on one of the active device s terminals (i.e. the base/gate or collector/drain) Because of nonlinear elements, may require a tank circuit to remove other of band components

26 AM modulator example tank circuit (a) the concept, (b) practical circuit. Note in (b) how the message and carrier source are superimposed onto the gate circuitry.

27 DSB transmitters Due to technological limitations, practical DSB systems are rarely implemented via ordinary multiplers. Balanced modulators Ring modulators Other nonlinear devices

28 Balanced modulator concept for DSB generation * *Only for purposes of illustrating the balanced modulator concept. Practical DSB modulators are implemented using nonlinear devices such as diode arrays

29 Ring modulator for DSB generation

30 Suppressed-sideband amplitude modulation If we have a DSB signal with symmetrical sidebands, we can suppress one of the sidebands without loss of information Therefore, we reduce transmission bandwidth from B = 2W B = W T DSB T SSB Double the number of users on a channel

31 Types of SSB Lower sideband: LSSB or LSB Upper sideband: USSB or USB The decision to choose one over the other is dictated by: Convention or prior assignment Technological considerations Neither USSB or LSSB is inherently better than the other

32 SSB signals 1 x () ()cos ˆ c t = Ac x t ωct x()sin t ωct 2 [ ] where xt ˆ( ) is the Hilbert transform of the message The in-phase and quadrature components are: 1 x ( ) ( ) and ( ) ˆ ci t = Ac x t xcq t =± Ac x( t) 2 and the envelope is At ( ) = A () ˆ c x t + x () t

33 SSB spectra (a) Generation of SSB from DSB using filter method, (b) USSB, (c) LSSB

34 SSB generation Filter method: use a high-q filter to suppress one of the sidebands. Phase methods: shift sidebands using a phase shift method to cancel one of them out Phase shift Weavers

35 Weaver s SSB modulator

36 VSB SSB method but with a trace of the other sideband left Practical SSB systems with imperfect filters are VSB VSB allows for messages with low frequency or DC content

37 Frequency conversion and demodulation Modulation: translate message to some carrier frequency Frequency translation: move a signal from one carrier frequency to another Demodulation: move modulated signal back to baseband Synchronous or product detectors Envelope detectors

38 Basic hetrodyne frequency converter Frequency converson via hetrodyning takes advantage of the property of the product of 2 cosine functions sum and difference 1 1 cosαcosβ= cos( α β ) + cos( α+β) 2 2

39 Frequency conversion via hetrodyning (multiplication) 1 1 x( t)cos2πft 1 cos2 π f2t = x( t)cos 2 π( f1 f2t) t+ x( t)cos2 π ( f1+ f2t) t X( f1 f2) + X( f1+ f2) 2 2 sum and the difference of 2 the frequencies We use a filter to select a particular component

40 Frequency translation example Convert 7 MHz USSB signal into a 50 MHz LSSB signal via hetrodyning

41 Synchronous detection example x () c t LPF x() t ~ cos2 π ( f ) LO = fc t X ( ) c f f c f X( f) Demodulation by translation to baseband f

42 Synchronous detection when there is an error in the local oscillator x () c t LPF x() t ~ cos2 π ( f +Δf) t c X ( ) c f X( f) f c f Δf f

43 Detector output single tone at f =Δf, and message is translated to a center frequency of Δf distorted message and obnoxious background tone Mandatory that the local oscillator and its phase match the carrier frequency

44 Envelope detection Suitable for AM signals or signals with a carrier Does not require synchronization Simple hardware: diode, resistor, capacitor Will work with suppressed carrier modulation systems if the receiver inserts a carrier

45 Envelope detection (a) Circuit; (b) Waveforms