TELE3113 Analogue and Digital Communications Phase-Locked Loop Wei Zhang firstname.lastname@example.orgSchool of Electrical Engineering and Telecommunications The University of New South Wales
Phase-Locked Loop (1)Block diagram. (Demodulation of FM Signals.) × FM wave s(t) e(t) Loop v(t) filter r(t) Voltage controlled oscillatorVoltage controlled oscillator (VCO) performs FM as r(t) = Av cos[2πfc t + φ2 (t)],where Av is the amplitude and the angle t φ2 (t) = 2πkv v(τ )dτ. 0 TELE3113 - Phase-Locked Loop. August 26, 2009. – p.1/
Phase-Locked Loop (2)Suppose the incoming FM wave is s(t) = Ac sin[2πfc t + φ1 (t)]and the angle t φ1 (t) = 2πkf m(τ )dτ. (1) 0After the multiplication of s(t) by r(t), the low-frequencycomponent is e(t) = km Ac Av sin[φe (t)],where km is the multiplier gain and φe (t) = φ1 (t) − φ2 (t). TELE3113 - Phase-Locked Loop. August 26, 2009. – p.2/
Phase-Locked Loop (3) When the phase error φe (t) = 0, the PLL is in phase-lock. When the phase error is small compared to 1, sin[φe (t)] ≈ φe (t), the PLL is near-phase-lock.Therefore, if φe is small compared to one, K0 e(t) = km Ac Av φe (t) = φe (t), kvwhere K0 = km kv Ac Av is called the loop-gain parameter of thePLL. TELE3113 - Phase-Locked Loop. August 26, 2009. – p.3/
Phase-Locked Loop (4)Linearized model of the PLL. K 0 / kv φ1 (t ) φe (t ) × e(t) v(t) ∑ + h(t) __ φ2 (t ) × ∫0 t dτ 2πkv TELE3113 - Phase-Locked Loop. August 26, 2009. – p.4/
Closed-loop GainConsider a negative feedback ampliﬁer, as follows. µ × I(t) O(t) ∑ + __ Network gain βThe closed-loop gain of the ampliﬁer is O(t) µ G = . I(t) 1 + µβ 1If µβ is large compared to one, G ≈ β . TELE3113 - Phase-Locked Loop. August 26, 2009. – p.5/
Phase-Locked Loop (5)If K0 is large compared to 1, then the closed-loop gain of thePLL is v(t) 1 ≈ , φ1 (t) βwhere β denotes the gain of the network generating FM waves.Therefore, 1 dφ1 (t) v(t) ≈ . 2πkv dtUsing (1), we continue to obtain kf v(t) ≈ m(t). kvNow the message signal m(t)is recovered from s(t). TELE3113 - Phase-Locked Loop. August 26, 2009. – p.6/
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